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Using quality control in optimizing opportunistic maintenance
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Using quality control in optimizing Using quality control in optimizing Using quality control in optimizing opportunistic maintenance Using quality control in optimizing opportunistic maintenance opportunistic maintenance opportunistic maintenance C. Dutoit ∗∗ P. Dehombreux ∗∗ E. Rivi` ere Lorph` evre ∗∗
C. Dutoit ∗ P. Dehombreux ∗ E. Rivi` ere Lorph` evre ∗ C. Dutoit ∗ P. Dehombreux ∗ E. Rivi` ere Lorph` evre ∗ C. Dutoit P. Dehombreux E.and Rivi` ere Lorph` evre ∗ of Mons, Machine Design Production Engineering ∗ University ∗ University of Mons, Machine Design and Production Engineering University of Mons, Machine Design and Production Engineering Department, Research Institute for Science and Management of Department, Research for Science Management of Risks, Risks, ∗ University of Mons,Institute Machine Design andand Production Engineering Mons, Belgium, (e-mail: [email protected]) Department, Research Institute for Science and Management of Risks, Mons,Research Belgium,Institute (e-mail:for [email protected]) Department, Science and Management of Mons, Belgium, (e-mail: [email protected]) Risks, Mons, Belgium, (e-mail: [email protected]) Abstract: production efficiency. efficiency. Abstract: Nowadays Nowadays companies companies are are constantly constantly looking looking for for maximum maximum production To achieve this goal, the actions taken aim to reduce the overall costs of the company. Thus, Abstract: Nowadays companies are constantly looking for maximum production efficiency. To achieve this goal, the actions taken aim to reduce the for overall costs ofproduction the company. Thus, Abstract: Nowadays companies are constantly looking maximum efficiency. measures are taken to ensure the availability of production equipment at the same time as To achieve this goal, the actions taken aim to reduce the overall costs of the company. Thus, measures are ensure thetaken availability of production equipment atthethe same time as To achieve thistaken goal,to actions aim atostudy reduce the overall costs ofthe company. Thus, good product quality. This article in order to optimize maintenance of measures are taken tothe ensure the proposes availability of production equipment at the same time asaa good product quality. This article proposes a study in order to optimize the maintenance of measures are taken to the ensure the proposes availability of production at the same timeofasa production system and control. A bibliographic is to good product quality. article a study in orderresearch toequipment optimize the maintenance production system andThis the quality quality control. A bibliographic research is developed developed to determine determine good product quality. This article proposes a study in order to optimize the maintenance of a the quality tools used optimize maintenance. The idea is to the production andcan thebe control. A bibliographic to determine the quality system tools that that can bequality used to to optimize maintenance.research ideais isdeveloped to determine determine the best best The production system and the quality control. A bibliographic research is developed to determine maintenance policy by using based on A numerical example is the quality tools that be information used to optimize The idea is determine the best maintenance policy bycan using basedmaintenance. on quality quality indicators. indicators. A to numerical example is the quality tools that be information used to optimize The idea is determine the best also treated on a batch production with opportunistic maintenance applied. maintenance policy bycan using information basedmaintenance. on quality indicators. A to numerical example is also treated on a batch production with opportunistic maintenance applied. maintenance policy by using information based on quality indicators. A numerical example is also treated on a batch production with opportunistic maintenance applied. © 2018, IFACon (International Federationwith of Automatic Control)maintenance Hosting by Elsevier Ltd. All rights reserved. also treated a batch production opportunistic applied. Keywords: Keywords: Quality Quality control, control, maintenance maintenance policy, policy, optimization, optimization, statistical statistical process process control. control. Keywords: Quality control, maintenance policy, optimization, statistical process control. Keywords: Quality control, maintenance policy, optimization, statistical process control. 1. INTRODUCTION INTRODUCTION process (reliability (reliability law). law). Despite Despite some some assumptions, assumptions, the the 1. process 1. INTRODUCTION process (reliability law). Despite some assumptions, the document provides a solid foundation for integrating qualdocument provides alaw). solid foundation forassumptions, integrating qual1. INTRODUCTION process (reliability some the Quality provides a solid Despite foundation for strategy integrating ity control into aa preventive preventive maintenance for qualcostQuality has has become become a a priority priority for for the the majority majority of of comcom- document ity control into maintenance strategy for costdocument provides a solid foundation for strategy integrating qualQuality has become a priority for the majority of com- ity panies. With technological advances and an increasingly control into a preventive maintenance for costeffective optimization. panies. technological advances and an increasingly optimization. Quality With has become a operators priority for majority of com- effective ity control into a preventive maintenance strategy for costpanies. With technological advances and an increasingly advanced automation, no the longer have complete effective optimization. advanced automation, operators no longer have complete Another interesting article panies. With technological advances and an increasingly effective optimization. advanced automation, operators no longer have complete Another interesting article is is that that of of Linderman Linderman et et al. al. control over over their their production production processes. processes. The The influx influx of of control Another interesting article is that of Linderman et al. (2005). This article advocates ”adaptive” maintenance advanced automation, operators no longer have complete control over their production processes. The influx of (2005). data (especially on the quality of products) is increasingly This article advocates ”adaptive” maintenance Another interesting article is that of Linderman et unal. data (especially on the quality ofprocesses. products) The is increasingly article advocates ”adaptive” maintenance based onThis quality control. When the process becomes control overUnfortunately, their production influx exof (2005). data (especially on the quality of data products) is increasingly important. these are not not always based on quality control. When the process becomes un(2005). This article advocates ”adaptive” maintenance important. Unfortunately, these data are always excontrol. schedule When the stable,on thequality maintenance is process revised becomes to speed speed unup data (especially on the quality of to products) isquality increasingly important. Unfortunately, data are not alwaystools ex- based ploited. In this this article, we these want describe stable, the maintenance schedule is revised to up based on control. When the process becomes unploited. In article, we want to describe thequality maintenance schedule is the revised to speed up maintenance. On the other hand, if process is stable, important. Unfortunately, these data are notquality alwaystools ex- stable, ploited. In this article, we want to describe quality tools maintenance. On the other hand, if the process is stable, that can be used in the organization of maintenance. stable, maintenance schedule revised to increased. speed up that canIn be usedarticle, in the organization of maintenance. On the other hand, ifis the process is stable, the timethe intervals between maintenance will be ploited. want to describe quality tools maintenance. that can bethis used in the we organization of maintenance. the time intervals between maintenance will be increased. maintenance. On the other hand, if the process is stable, Maintenance andinquality quality are intimately intimately linked. Indeed, Indeed, the intervals between maintenance will be increased. Thetime optimization is done done on on the costs costs generated generated by the the that can be used the organization of maintenance. Maintenance and are linked. The optimization is the by the time intervals between maintenance will be increased. Maintenance and quality are will intimately linked. Indeed, poorly maintained equipment inevitably see the qualThe optimization is done on the costs generated by the operation of the equipment. Again, it is assumed that poorly maintained equipment will inevitably see the qual- operation of the equipment. it is generated assumed that the Maintenance and quality arecompared intimately Indeed, The optimization done onAgain, the costs by the poorly maintained equipment will inevitably see the qual- operation ity of its its products degrade tolinked. maintained of the it is assumed that the process begins in aaisin-control state law process begins inequipment. in-controlAgain, state whose whose law of of reliability reliability ity of products degrade compared to aasee maintained poorly maintained equipment will inevitably the qualoperation of the equipment. Again, it is assumed that the ity of its products degrade compared to a (1999) maintained equipment. Moreover, Ollila and Malmipuro have process begins in a in-control state whose law of reliability is known (Weibull distribution). Inspections take place equipment. Moreover,degrade Ollila and Malmipuro (1999) have is known (Weibull distribution). Inspections take place ity of its products compared to a maintained process begins in a in-control state whose law of reliability equipment. Moreover, Ollila and of Malmipuro (1999) have is highlighted the the important impact maintenance on qualqualknown distribution). take place after hours(Weibull of production production to verify verifyInspections that the the process process has highlighted important impact maintenance on after hours of to that has equipment. Moreover, Ollila and of Malmipuro (1999) have is known distribution). Inspections take place highlighted the important impact of maintenance on quality. They even conclude a case study by showing that after hours(Weibull of production toThe verify that thecharacteristic process has not become out of control. measured ity. They even conclude a case study by showing that not become outproduction of control.toThe measured highlighted the important of maintenance on qualafter hours of verify that thecharacteristic process has ity. They even conclude casemost study by showing that maintenance is one one of the the aimpact three important causes of not become outaa ofcontrol control. The