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Maintenance Decisions of Part Agent Based on Failure Probability of a Part Using Bayesian Estimation
Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 29 (2015) 692 – 697
The 22nd CIRP conference on Life Cycle Engineering
Maintenance decisions of part agent based on failure probability of a part using Bayesian estimation Keisuke Nanjoa,*, Yuki Yamamoria, Yumihito Yokokia, Yuta Sakamotoa , Hiroyuki Hiraokaa a
Department of Precision Mechanics, Chuo University, 1-13-27 Kasuga, Bunkyoku, Tokyo, Japan * Tel.: +81-3-3817-1711; fax: +81-3-3817-1711. E-mail address: [email protected]
Abstract To realize effective reuse of mechanical parts for the development of a sustainable society, it is essential to manage individual parts over their entire life cycle. For that purpose, we are developing a part agent system using network agents. This paper describes a method for a part agent to predict possible states of its corresponding part in the near future. Bayesian network is applied to estimate a failure probability of the part and a simple deterioration model is applied to evaluate properties of the part. Initial results are shown on a life cycle simulation of the developed part agent. © 2015 The Authors. Published by Elsevier B.V.access article under the CC BY-NC-ND license © 2015 Published by Elsevier B.V. This is an open Peer-review under responsibility of the International Scientific Committee of the Conference “22nd CIRP conference on Life Cycle (http://creativecommons.org/licenses/by-nc-nd/4.0/). Engineering. Peer-review under responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering Keywords: Part agent ; Bayesian estimation ; Life cycle
1. Introduction To realize effective part reuse for the development of a sustainable society [1], it is essential to manage individual parts with different reuse history over their entire life cycle. Manufacturers that need the quantity and quality of available used parts for reuse-based production have difficulties to predict such information due to the uncontrollable and unpredictable diversity of user behavior. On the other hand, product users also have difficulties to carry out appropriate maintenance on many and various parts in their products. Based on these considerations, we propose a scheme whereby a part “manages” itself and supports user maintenance activities. For this purpose, we are developing network agents that are programmed to follow their real-life counterpart parts throughout their life cycle. We refer to this network agent as a “part agent” [2]. A part agent provides users with appropriate advices on the reuse of its part and promotes the circulation of reused parts. Predictions of failures and deterioration are required for part agents to generate appropriate advices on reuse of part. However, in spite of many researches, failures of individual
part are difficult to foresee mainly because of their probabilistic nature. Hence, we propose application of Bayesian estimation to overcome this problem. A part agent combines the foreseen probability of failure with the value, cost and environment load estimated using a simple deterioration model, and creates advices based on the predicted near-future state of the part in its life cycle. In this paper, we propose a function of part agent that gives the consumer advice on the reuse of its corresponding part considering the future state in the life cycle. This paper describes how the part agent creates the advice based on the probability of failures of the part estimated using a Bayesian network as well as various properties based on predicted deterioration of the part. First, the concept of part agent is described in the next section. Then, the mechanism of part agent to create advice on the reuse of part is explained in section 3. In section 4, a life cycle simulation conducted to evaluate the mechanism is described with some initial results. The paper is concluded in section 5.
2212-8271 © 2015 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering doi:10.1016/j.procir.2015.02.204
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Keisuke Nanjo et al. / Procedia CIRP 29 (2015) 692 – 697
2. Conceptual scheme of the part agent A part agent manages all information about its corresponding part throughout its life cycle. The proposal assumes the spread of networks and high-precision RFID technology [3]. A part agent is generated at the manufacturing phase of core parts, when an RFID tag is attached to its corresponding part. The part agent identifies the ID of the RFID tag during the part’s life cycle, tracking the part through the network. We chose an RFID tag for identification because RFIDs have a higher resistance to smudge or discoloration than printed bar codes during the long period of a part’s life cycle. Fig 1 shows the conceptual scheme of the part agent. The part agent communicates with various functions within the network and collects the information needed to manage its corresponding part such as product design information, predicted deterioration of parts, logistic information, or market information. It also communicates with local functions on-site, such as sensory functions that detect the state of the part, storage functions for individual part data, and management and control functions of the product. Communication is established using information agents that are subordinate network agents generated by the part agents.
of the part with the operations of its user and the current status of the part, as explained in 3.3. The other is the simulated state of the part, including its environmental load, value, and cost. These values are estimated for every life cycle stage in the near future using the current status of the part and information about its deterioration, as described in 3.4. Possibility of failures is also taken into consideration in the estimation of life cycle stage.