measured characteristic is reported on card. Sometimes, between is reported on control card. Sometimes, between two two maintenance is of three most important causes of ity. They even conclude a case study by showing that not become out of control. The measured characteristic maintenance is one ofThe thequality three most important causes of is quality degradation. control makes it possible reported on a control card. Sometimes, between twoa samplings (j and j + 1 ), a failure occurs and causes quality degradation. The quality control makes it possible samplings (j and j + 1 ), a failure occurs and causes maintenance is one ofThe the three important causes of change is reported a control Sometimes, between twoa quality degradation. to detect drifts. These drifts canmost act as as alarms to trigger samplings (jonand j + 1 ),card. a state. failure occurs and causes a quality control makes itto possible to an an out-of-control The process continues to detect drifts. These drifts can act alarms trigger change to out-of-control state. The process continues quality degradation. The quality makes ittopossible samplings (j and j +only 1 ),allows a state. failure occurs and causes a to detect drifts. These drifts can control act as alarms trigger change maintenance actions. The methodology for determining to an out-of-control The process continues and the control card detection of the problem maintenance actions. The methodology for determining the to control card only allows detection of thecontinues problem to detect drifts. Thesepolicy driftsmethodology can act as alarms tooptimal trigger and change an out-of-control state. The process maintenance actions. The for determining the best maintenance to be applied and the and the control card only allows detection of the problem at j + 1 sampling. The ”adaptive” maintenance model is + 1 control sampling. The ”adaptive” maintenance model is the best maintenance policy to be applied for and the optimal at maintenance actions. will Thebemethodology andjj + the1 card only allows detection ofscenarios the model problem the best maintenance policy to be applied and determining sampling parameters discussed. at sampling. maintenance is the optimal illustrated in Fig. Fig. 1.The In ”adaptive” fact, three different are sampling parameters will be discussed. illustrated in 1. In fact, three different scenarios are the best maintenance policy be applied and the optimal illustrated at j + 1 sampling. ”adaptive” maintenance modelare is sampling parameters will be to discussed. in the Fig.first, 1.The Inthe fact, three different scenarios proposed. In out-of-control state is detected detected proposed. In first, out-of-control state is sampling parameters will be discussed. illustrated in the Fig. 1. Inthe fact, three different scenarios are 2. LITERATURE REVIEW proposed. In the first, the out-of-control state is detected and corrective maintenance is organized to restart the pro2. LITERATURE REVIEW and corrective maintenance is organized tostate restart the proproposed. the first, out-of-control is detected detected 2. LITERATURE REVIEW and corrective maintenance is organized to restart the process. In the theInsecond, second, thethe out-of-control state is not not cess. In the out-of-control state is detected 2. LITERATURE REVIEW and corrective maintenance is organized to restart the proIn this section, we will present documents integrating a cess. In the second, the out-of-control state is not detected before scheduled preventive maintenance. Therefore the In this section, we will present documents integrating a before scheduled preventive maintenance. Therefore the cess. In the second, the out-of-control state is not detected In this section, we will present documents integrating a methodology to use quality control information to manage before scheduled preventive maintenance. maintenance operations highlight and repair the failure Therefore the methodology to use quality control information to manage operations highlight and repair the failure In this section, we will present documents integrating before scheduled preventive Therefore the methodology to control information toCassady managea maintenance maintenance. A use firstquality interesting article is that that of maintenance and under repair the failure and allow theoperations system tohighlight bemaintenance. brought control. In maintenance. A first interesting article is of Cassady and allow the system to be brought under control. In methodology to use quality control information to manage maintenance operations highlight and repair the failure maintenance. Athis firstwork, interesting articledevelop is thataof Cassady and et al. (2000). In the authors preventive allow the under control. In the third scenario, the process remains under control (no system to be brought et al. (2000). InAthis the authors develop preventive scenario, the process remains under under control (no maintenance. firstwork, interesting is control. thata Cassady and third allow thea system to be brought control. In et al. (2000). In this work, the authors develop aof preventive maintenance strategy based on article quality In fact, fact, the the third scenario, the process remains under control (no failure) until preventive maintenance operation is perpermaintenance strategy based on quality control. In failure) until a preventive maintenance operation is et control al. (2000). In this work, theproduction authors develop a preventive the third scenario, the process remains under control (no maintenance strategy based on quality control. In fact, a card controls the process. When a failure) a preventive maintenance operationAGAN, is performed. until Despite some assumptions assumptions (maintenance amaintenance control cardstrategy controlsbased the production process. When Despite some (maintenance on quality control. Inand fact,aa formed. failure) until a Tagushi, preventive maintenance operationAGAN, is that perafailure control card the controls thebecomes production When occurs, process out process. of control formed. Despite some assumptions (maintenance AGAN, loss function of ...), the article demonstrates failure occurs, the process becomes out of control and a loss function of Tagushi, ...), the article demonstrates that a control card on controls thebecomes production process. When formed. Despite somequality assumptions (maintenance AGAN, failure occurs, the process out of control and aa loss jump appears the control board, allowing corrective function of Tagushi, ...), the article demonstrates that a model integrating control and maintenance can jump on the control board,out allowing corrective model integrating quality anddemonstrates maintenance that can failureappears occurs, the process becomes of control and a aabe loss function of Tagushi, ...), control the article jump appears on the control board, allowing corrective maintenance to occur. In order to avoid failures, preventive model integrating quality control and maintenance can beneficial. maintenance occur. order to avoid allowing failures, preventive beneficial. jump appearsto the In control board, corrective a model integrating quality control and maintenance can maintenance to occur. In order to avoidto failures, is on carried out according timepreventive period p. p. be be beneficial. maintenance is carried out according to aa time period We can also also cite cite Alsyouf Alsyouf (2007), (2007), which which has has demonstrated demonstrated maintenance to occur. In order to avoid failures, preventive be beneficial. maintenance is carried out according to a time period p. We The article allows optimizing the periodicity of preventive can The article allows optimizing the periodicity of preventive We can also cite Alsyouf (2007), which has demonstrated the benefits of a maintenance policy on the quality of prodprodmaintenance is carried out according to a time period p. The article allows optimizing the periodicity of preventive maintenance p and and the parameters parameters of the the control control board the ofcite a maintenance policy on the quality of We benefits can also Alsyouf (2007), which hasquality demonstrated maintenance p the of board the benefits of a on maintenance ucts (and thus profitability). This article has proved policy on the of prodThe article allows optimizing thethe periodicity of preventive maintenance p order and the parameters of the control board (sampling) in to reduce costs, from a given (and thus profitability). This article hasofproved the benefits of a on maintenance policy on the quality prod(sampling) order to parameters reduce the costs, from a board given ucts maintenancein and the the control (sampling) inp order to reduce the of costs, from a given ucts (and thus on profitability). This article has proved ucts (and thus on profitability). This article has proved (sampling) in order to reduce the costs, from a given 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Copyright © 2018 IFAC 643 Copyright © under 2018 IFAC 643 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 643 10.1016/j.ifacol.2018.09.643 Copyright © 2018 IFAC 643
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Fig. 1. Simulation principle in Linderman et al. (2005) that the implementation of an effective maintenance policy reduces failures, operating costs and improves product quality. The advantage of this article is that it provides an industrial study case (a Swedish stationery). However, this article is not based on statistical monitoring of the process. Rather, it is an application of TPM based on the collection of various data (expected operating time, planned production rate, planned and unplanned downtime, poor quality products, etc.). The work of Ben-Daya and Duffuaa (1995) also makes an important contribution to the maintenancequality approach. In this work, the authors identify links between quality and maintenance. In fact, they propose two approaches: one is based on the imperfect maintenance concept and the other uses Tagushi’s approach to quality and maintenance (Rahim and Ben-Daya (2001)). In the work of Lu et al. (2016), the authors propose a model where the improvement of the quality of the products intervenes in the decision-making of preventive maintenance. In fact, economic losses due to poor quality products are included in the total cost, which is minimized to get the best planning for preventive maintenance operations. A case study then shows that the model achieves better economic performance than traditional preventive maintenance. In this paper, the problem concerns a single machine subjected to a degradation reducing the quality of the products and increasing the rate of failure. When a failure occurs, a corrective maintenance operation restores the machine to the state before failure (ABAO). Preventive maintenance takes place when the failure rate reaches a threshold. This maintenance reduces the failure rate and improves the quality of the products. This is an imperfect maintenance (between AGAN and ABAO). In the model, it is considered that product quality degradation is a random process that can be modeled by a Gamma process (variable X (t)). Regarding the reliability of the machine, the authors use Weibull’s law. They thus obtain the analytical form of the failure rate. Then, for optimization, a total cost is calculated (maintenances and quality). For quality, the cost generated is based on the loss function of Tagushi but the cost is adapted by integrating the variable X (t) generated by the Gamma process. By minimizing the total cost, it is possible to determine the threshold of the failure rate to be applied for preventive maintenance. In the paper of Rivera-Gomez et al. (2016), the authors are also interested in an economic optimization of a manufacturing system subject to degradation. This degradation causes defects (non-quality) in the products. Revisions make it possible to mitigate the effects of deterioration. The aim here is to determine the frequency at which revisions are to be performed. This is a general model in which the costs incurred include repairs, revisions, arrears of 644
production, defects, production costs and subcontracting costs. Here, when the production machine is no longer able to supply the product to the customer (due to failure or bad products), a second machine is used for manufacturing (subcontracting). This second machine, however, has a higher cost than the first one and so it is avoided to use it too frequently. The economic optimization aims at determining the best maintenance policy (revision) and the best use of the subcontracting option (second machine). The production system evolves according to a semiMarkovian process, returns in ABAO condition after a corrective maintenance (repair) and becomes AGAN after a preventive maintenance. The authors also use a correlation between the degradation of product quality and the age of the machine. The rate of defective parts is directly related to the age of the machine. A numerical example is treated to conclude the article. In the paper of Gouiaa-Mtibaa et al. (2016), models integrating the effects of non-quality and of preventive maintenance are developed. The objective is to determine an optimal maintenance and quality control strategy taking into account a rate of quality loss and the impact of the recovery activities of the wrong products. Two different strategies are proposed. In the first, the batches of products are sold at a reduced price because of the progressive loss of quality due to the degradation of the machine. The objective is to determine the optimum number of batches to be produced (N1 ) before each preventive maintenance operation by maximizing the total benefit per unit of time (P T1 ). The second strategy proposes to rework all the products of poor quality in order to sell them at the maximum price Pmax . Here, it is desired to determine the number of batches produced and reworked (N2 ) before each preventive maintenance operation in order to maximize the total profit per unit time (P T2 ). If a fault occurs between preventive maintenance, a corrective maintenance operation is performed. The advantage of this work is that it links directly the preventive maintenance action to the degradation of the quality of a product (batch of products). The approach is original but does not use statistical control of product quality. Rather, it is based on a rate of loss of quality (taken constant in the numerical example treated). The work of Azadeh et al. (2016) aims to determine the best maintenance policy to minimize the average of the total cost per unit of time (maintenance costs and quality costs). Here, the authors consider the use of buffer stocks to meet demand despite breakdowns or preventive maintenance. The system under study is illustrated in Fig. 2. This is a series of production machines separated by buffer stocks to ensure continuous operation. Each machine produces a certain rate of non-conforming products. The size of intermediate stocks may vary. A simulation is performed and the values of buffer stocks and nonconformity thresholds are determined to obtain the minimum average total cost using the Tagushi method. Here, preventive maintenance operations are carried out when the rate of non-conforming products reaches a certain threshold and the corrective maintenance operations are carried out when the rate of non-conforming products exceeds another threshold. The size of the buffer stocks also intervenes because the storage costs depend on the
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Fig. 2. Production line in Azadeh et al. (2016) number of items present in the stock. It is assumed that the rate of non-compliant items increases in a random manner according to an established relationship. A case study is then developed on two production machines. In Chen (2013) paper, the author develops a model integrating maintenance and product quality. The originality is to take into account the existence of errors in preventive maintenance and the possibility of reworking a certain percentage of the products of poor quality. Here, preventive maintenance is applied when the system is under control. Effective preventive maintenance results in a reduced failure rate for the machine. On the other hand, there is a certain probability that this maintenance operation is inappropriate and causes the system to change to an out-of-control condition. Inspections are carried out to determine the state of the production system and the quality of the products. However, these inspections have a cost and one of the objectives of the model is to optimize the planning of the inspections. Economic optimization involves minimizing the total cost. The latter includes the cost of installation, the cost of storage, the cost of recoveries of non-conforming products, the cost of inspections and preventive maintenance, and finally a cost of late deliveries. The Tambe and Kulkarni (2015) paper describes a model integrating maintenance and quality applied to batch production. In fact, this model studies the production of a set of parts manufactured by die casting. Here, quality control is performed to determine whether the parts produced are compliant or non-compliant. The system produces a P1 rate of conforming parts when it is under control and a P2 rate when it is out of control. Switching from in-control to out-of-control occurs when there is a failure in one of the components of the machine. Corrective maintenance is performed when a fault is detected. However, when changing the type of part produced (mold change), the authors take the opportunity to apply preventive maintenance if necessary. Optimization leads to the determination of the best parameters for quality control and the best maintenance strategies to be applied to the components of the production system. The model developed is very interesting in the context of optimization of quality control and opportunistic maintenance. To synthesize this literature review, we present in this paragraph the advantages and disadvantages of the models proposed in the articles presented. Many articles combine corrective maintenance and preventive maintenance on a single-component machine (Cassady et al. (2000), Linderman et al. (2005), Ben-Daya and Duffuaa (1995), Lu et al. (2016), etc.). However, in these models, preventive maintenance has time periods which are varied to find the optimal value. In reality, time periods of preventive maintenance can be fixed by external events (tool changes, 645
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production stoppage, ...) The term opportunistic maintenance is used to describe this situation. We wanted to study this particular situation and we based ourselves on this Tambe and Kulkarni (2015) document to develop our first model. However, in this paper, the authors rely on a genetic algorithm and on simulated annealing. Here, we will instead perform the simulation using the Monte Carlo method. In fact, in the Tambe and Kulkarni (2015) article, preventive maintenance (conducted at an opportunity) is carried out based on the actual age of the components. Here, we will test different strategies of preventive maintenance (by random drawing) and we will compare them to determine the best. We will also rely on the quality control elements performed in the work of Cassady et al. (2000) and Linderman et al. (2005)]. 3. MODEL DEFINITION The goal of the model is to determine the best maintenance policy and the best quality control parameters for batch production. For the maintenance, the more maintenance actions are performed, the less failures there will be (so less non-compliant products). On the other hand, maintenance costs will increase. There is therefore an optimum to determine. For quality control, the more frequent will be the sampling, the sooner the failures will be detected and therefore, there will be fewer non-compliant products. In addition, taking large samples (Ns large) increases the accuracy of the detections (the risk of not detecting a failure decreases when Ns increases). Again, an optimum is to be determined for the quality control parameters. The realized model applies to a batch production where m different products are produced on the same machine. This machine itself consists of n different components. A model is used to determine the best preventive maintenance policy and the best quality control parameters for a given production sequence. 3.1 Parameters Here are the parameters used in the model (Table 1). 3.2 Methodology The methodology is shown in Fig. 3. After choosing the data, the first step is to propose a preventive maintenance strategy. For this, we randomly draw a maintenance strategy. By component, we fix a replacement during the production of m lots and as many repairs as we want. However, a repair can not occur when a replacement is planned. The definition of the maintenance strategy concerns the n components of the machine. At the end of the production of a batch, this strategy informs us of the maintenance operation that will be performed on the components: replacement, repair or no operation. This maintenance strategy is presented as an n x m matrix. For example, for a 2-component machine that makes 3 different batches, a typical M maintenance strategy is given in Eq.1.
0 2 1 M= 1 0 2
(1)
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Table 1. Parameters of the model Parameters n m Tjob MTTRA MTTrA ρ β η PR CLP CLM CP CC CSP µ1 σ µ2 δ Hs Ns Cs Tins
Data choice (Table 1) Indexi=0
Definition Number of components of the machine Number of batches Batch production time (h) Replacement time (h) Repair time (h) Maintenance efficiency Shape parameter of the Weibull distribution Scale parameter of the Weibull distribution (h) Production rate (products/h) Cost of losses of production (e/products) Cost of labor in maintenance (e/h) Cost of a product (h) Cost of component (new) (e) Cost of spare part (e) Mean of the quality indicator in normal conditions Standard deviation of the quality indicator Mean of the quality indicator in case of failure Maximum deviation for quality acceptance Sampling period (h) Sample size Sample cost (e/element) Inspection time (h)
Yes End of m batches ?