Fig.2 Framework of part agent for advice generation.
3.2. Expansion of life cycle model for estimation of future states of part
Fig.1 Conceptual scheme of the part agent.
3. Agent advice based on life cycle information using a Bayesian network 3.1. Framework of the part agent Fig.2 shows a basic framework for a part agent to advise its user based on the life cycle model of a part. At each time step, the part agent predicts possible states of the part in the near future, and evaluates those options in order to give advice to the user [4]. A part agent expands the life cycle to evaluate each optional expanded life cycle path for several time steps in the future as described in 3.2. We developed the evaluation to be based on two kinds of information. One is the possibility of failures. Considering its probabilistic nature, we applied a Bayesian network for the failure model that relates the failure
Fig 3 illustrates an example of expansion where a life cycle of a part shown on the left is expanded into an expanded life cycle model with a tree structure shown on the right. The expanded life cycle represents possible changes in the life cycle of the part over time. An expanded life cycle path represents a transfer from an expanded life cycle stage to another stage in one time step. Each expanded stage has values required or generated there for the step, such as cost, environmental load, and value. Probability is assigned to each expanded life cycle path. It represents a probability that the part agent takes that path and is estimated considering the probability of failures of the part.
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Keisuke Nanjo et al. / Procedia CIRP 29 (2015) 692 – 697 Fig.3 Expansion of life cycle model.
3.3. Estimation of failure probability based on user’s operations and state of part
described in 4.3. Note that electronic tags are not considered in the simulation. Initial results of the simulation are shown in 4.4 with discussions. 4.1. Simulation process
Failures of parts occur depending on their usage environment such as temperature, as well as their usage levels such as frequency and intensity. However, the quantitative relationship between the occurrence of failure and those factors cannot be clearly determined due to its probabilistic nature. To deal with this problem, a Bayesian network is employed to capture the causal effects of various factors on the failure of parts. See Appendix for a brief explanation of Bayesian network. As we consider that failures are mainly affected by the state of part and the user's operations, we provide part agents with capabilities to collect sensory data on the status of the part and the user's operations. Prior probabilities of the Bayesian network are derived from the collected information. 3.4. Evaluation of value, cost and environment load based on deterioration Various models are required for part agents to evaluate appropriate maintenance actions. They include; a value model that represents changes to the value of the part; a cost model that represents the required cost for the part; an environmental load model that represents the environment load put on the part; and a user model that represents a user's behavior in relation to the part. As we consider these models are mainly based on the deterioration, a deterioration model of the part is also required to represent how the part deteriorates. We developed these models though they are still very simple ones as described in 4. Based on these models, the total performance index (TPI) [5] is derived for the evaluation of a stage. TPI provides a proper evaluation of the performance of a part throughout its life cycle by balancing its value, environmental load and costs and is given in the following equation (1).
ܶܲ ܫൌ
௩௨ ξ௦௧ൈ௩௧ௗ
A simple life cycle, shown in Fig 4, is defined for the simulation consisting of five stages that are 'produce' stage, 'sell' stage, 'use' stage, 'repair' stage, and 'dispose' stage. Paths connecting these stages for one time step are also defined. They are 'produce to sell,' 'sell to use,' 'use to repair,' 'repair to use,' 'use to dispose.' Note that paths representing staying in the same stage are also defined, that are 'produce to produce,' 'sell to sell,' 'use to use,' and 'repair to repair,' though they are not shown in Fig.4. Fig 5 shows an expanded life cycle generated from the simple life cycle in Fig 4 when the part is in the 'use' stage. The part agent calculates expected value, cost, environmental value and TPI for each candidate stage. It takes the path to the stage with the best expectation that is the highest TPI in this simulation. This evaluation may be changed according to the user’s preference, for example, lowest cost instead of highest TPI.