Production of bacth i
Yes
Failure during batch i ? No
We still need to know how to detect failures. Indeed, their detection is important because these failures lead to an increase in the rate of non-compliant products and need a repair action that brings back the system under control. This detection is carried out through the quality control. The principle used for the simulation is shown in Fig.4. The quality control parameters are first fixed (Ns, Hs, Cs, ...). Then, a Monte Carlo simulation is performed: the failure times of each of the n components are determined. For this simulation, we use the Weibull reliability law whose expression is recalled in Eq.2. t−γ β η )
No : i=i+1
Repair
In this matrix, the digit 0 indicates that no maintenance operation is performed. The number 1 indicates that a repair is planned. Finally, the number 2 indicates that a replacement is planned. Thus, in the matrix M presented above, the component 1 of the machine (first line) will be replaced at the end of the second job and repaired at the end of the third job. On the other hand, the second component of the machine will be repaired at the end of the first job and replaced at the end of the third job. When the maintenance strategy is defined, the batch production is started. During batch production, a failure may occur. This leads to a repair of the failed component. At the end of batch production, the maintenance strategy is applied to the machine. Then the production of the next batch begins and so on until the end of the jobs. At the end of the jobs, the total cost of batch production is calculated (production, maintenance and quality control).
R(t) = e−(
Random draw of a maintenance policy M
Compute C, the total cost, based on M and resimule
(2)
It is assumed that the quality indicator follows a normal distribution and that the occurrence of a failure moves the mean of the normal distribution from µ1 to µ2 . The control chart used is an mean Shewhart chart. The production simulation then begins. During batch production, a quality control is carried out. In fact, we take Ns products (samples) at time interval Hs (sampling period). This sampling is made by random drawing on the above-mentioned 646
End of batch i : application of the maintenance policy (M )
Fig. 3. Methodology used
Data choice (Table 1)
Failure simulation and modification of the quality indicator’s law
Repair Failure Failure or false alarm
Production simulation and sampling based on the quality indicator’s law
False alarm
No
Number of noncompliant products > Ts ? Yes
Inspection
Fig. 4. Quality control (simulation principle) normal laws. If the value obtained has a greater difference than δ compared with µ1 , an inspection is started to determine if a problem has occurred. If a failure has occurred, a repair is performed. The purpose of quality control is to detect failures and thus avoid prolonged production of noncompliant products. Indeed, the appearance of a failure causes the increase in the rate of non-compliant products
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manufactured and therefore, the increase in costs related to non-quality. 4. NUMERICAL EXAMPLE In this section, an example similar to that proposed in the Tambe and Kulkarni (2015) article is treated. It is a die casting machine. It manufactures a series of identical products and then the mold is modified and the machine then produces other parts. We will limit ourselves here to one component. The component selected is the one which failures lead to many quality defects in the parts produced. This component is a piston.
(2) Detecting a failure causes a repair of the affected component (3) When the system is under control, the quality indicator follows a normal distribution with mean µ1 and standard deviation σ. (4) When the system is under control, the quality indicator follows a normal distribution with mean µ2 and standard deviation σ. (5) Resources needed for maintenance actions are always available (6) The maintenance efficiency ρ is known for the component studied. 4.3 Developments
4.1 Parameters definition We need to define a series of parameters (see Table 2).For the component and the products, we give the values of the parameters defined previously. Table 2. Parameters for the example Parameters n m Tjob MTTRA MTTrA ρ β η PR CLP CLM CP CC CSP µ1 σ µ2 δ Hs Ns Cs Tins
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Values 1 5 [105 189 304 345 400] 6 5 0.7 2.69 3744 150 150 30 100 120000 50000 20 0.1 20.1 0.15 50 10 (maximum value) 10 0.2
Here we develop the method for the numerical example. The first step is to randomly draw a maintenance strategy. The maintenance strategy is therefore presented here in the form of a 1 x 5 matrix. Each column corresponds to the maintenance action performed at the end of the batches. Then the Monte Carlo simulation is performed. Thanks to this simulation, the failure time of the component is known. The successive realization of the 5 jobs begins, that is to say that the production of the 5 products is launched. During the manufacture of a product, we look at whether a failure occurs. To find out, we need to compare the failure time to the end time of the job. In fact, quality control will enable us to detect failures. In fact, the failure causes a change in the quality indicator. Therefore, samples of Ns produced are taken at time interval Hs. When the number of defective products among those taken exceeds Ts (acceptance limit), an inspection is started to check if the machine is in a normal state. If a failure has occurred, it will be detected through the inspection. A repair is then performed. Finally, at the end of a job, the preventive maintenance strategy is applied. To average the results of the chosen strategy, the Monte Carlo simulation is repeated a large number of times (10000 for example). The operation is repeated on several different strategies in order to find the best strategy.
The maintenance efficiency ρ will be used during repairs to find the effective age of the component (imperfect maintenance, Eq.3). (3) v2 = v + ρT In equation 3, v2 symbolizes the age after the repair and v represents the age before the production period T. We also need to define other parameters for the products. These parameters will be used to determine the total cost generated by a given strategy. We will consider here that the machine manufactures 5 different products (m = 5) but whose characteristics are the same. The only difference between products is the batch production time (that is the reason why Tjob is a vector). 4.2 Hypotheses Some hypotheses have been taken to realize the model: (1) Given its average lifespan (compared with job completion times), the component can fail only once during the realization of the m jobs 647
4.4 Results In this section, we decided to vary Ns between 1 and 10. For each value of Ns , we compared 20 different maintenance policies (Matrix M). Then we simulated each configuration (Ns -M) 1000 times (1000 simulations). For each configuration, Ts was varying between 0 and the maximal value of Ns . In the figures 6 and 5, we present the results. The best maintenance policy is given in Eq.4 and the best Ns value is given in Eq.5. The acceptance limit Ts is given in Eq.6. This maintenance policy and these quality control parameters lead to the total cost given in Eq.7. M = [0 0 0 2 0]
(4)
Ns = 4
(5)
Ts = 0
(6)
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Fig. 5. Total cost in function of the number of simulation .
is real since the model gives the best maintenance strategy to apply. In addition, it provides a control plan (Hs , Ns , inspection initiated if detection of non-compliance). On the actual system, it remains to define the defect (dimension out of tolerance, visual defect, ..) and the method of measurement. This model already has a certain complexity since it integrates many parameters (imperfect maintenance, control card, various costs, ...). However, the model can still be improved. Indeed, here we have assumed that maintenance resources are always available. However, this is not always the case in reality and must be taken into account. There are also many variables that affect the total cost (Hs , reliabity law, control limits, cost paramaters,...). Further works are needed to find their best values in order to minimize the total cost. Then, there are many different control charts (Shewhart, CUSUM, ...), we could worry about the best control card to apply for quality control. REFERENCES
Fig. 6. Total cost in function of the sample size Ns Ctot = 398441, 87 (7) That means that the best maintenance policy is to peform a replacement at the end of the fourth batch and to do no repair. The quality control consist of taking 4 products every 50h. If, within this 4 products, there is at least one product outside the quality acceptance interval, a inspection is launched to know if a repair action is needed. In the figures 6 and 5, we present the results. The number of Monte Carlo simulations has a great impact on the accuracy for the total cost. By doing 1000 simulations, we see in Fig.5 that convergence is ensured. In Fig.6, we see that the total cost is minimized for a Ns value of 4. 5. CONCLUSION A literature review was carried out to report on existing techniques and models on the integration of quality control and maintenance policies. Based on the article of Tambe and Kulkarni (2015), we realized a first model integrating production, maintenance and quality control. This first model makes it possible to define the best maintenance policy and the best quality control to be applied to a machine that produces batches of products. This model can be applied to a real system with a history of failure times is available (which allows an estimation of reliability laws) and when the effect of failures on quality is known (jump in the average indicator for example). The interest 648
Alsyouf, I. (2007). The role of maintenance in improving companies productivity and profitability. International Journal of Production economics, 105, 70–78. Azadeh, A., Sheikhalishahi, M., Mortazavi, S., and Jooghi, E.A. (2016). Joint quality control and preventive maintenance strategy: a unique taguchi approach. Springer. Ben-Daya, M. and Duffuaa, S. (1995). Maintenance and quality: the missing link. Journal of Quality in Maintenance Engineering, 1, 20–26. Cassady, R., Bowden, R., Liew, L., and Pohl, E. (2000). Combining preventive maintenance and statistical process control: a preliminary investigation. IIE Transactions, 32, 471–478. Chen, Y.C. (2013). An optimal production and inspection strategy with preventive maintenance error and rework. Journal of Manufacturing Systems, 32, 99–106. Gouiaa-Mtibaa, A., Dellagi, S., Achour, Z., and Erray, W. (2016). Development of integrated maintenance-quality policy according to imperfect quality item produced. IFAC-PapersOnLine, 49-12, 1400–1405. Linderman, K., McKone-Sweet, K., and Anderson, J. (2005). An integrated systems approach to process control and maintenance. European Journal of Operational Research, 164, 324–340. Lu, B., Zhou, X., and Li, Y. (2016). Joint modeling of preventive maintenance and quality improvement for deteriorating single-machine manufacturing systems. Computers and Industrial Engineering, 91, 188–196. Ollila, A. and Malmipuro, M. (1999). Maintenance has a role in quality. The TQM Journal, 11, 17–21. Rahim, M. and Ben-Daya, M. (2001). Integrated models in production planning, inventory, quality and maintenance. Springer US. Rivera-Gomez, H., Gharbi, A., Kenn´e, J., MontanoArango, O., and Hernandez-Gress, E. (2016). Production control problem integrating overhaul and subcontracting strategies for a quality deteriorating manufacturing system. Int. J. Production Economics, 171, 134– 150. Tambe, P. and Kulkarni, M. (2015). A superimposition based approach for maintenance and quality plan optimization with production schedule, availability, repair time and detection time constraints for a single machine. Journal of Manufacturings Systems, 37, 17–32.
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Using quality control in optimizing Using quality control in optimizing Using quality control in optimizing opportunistic maintenance Using quality control in optimizing opportunistic maintenance opportunistic maintenance opportunistic maintenance C. Dutoit ∗∗ P. Dehombreux ∗∗ E. Rivi` ere Lorph` evre ∗∗
C. Dutoit ∗ P. Dehombreux ∗ E. Rivi` ere Lorph` evre ∗ C. Dutoit ∗ P. Dehombreux ∗ E. Rivi` ere Lorph` evre ∗ C. Dutoit P. Dehombreux E.and Rivi` ere Lorph` evre ∗ of Mons, Machine Design Production Engineering ∗ University ∗ University of Mons, Machine Design and Production Engineering University of Mons, Machine Design and Production Engineering Department, Research Institute for Science and Management of Department, Research for Science Management of Risks, Risks, ∗ University of Mons,Institute Machine Design andand Production Engineering Mons, Belgium, (e-mail: [email protected]) Department, Research Institute for Science and Management of Risks, Mons,Research Belgium,Institute (e-mail:for [email protected]) Department, Science and Management of Mons, Belgium, (e-mail: [email protected]) Risks, Mons, Belgium, (e-mail: [email protected]) Abstract: production efficiency. efficiency. Abstract: Nowadays Nowadays companies companies are are constantly constantly looking looking for for maximum maximum production To achieve this goal, the actions taken aim to reduce the overall costs of the company. Thus, Abstract: Nowadays companies are constantly looking for maximum production efficiency. To achieve this goal, the actions taken aim to reduce the for overall costs ofproduction the company. Thus, Abstract: Nowadays companies are constantly looking maximum efficiency. measures are taken to ensure the availability of production equipment at the same time as To achieve this goal, the actions taken aim to reduce the overall costs of the company. Thus, measures are ensure thetaken availability of production equipment atthethe same time as To achieve thistaken goal,to actions aim atostudy reduce the overall costs ofthe company. Thus, good product quality. This article in order to optimize maintenance of measures are taken tothe ensure the proposes availability of production equipment at the same time asaa good product quality. This article proposes a study in order to optimize the maintenance of measures are taken to the ensure the proposes availability of production at the same timeofasa production system and control. A bibliographic is to good product quality. article a study in orderresearch toequipment optimize the maintenance production system andThis the quality quality control. A bibliographic research is developed developed to determine determine good product quality. This article proposes a study in order to optimize the maintenance of a the quality tools used optimize maintenance. The idea is to the production andcan thebe control. A bibliographic to determine the quality system tools that that can bequality used to to optimize maintenance.research ideais isdeveloped to determine determine the best best The production system and the quality control. A bibliographic research is developed to determine maintenance policy by using based on A numerical example is the quality tools that be information used to optimize The idea is determine the best maintenance policy bycan using basedmaintenance. on quality quality indicators. indicators. A to numerical example is the quality tools that be information used to optimize The idea is determine the best also treated on a batch production with opportunistic maintenance applied. maintenance policy bycan using information basedmaintenance. on quality indicators. A to numerical example is also treated on a batch production with opportunistic maintenance applied. maintenance policy by using information based on quality indicators. A numerical example is also treated on a batch production with opportunistic maintenance applied. © 2018, IFACon (International Federationwith of Automatic Control)maintenance Hosting by Elsevier Ltd. All rights reserved. also treated a batch production opportunistic applied. Keywords: Keywords: Quality Quality control, control, maintenance maintenance policy, policy, optimization, optimization, statistical statistical process process control. control. Keywords: Quality control, maintenance policy, optimization, statistical process control. Keywords: Quality control, maintenance policy, optimization, statistical process control. 1. INTRODUCTION INTRODUCTION process (reliability (reliability law). law). Despite Despite some some assumptions, assumptions, the the 1. process 1. INTRODUCTION process (reliability law). Despite some assumptions, the document provides a solid foundation for integrating qualdocument provides alaw). solid foundation forassumptions, integrating qual1. INTRODUCTION process (reliability some the Quality provides a solid Despite foundation for strategy integrating ity control into aa preventive preventive maintenance for qualcostQuality has has become become a a priority priority for for the the majority majority of of comcom- document ity control into maintenance strategy for costdocument provides a solid foundation for strategy integrating qualQuality has become a priority for the majority of com- ity panies. With technological advances and an increasingly control into a preventive maintenance for costeffective optimization. panies. technological advances and an increasingly optimization. Quality With has become a operators priority for majority of com- effective ity control into a preventive maintenance strategy for costpanies. With technological advances and an increasingly advanced automation, no the longer have complete effective optimization. advanced automation, operators no longer have complete Another interesting article panies. With technological advances and an increasingly effective optimization. advanced automation, operators no longer have complete Another interesting article is is that that of of Linderman Linderman et et al. al. control over over their their production production processes. processes. The The influx influx of of control Another interesting article is that of Linderman et al. (2005). This article advocates ”adaptive” maintenance advanced automation, operators no longer have complete control over their production processes. The influx of (2005). data (especially on the quality of products) is increasingly This article advocates ”adaptive” maintenance Another interesting article is that of Linderman et unal. data (especially on the quality ofprocesses. products) The is increasingly article advocates ”adaptive” maintenance based onThis quality control. When the process becomes control overUnfortunately, their production influx exof (2005). data (especially on the quality of data products) is increasingly important. these are not not always based on quality control. When the process becomes un(2005). This article advocates ”adaptive” maintenance important. Unfortunately, these data are always excontrol. schedule When the stable,on thequality maintenance is process revised becomes to speed speed unup data (especially on the quality of to products) isquality increasingly important. Unfortunately, data are not alwaystools ex- based ploited. In this this article, we these want describe stable, the maintenance schedule is revised to up based on control. When the process becomes unploited. In article, we want to describe thequality maintenance schedule is the revised to speed up maintenance. On the other hand, if process is stable, important. Unfortunately, these data are notquality alwaystools ex- stable, ploited. In this article, we want to describe quality tools maintenance. On the other hand, if the process is stable, that can be used in the organization of maintenance. stable, maintenance schedule revised to increased. speed up that canIn be usedarticle, in the organization of maintenance. On the other hand, ifis the process is stable, the timethe intervals between maintenance will be ploited. want to describe quality tools maintenance. that can bethis used in the we organization of maintenance. the time intervals between maintenance will be increased. maintenance. On the other hand, if the process is stable, Maintenance andinquality quality are intimately intimately linked. Indeed, Indeed, the intervals between maintenance will be increased. Thetime optimization is done done on on the costs costs generated generated by the the that can be used the organization of maintenance. Maintenance and are linked. The optimization is the by the time intervals between maintenance will be increased. Maintenance and quality are will intimately linked. Indeed, poorly maintained equipment inevitably see the qualThe optimization is done on the costs generated by the operation of the equipment. Again, it is assumed that poorly maintained equipment will inevitably see the qual- operation of the equipment. it is generated assumed that the Maintenance and quality arecompared intimately Indeed, The optimization done onAgain, the costs by the poorly maintained equipment will inevitably see the qual- operation ity of its its products degrade tolinked. maintained of the it is assumed that the process begins in aaisin-control state law process begins inequipment. in-controlAgain, state whose whose law of of reliability reliability ity of products degrade compared to aasee maintained poorly maintained equipment will inevitably the qualoperation of the equipment. Again, it is assumed that the ity of its products degrade compared to a (1999) maintained equipment. Moreover, Ollila and Malmipuro have process begins in a in-control state whose law of reliability is known (Weibull distribution). Inspections take place equipment. Moreover,degrade Ollila and Malmipuro (1999) have is known (Weibull distribution). Inspections take place ity of its products compared to a maintained process begins in a in-control state whose law of reliability equipment. Moreover, Ollila and of Malmipuro (1999) have is highlighted the the important impact maintenance on qualqualknown distribution). take place after hours(Weibull of production production to verify verifyInspections that the the process process has highlighted important impact maintenance on after hours of to that has equipment. Moreover, Ollila and of Malmipuro (1999) have is known distribution). Inspections take place highlighted the important impact of maintenance on quality. They even conclude a case study by showing that after hours(Weibull of production toThe verify that thecharacteristic process has not become out of control. measured ity. They even conclude a case study by showing that not become outproduction of control.toThe measured highlighted the important of