Fig.4 A simple life cycle model.
(1)
A large TPI indicates that the value is high compared to the environmental load and cost. The expected TPI of the stage is calculated using equation (1) based on the expectations of value, cost and environmental load. A part agent then propose to the user a choice of life cycle with the highest expected TPI. 4. Life cycle simulation We developed a simulation for maintenance decisions of part agent based on the scheme described in 3. A part agent evaluates its maintained part based on the estimation of probabilities and proposes maintenance actions for the part based on the result. Life cycle model is expanded as described in 4.1 for each step in the simulation. Failure is estimated as described in 4.2 and properties of the part are calculated as
Fig.5 Expanded life cycle model.
4.2. Estimation of failure probability using Bayesian network Bayesian estimation is used to estimate the possibility of failure of the part based on the operational history of its user and the current status of the part. Probability of the life cycle path to the repair stage is defined based on the result of this estimation. Note that the probability to disposal stage is fixed in this simulation. As an example, Fig 6 illustrates our method of simulation. Circles represent the stages and squares represent the paths. A symbol shown in a circle, such as u1, denotes expected value of the stage calculated by the simulation. A symbol in a square, such as Pu1, denotes the probability of the path. Probability of failure of the part derived from Bayesian network is used to determine the probability of the path.
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Dotted arrows starting from ‘Start’ stage show the current options for the part agent. Using these estimated values and taking into account the probabilities of the corresponding paths, the total expected value for all the branches starting ‘Use1’ stage is calculated as shown in the following equation (2). ݁݁ݑ݈ܽݒ݀݁ݐܿ݁ݔሺܷͳ݁ݏሻ ൌ ͳݑ ሺ ʹݑൈ ܲ ʹݑ ʹݎൈ ܲ ʹݎ ݀ʹ ൈ ܲ݀ʹሻ (2) Similarly, expected values of ‘Repair1’ and ‘Dispose1’ are calculated. Part agent then selects next life cycle stage based on expectations calculated by their expected values and the probabilities of paths to those stages that are derived from probability of failure of the part using Bayesian estimation. Fig.7 Representation of causal relations
Prior probabilities on operations with a low probability of 0.10 and high probability of 0.90 are provided for Users 1 to 8, as shown in Table 1. A calculation is made with conditional probabilities provided as shown in Fig 8. Table 1. Prior probability for the operation of users. User 1 User 2 User 3 User 4 User 5 User 6 User 7 User 8
P(Op1)
P(Op2)
P(Op3)
0.10 0.10 0.10 0.10 0.90 0.90 0.90 0.90
0.10 0.10 0.90 0.90 0.10 0.10 0.90 0.90
0.10 0.90 0.10 0.90 0.10 0.90 0.10 0.90
Fig.6 Example of the value of life cycle path.
We have defined the causal network model of between parts and user as shown in Fig 7, to estimate the probability of failure of the part. The causal network model represents the causal relations among the occurrences of events. In the figure, events shown as white boxes represent input events, those in dark blue represent observable events, those in light blue represent unobservable events, and those in gray represent target events whose probability is yet to be estimated. We assume three operations 1 to 3 for the consumer’s operation, and two states 1 and 2 for the state of the part that are observable using sensors. Operations 1 to 3 affect the occurrences of defects 1 and 2. Defect 1 affects the occurrence of state 1, and defect 2 affects the occurrence of state 2. We assume that costly maintenance is required when defect 2 occurs.
Fig.8 Conditional probability tables.
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4.3. Evaluation of life cycle stages based on deterioration model To create a simulation to estimate the future state of a part, we assume that a part deteriorates with operational time. Our deterioration model of the part is shown in Fig 9. The performance of the part decreases with its operational time. When the part is repaired, some performance is recovered. In this simulation, it decreases 5 percent of initial performance for each step of use and is recovered for 40 percent within initial performance on repair. The properties of parts are updated in the stages for each time step as shown in Table 2. P denotes the current performance of the part and Pmax denotes its initial performance when it is newly produced. Note that we took a simple assumption where the cost and the environmental load depend on P and Pmax.