maintenance on qualafter hours of verify that thecharacteristic process has ity. They even conclude casemost study by showing that maintenance is one one of the the aimpact three important causes of not become outaa ofcontrol control. The measured characteristic is reported on card. Sometimes, between is reported on control card. Sometimes, between two two maintenance is of three most important causes of ity. They even conclude a case study by showing that not become out of control. The measured characteristic maintenance is one ofThe thequality three most important causes of is quality degradation. control makes it possible reported on a control card. Sometimes, between twoa samplings (j and j + 1 ), a failure occurs and causes quality degradation. The quality control makes it possible samplings (j and j + 1 ), a failure occurs and causes maintenance is one ofThe the three important causes of change is reported a control Sometimes, between twoa quality degradation. to detect drifts. These drifts canmost act as as alarms to trigger samplings (jonand j + 1 ),card. a state. failure occurs and causes a quality control makes itto possible to an an out-of-control The process continues to detect drifts. These drifts can act alarms trigger change to out-of-control state. The process continues quality degradation. The quality makes ittopossible samplings (j and j +only 1 ),allows a state. failure occurs and causes a to detect drifts. These drifts can control act as alarms trigger change maintenance actions. The methodology for determining to an out-of-control The process continues and the control card detection of the problem maintenance actions. The methodology for determining the to control card only allows detection of thecontinues problem to detect drifts. Thesepolicy driftsmethodology can act as alarms tooptimal trigger and change an out-of-control state. The process maintenance actions. The for determining the best maintenance to be applied and the and the control card only allows detection of the problem at j + 1 sampling. The ”adaptive” maintenance model is + 1 control sampling. The ”adaptive” maintenance model is the best maintenance policy to be applied for and the optimal at maintenance actions. will Thebemethodology andjj + the1 card only allows detection ofscenarios the model problem the best maintenance policy to be applied and determining sampling parameters discussed. at sampling. maintenance is the optimal illustrated in Fig. Fig. 1.The In ”adaptive” fact, three different are sampling parameters will be discussed. illustrated in 1. In fact, three different scenarios are the best maintenance policy be applied and the optimal illustrated at j + 1 sampling. ”adaptive” maintenance modelare is sampling parameters will be to discussed. in the Fig.first, 1.The Inthe fact, three different scenarios proposed. In out-of-control state is detected detected proposed. In first, out-of-control state is sampling parameters will be discussed. illustrated in the Fig. 1. Inthe fact, three different scenarios are 2. LITERATURE REVIEW proposed. In the first, the out-of-control state is detected and corrective maintenance is organized to restart the pro2. LITERATURE REVIEW and corrective maintenance is organized tostate restart the proproposed. the first, out-of-control is detected detected 2. LITERATURE REVIEW and corrective maintenance is organized to restart the process. In the theInsecond, second, thethe out-of-control state is not not cess. In the out-of-control state is detected 2. LITERATURE REVIEW and corrective maintenance is organized to restart the proIn this section, we will present documents integrating a cess. In the second, the out-of-control state is not detected before scheduled preventive maintenance. Therefore the In this section, we will present documents integrating a before scheduled preventive maintenance. Therefore the cess. In the second, the out-of-control state is not detected In this section, we will present documents integrating a methodology to use quality control information to manage before scheduled preventive maintenance. maintenance operations highlight and repair the failure Therefore the methodology to use quality control information to manage operations highlight and repair the failure In this section, we will present documents integrating before scheduled preventive Therefore the methodology to control information toCassady managea maintenance maintenance. A use firstquality interesting article is that that of maintenance and under repair the failure and allow theoperations system tohighlight bemaintenance. brought control. In maintenance. A first interesting article is of Cassady and allow the system to be brought under control. In methodology to use quality control information to manage maintenance operations highlight and repair the failure maintenance. Athis firstwork, interesting articledevelop is thataof Cassady and et al. (2000). In the authors preventive allow the under control. In the third scenario, the process remains under control (no system to be brought et al. (2000). InAthis the authors develop preventive scenario, the process remains under under control (no maintenance. firstwork, interesting is control. thata Cassady and third allow thea system to be brought control. In et al. (2000). In this work, the authors develop aof preventive maintenance strategy based on article quality In fact, fact, the the third scenario, the process remains under control (no failure) until preventive maintenance operation is perpermaintenance strategy based on quality control. In failure) until a preventive maintenance operation is et control al. (2000). In this work, theproduction authors develop a preventive the third scenario, the process remains under control (no maintenance strategy based on quality control. In fact, a card controls the process. When a failure) a preventive maintenance operationAGAN, is performed. until Despite some assumptions assumptions (maintenance amaintenance control cardstrategy controlsbased the production process. When Despite some (maintenance on quality control. Inand fact,aa formed. failure) until a Tagushi, preventive maintenance operationAGAN, is that perafailure control card the controls thebecomes production When occurs, process out process. of control formed. Despite some assumptions (maintenance AGAN, loss function of ...), the article demonstrates failure occurs, the process becomes out of control and a loss function of Tagushi, ...), the article demonstrates that a control card on controls thebecomes production process. When formed. Despite somequality assumptions (maintenance AGAN, failure occurs, the process out of control and aa loss jump appears the control board, allowing corrective function of Tagushi, ...), the article demonstrates that a model integrating control and maintenance can jump on the control board,out allowing corrective model integrating quality anddemonstrates maintenance that can failureappears occurs, the process becomes of control and a aabe loss function of Tagushi, ...), control the article jump appears on the control board, allowing corrective maintenance to occur. In order to avoid failures, preventive model integrating quality control and maintenance can beneficial. maintenance occur. order to avoid allowing failures, preventive beneficial. jump appearsto the In control board, corrective a model integrating quality control and maintenance can maintenance to occur. In order to avoidto failures, is on carried out according timepreventive period p. p. be be beneficial. maintenance is carried out according to aa time period We can also also cite cite Alsyouf Alsyouf (2007), (2007), which which has has demonstrated demonstrated maintenance to occur. In order to avoid failures, preventive be beneficial. maintenance is carried out according to a time period p. We The article allows optimizing the periodicity of preventive can The article allows optimizing the periodicity of preventive We can also cite Alsyouf (2007), which has demonstrated the benefits of a maintenance policy on the quality of prodprodmaintenance is carried out according to a time period p. The article allows optimizing the periodicity of preventive maintenance p and and the parameters parameters of the the control control board the ofcite a maintenance policy on the quality of We benefits can also Alsyouf (2007), which hasquality demonstrated maintenance p the of board the benefits of a on maintenance ucts (and thus profitability). This article has proved policy on the of prodThe article allows optimizing thethe periodicity of preventive maintenance p order and the parameters of the control board (sampling) in to reduce costs, from a given (and thus profitability). This article hasofproved the benefits of a on maintenance policy on the quality prod(sampling) order to parameters reduce the costs, from a board given ucts maintenancein and the the control (sampling) inp order to reduce the of costs, from a given ucts (and thus on profitability). This article has proved ucts (and thus on profitability). This article has proved (sampling) in order to reduce the costs, from a given 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Copyright © 2018 IFAC 643 Copyright © under 2018 IFAC 643 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 643 10.1016/j.ifacol.2018.09.643 Copyright © 2018 IFAC 643
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Fig. 1. Simulation principle in Linderman et al. (2005) that the implementation of an effective maintenance policy reduces failures, operating costs and improves product quality. The advantage of this article is that it provides an industrial study case (a Swedish stationery). However, this article is not based on statistical monitoring of the process. Rather, it is an application of TPM based on the collection of various data (expected operating time, planned production rate, planned and unplanned downtime, poor quality products, etc.). The work of Ben-Daya and Duffuaa (1995) also makes an important contribution to the maintenancequality approach. In this work, the authors identify links between quality and maintenance. In fact, they propose two approaches: one is based on the imperfect maintenance concept and the other uses Tagushi’s approach to quality and maintenance (Rahim and Ben-Daya (2001)). In the work of Lu et al. (2016), the authors propose a model where the improvement of the quality of the products intervenes in the decision-making of preventive maintenance. In fact, economic losses due to poor quality products are included in the total cost, which is minimized to get the best planning for preventive maintenance operations. A case study then shows that the model achieves better economic performance than traditional preventive maintenance. In this paper, the problem concerns a single machine subjected to a degradation reducing the quality of the products and increasing the rate of failure. When a failure occurs, a corrective maintenance operation restores the machine to the state before failure (ABAO). Preventive maintenance takes place when the failure rate reaches a threshold. This maintenance reduces the failure rate and improves the quality of the products. This is an imperfect maintenance (between AGAN and ABAO). In the model, it is considered that product quality degradation is a random process that can be modeled by a Gamma process (variable X (t)). Regarding the reliability of the machine, the authors use Weibull’s law. They thus obtain the analytical form of the failure rate. Then, for optimization, a total cost is calculated (maintenances and quality). For quality, the cost generated is based on the loss function of Tagushi but the cost is adapted by integrating the variable X (t) generated by the Gamma process. By minimizing the total cost, it is possible to determine the threshold of the failure rate to be applied for preventive maintenance. In the paper of Rivera-Gomez et al. (2016), the authors are also interested in an economic optimization of a manufacturing system subject to degradation. This degradation causes defects (non-quality) in the products. Revisions make it possible to mitigate the effects of deterioration. The aim here is to determine the frequency at which revisions are to be performed. This is a general model in which the costs incurred include repairs, revisions, arrears of 644
production, defects, production costs and subcontracting costs. Here, when the production machine is no longer able to supply the product to the customer (due to failure or bad products), a second machine is used for manufacturing (subcontracting). This second machine, however, has a higher cost than the first one and so it is avoided to use it too frequently. The economic optimization aims at determining the best maintenance policy (revision) and the best use of the subcontracting option (second machine). The production system evolves according to a semiMarkovian process, returns in ABAO condition after a corrective maintenance (repair) and becomes AGAN after a preventive maintenance. The authors also use a correlation between the degradation of product quality and the age of the machine. The rate of defective parts is directly related to the age of the machine. A numerical example is treated to conclude the article. In the paper of Gouiaa-Mtibaa et al. (2016), models integrating the effects of non-quality and of preventive maintenance are developed. The objective is to determine an optimal maintenance and quality control strategy taking into account a rate of quality loss and the impact of the recovery activities of the wrong products. Two different strategies are proposed. In the first, the batches of products are sold at a reduced price because of the progressive loss of quality due to the degradation of the machine. The objective is to determine the optimum number of batches to be produced (N1 ) before each preventive maintenance operation by maximizing the total benefit per unit of time (P T1 ). The second strategy proposes to rework all the products of poor quality in order to sell them at the maximum price Pmax . Here, it is desired to determine the number of batches produced and reworked (N2 ) before each preventive maintenance operation in order to maximize the total profit per unit time (P T2 ). If a fault occurs between preventive maintenance, a corrective maintenance operation is performed. The advantage of this work is that it links directly the preventive maintenance action to the degradation of the quality of a product (batch of products). The approach is original but does not use statistical control of product quality. Rather, it is based on a rate of loss of quality (taken constant in the numerical example treated). The work of Azadeh et al. (2016) aims to determine the best maintenance policy to minimize the average of the total cost per unit of time (maintenance costs and quality costs). Here, the authors consider the use of buffer stocks to meet demand despite breakdowns or preventive maintenance. The system under study is illustrated in Fig. 2. This is a series of production machines separated by buffer stocks to ensure continuous operation. Each machine produces a certain rate of non-conforming products. The size of intermediate stocks may vary. A simulation is performed and the values of buffer stocks and nonconformity thresholds are determined to obtain the minimum average total cost using the Tagushi method. Here, preventive maintenance operations are carried out when the rate of non-conforming products reaches a certain threshold and the corrective maintenance operations are carried out when the rate of non-conforming products exceeds another threshold. The size of the buffer stocks also intervenes because the storage costs depend on the
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Fig. 2. Production line in Azadeh et al. (2016) number of items present in the stock. It is assumed that the rate of non-compliant items increases in a random manner according to an established relationship. A case study is then developed on two production machines. In Chen (2013) paper, the author develops a model integrating maintenance and product quality. The originality is to take into account the existence of errors in preventive maintenance and the possibility of reworking a certain percentage of the products of poor quality. Here, preventive maintenance is applied when the system is under control. Effective preventive maintenance results in a reduced failure rate for the machine. On the other hand, there is a certain probability that this maintenance operation is inappropriate and causes the system to change to an out-of-control condition. Inspections are carried out to determine the state of the production system and the quality of the products. However, these inspections have a cost and one of the objectives of the model is to optimize the planning of the inspections. Economic optimization involves minimizing the total cost. The latter includes the cost of installation, the cost of storage, the cost of recoveries of non-conforming products, the cost of inspections and preventive maintenance, and finally a cost of late deliveries. The Tambe and Kulkarni (2015) paper describes a model integrating maintenance and quality applied to batch production. In fact, this model studies the production of a set of parts manufactured by die casting. Here, quality control is performed to determine whether the parts produced are compliant or non-compliant. The system produces a P1 rate of conforming parts when it is under control and a P2 rate when it is out of control. Switching from in-control to out-of-control occurs when there is a failure in one of the components of the machine. Corrective maintenance is performed when a fault is detected. However, when changing the type of part produced (mold change), the authors take the opportunity to apply preventive maintenance if necessary. Optimization leads to the determination of the best parameters for quality control and the best maintenance strategies to be applied to the components of the production system. The model developed is very interesting in the context of optimization of quality control and opportunistic maintenance. To synthesize this literature review, we present in this paragraph the advantages and disadvantages of the models proposed in the articles presented. Many articles combine corrective maintenance and preventive maintenance on a single-component machine (Cassady et al. (2000), Linderman et al. (2005), Ben-Daya and Duffuaa (1995), Lu et al. (2016), etc.). However, in these models, preventive maintenance has time periods which are varied to find the optimal value. In reality, time periods of preventive maintenance can be fixed by external events (tool changes, 645
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production stoppage, ...) The term opportunistic maintenance is used to describe this situation. We wanted to study this particular situation and we based ourselves on this Tambe and Kulkarni (2015) document to develop our first model. However, in this paper, the authors rely on a genetic algorithm and on simulated annealing. Here, we will instead perform the simulation using the Monte Carlo method. In fact, in the Tambe and Kulkarni (2015) article, preventive maintenance (conducted at an opportunity) is carried out based on the actual age of the components. Here, we will test different strategies of preventive maintenance (by random drawing) and we will compare them to determine the best. We will also rely on the quality control elements performed in the work of Cassady et al. (2000) and Linderman et al. (2005)]. 3. MODEL DEFINITION The goal of the model is to determine the best maintenance policy and the best quality control parameters for batch production. For the maintenance, the more maintenance actions are performed, the less failures there will be (so less non-compliant products). On the other hand, maintenance costs will increase. There is therefore an optimum to determine. For quality control, the more frequent will be the sampling, the sooner the failures will be detected and therefore, there will be fewer non-compliant products. In addition, taking large samples (Ns large) increases the accuracy of the detections (the risk of not detecting a failure decreases when Ns increases). Again, an optimum is to be determined for the quality control parameters. The realized model applies to a batch production where m different products are produced on the same machine. This machine itself consists of n different components. A model is used to determine the best preventive maintenance policy and the best quality control parameters for a given production sequence. 3.1 Parameters Here are the parameters used in the model (Table 1). 3.2 Methodology The methodology is shown in Fig. 3. After choosing the data, the first step is to propose a preventive maintenance strategy. For this, we randomly draw a maintenance strategy. By component, we fix a replacement during the production of m lots and as many repairs as we want. However, a repair can not occur when a replacement is planned. The definition of the maintenance strategy concerns the n components of the machine. At the end of the production of a batch, this strategy informs us of the maintenance operation that will be performed on the components: replacement, repair or no operation. This maintenance strategy is presented as an n x m matrix. For example, for a 2-component machine that makes 3 different batches, a typical M maintenance strategy is given in Eq.1.
0 2 1 M= 1 0 2
(1)
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Table 1. Parameters of the model Parameters n m Tjob MTTRA MTTrA ρ β η PR CLP CLM CP CC CSP µ1 σ µ2 δ Hs Ns Cs Tins
Data choice (Table 1) Indexi=0
Definition Number of components of the machine Number of batches Batch production time (h) Replacement time (h) Repair time (h) Maintenance efficiency Shape parameter of the Weibull distribution Scale parameter of the Weibull distribution (h) Production rate (products/h) Cost of losses of production (e/products) Cost of labor in maintenance (e/h) Cost of a product (h) Cost of component (new) (e) Cost of spare part (e) Mean of the quality indicator in normal conditions Standard deviation of the quality indicator Mean of the quality indicator in case of failure Maximum deviation for quality acceptance Sampling period (h) Sample size Sample cost (e/element) Inspection time (h)
Yes End of m batches ?
Production of bacth i
Yes
Failure during batch i ? No
We still need to know how to detect failures. Indeed, their detection is important because these failures lead to an increase in the rate of non-compliant products and need a repair action that brings back the system under control. This detection is carried out through the quality control. The principle used for the simulation is shown in Fig.4. The quality control parameters are first fixed (Ns, Hs, Cs, ...). Then, a Monte Carlo simulation is performed: the failure times of each of the n components are determined. For this simulation, we use the Weibull reliability law whose expression is recalled in Eq.2. t−γ β η )
No : i=i+1
Repair
In this matrix, the digit 0 indicates that no maintenance operation is performed. The number 1 indicates that a repair is planned. Finally, the number 2 indicates that a replacement is planned. Thus, in the matrix M presented above, the component 1 of the machine (first line) will be replaced at the end of the second job and repaired at the end of the third job. On the other hand, the second component of the machine will be repaired at the end of the first job and replaced at the end of the third job. When the maintenance strategy is defined, the batch production is started. During batch production, a failure may occur. This leads to a repair of the failed component. At the end of batch production, the maintenance strategy is applied to the machine. Then the production of the next batch begins and so on until the end of the jobs. At the end of the jobs, the total cost of batch production is calculated (production, maintenance and quality control).
R(t) = e−(
Random draw of a maintenance policy M
Compute C, the total cost, based on M and resimule
(2)
It is assumed that the quality indicator follows a normal distribution and that the occurrence of a failure moves the mean of the normal distribution from µ1 to µ2 . The control chart used is an mean Shewhart chart. The production simulation then begins. During batch production, a quality control is carried out. In fact, we take Ns products (samples) at time interval Hs (sampling period). This sampling is made by random drawing on the above-mentioned 646
End of batch i : application of the maintenance policy (M )
Fig. 3. Methodology used
Data choice (Table 1)
Failure simulation and modification of the quality indicator’s law
Repair Failure Failure or false alarm
Production simulation and sampling based on the quality indicator’s law
False alarm
No
Number of noncompliant products > Ts ? Yes
Inspection
Fig. 4. Quality control (simulation principle) normal laws. If the value obtained has a greater difference than δ compared with µ1 , an inspection is started to determine if a problem has occurred. If a failure has occurred, a repair is performed. The purpose of quality control is to detect failures and thus avoid prolonged production of noncompliant products. Indeed, the appearance of a failure causes the increase in the rate of non-compliant products
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manufactured and therefore, the increase in costs related to non-quality. 4. NUMERICAL EXAMPLE In this section, an example similar to that proposed in the Tambe and Kulkarni (2015) article is treated. It is a die casting machine. It manufactures a series of identical products and then the mold is modified and the machine then produces other parts. We will limit ourselves here to one component. The component selected is the one which failures lead to many quality defects in the parts produced. This component is a piston.
(2) Detecting a failure causes a repair of the affected component (3) When the system is under control, the quality indicator follows a normal distribution with mean µ1 and standard deviation σ. (4) When the system is under control, the quality indicator follows a normal distribution with mean µ2 and standard deviation σ. (5) Resources needed for maintenance actions are always available (6) The maintenance efficiency ρ is known for the component studied. 4.3 Developments
4.1 Parameters definition We need to define a series of parameters (see Table 2).For the component and the products, we give the values of the parameters defined previously. Table 2. Parameters for the example Parameters n m Tjob MTTRA MTTrA ρ β η PR CLP CLM CP CC CSP µ1 σ µ2 δ Hs Ns Cs Tins
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Values 1 5 [105 189 304 345 400] 6 5 0.7 2.69 3744 150 150 30 100 120000 50000 20 0.1 20.1 0.15 50 10 (maximum value) 10 0.2
Here we develop the method for the numerical example. The first step is to randomly draw a maintenance strategy. The maintenance strategy is therefore presented here in the form of a 1 x 5 matrix. Each column corresponds to the maintenance action performed at the end of the batches. Then the Monte Carlo simulation is performed. Thanks to this simulation, the failure time of the component is known. The successive realization of the 5 jobs begins, that is to say that the production of the 5 products is launched. During the manufacture of a product, we look at whether a failure occurs. To find out, we need to compare the failure time to the end time of the job. In fact, quality control will enable us to detect failures. In fact, the failure causes a change in the quality indicator. Therefore, samples of Ns produced are taken at time interval Hs. When the number of defective products among those taken exceeds Ts (acceptance limit), an inspection is started to check if the machine is in a normal state. If a failure has occurred, it will be detected through the inspection. A repair is then performed. Finally, at the end of a job, the preventive maintenance strategy is applied. To average the results of the chosen strategy, the Monte Carlo simulation is repeated a large number of times (10000 for example). The operation is repeated on several different strategies in order to find the best strategy.
The maintenance efficiency ρ will be used during repairs to find the effective age of the component (imperfect maintenance, Eq.3). (3) v2 = v + ρT In equation 3, v2 symbolizes the age after the repair and v represents the age before the production period T. We also need to define other parameters for the products. These parameters will be used to determine the total cost generated by a given strategy. We will consider here that the machine manufactures 5 different products (m = 5) but whose characteristics are the same. The only difference between products is the batch production time (that is the reason why Tjob is a vector). 4.2 Hypotheses Some hypotheses have been taken to realize the model: (1) Given its average lifespan (compared with job completion times), the component can fail only once during the realization of the m jobs 647
4.4 Results In this section, we decided to vary Ns between 1 and 10. For each value of Ns , we compared 20 different maintenance policies (Matrix M). Then we simulated each configuration (Ns -M) 1000 times (1000 simulations). For each configuration, Ts was varying between 0 and the maximal value of Ns . In the figures 6 and 5, we present the results. The best maintenance policy is given in Eq.4 and the best Ns value is given in Eq.5. The acceptance limit Ts is given in Eq.6. This maintenance policy and these quality control parameters lead to the total cost given in Eq.7. M = [0 0 0 2 0]
(4)
Ns = 4
(5)
Ts = 0
(6)
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Fig. 5. Total cost in function of the number of simulation .
is real since the model gives the best maintenance strategy to apply. In addition, it provides a control plan (Hs , Ns , inspection initiated if detection of non-compliance). On the actual system, it remains to define the defect (dimension out of tolerance, visual defect, ..) and the method of measurement. This model already has a certain complexity since it integrates many parameters (imperfect maintenance, control card, various costs, ...). However, the model can still be improved. Indeed, here we have assumed that maintenance resources are always available. However, this is not always the case in reality and must be taken into account. There are also many variables that affect the total cost (Hs , reliabity law, control limits, cost paramaters,...). Further works are needed to find their best values in order to minimize the total cost. Then, there are many different control charts (Shewhart, CUSUM, ...), we could worry about the best control card to apply for quality control. REFERENCES
Fig. 6. Total cost in function of the sample size Ns Ctot = 398441, 87 (7) That means that the best maintenance policy is to peform a replacement at the end of the fourth batch and to do no repair. The quality control consist of taking 4 products every 50h. If, within this 4 products, there is at least one product outside the quality acceptance interval, a inspection is launched to know if a repair action is needed. In the figures 6 and 5, we present the results. The number of Monte Carlo simulations has a great impact on the accuracy for the total cost. By doing 1000 simulations, we see in Fig.5 that convergence is ensured. In Fig.6, we see that the total cost is minimized for a Ns value of 4. 5. CONCLUSION A literature review was carried out to report on existing techniques and models on the integration of quality control and maintenance policies. Based on the article of Tambe and Kulkarni (2015), we realized a first model integrating production, maintenance and quality control. This first model makes it possible to define the best maintenance policy and the best quality control to be applied to a machine that produces batches of products. This model can be applied to a real system with a history of failure times is available (which allows an estimation of reliability laws) and when the effect of failures on quality is known (jump in the average indicator for example). The interest 648
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