Fig 9. Deterioration model Table 2. Properties of stages. Value Produce Sell Use Repair Dispose
0 0 P 0 0
Cost
Environmental load
0 P 0.2×ܲ௫ 㸫0.1×P 0.5×ܲ௫ 0.2×ܲ௫
0 0.1×P 0.2×ܲ௫ 㸫0.1×P 0.2×ܲ௫ ܲ௫
ܲ ݎൌ ܲሺܯȁʹܦሻ ሺͲǤͳ ൈ
ܲ௫ െ ܲ ሻ െ ͲǤͲͷ ܲ௫
(4)
4.4. Simulation results To evaluate our method of prediction, simulation of a part agent was performed with eight users for 20 steps choosing an appropriate stage in each step. Fig 10 shows the average of TPI by performing this simulation for 10 times. The solid line represents the results of eight users, and the dotted line represents the results without Bayesian estimation. Longer use of part is observed with failure prediction. We consider, when the part is deteriorated, expectation for use gets higher with high expectation of repair anticipated in the next step than expectation of repair in this step. Total value of TPI in 20 steps for User 1, that is 121.2, is smaller than that without Bayesian estimation that is 140.0, because the failure of part is not simulated and failure probability does not affect TPI in this simulation. Differences in behaviors of part are observed among users, but they are little in quantity. In this simulation, deterioration is not taken into account in failure model represented with Bayesian network shown in Fig. 8. This makes probability Pr for transition to repair stage irrelevant to deterioration of the part, which leads to little difference of expectation of repair stage by the intensity of use. In this paper, we deal with failure model and deterioration model separately. However, their mutual relation should be considered in the next step of development. We will also propagate this method to the estimation of cost and environmental load too and investigate the effectiveness of our system in detail.
Table 3. Probabilities of paths. To From Produce Sell Use Repair Dispose
Produce
Sell
0.1
0.9 ͲǤ͵
Use
Repair
Dispose
ͲǤ Pu ͲǤͻ
Pr ͲǤͳ
0.05 1.0
Pr and Pu in Table 3, representing probabilities whether the part is repaired or not, are calculated by the following equations. Coefficient 0.1 multiplied to the term of the deterioration represents how the deterioration is emphasized in the decision and may depend on preference of the user. ܲ ݑൌ ͳǤͲ െ ሼܲሺܯȁʹܦሻ ൬ͲǤͳ ൈ
ܲ௫ െ ܲ ൰ሽ ܲ௫
(3)
Fig.10 Simulation result.
5. Conclusion It is required for part agents to give users appropriate advices on maintenance in order to promote the reuse of parts. We proposed a function of part agent that gives the consumer advice on whether its corresponding part should be repaired or not considering the future state in the life cycle. The function creates the advice by calculating the expected future TPI of
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the part based on its deterioration and failure probability estimated by Bayesian network. A simulation of the system is made to evaluate its effectiveness and its first result is reported. We expect flexible maintenance will be achieved using part agents with this function for the cases where predetermined maintenance cannot be applied. The remaining issues and future prospects are communication among multiple part agents, creation of a more realistic deterioration model for parts and establishment of mutual relations between failure probability and deterioration. When multiple part agents are considered, the mutual P(B|A,C) A C effects among parts and part 0 1 agents should be dealt with, 0 0 p11 p21 including their appropriate communication. 0 1 p12 p22 Deterioration may vary 1 0 p13 p23 depending on the parts and its 1 1 p14 p24 environments. We need to create a deterioration model based on deterioration data of real parts. Relations among models including the model for failure estimation and the model for estimating deterioration should be developed for more precise and practical application. Acknowledgements This work was supported by JSPS KAKENHI Grant Number 24560165. References [1] Hauschild, M., Jeswiet, J., Alting, L., From Life Cycle Assessment to Sustainable Production: Status and Perspectives, Annals of CIRP; 2005, 54/2:535–555. [2] Hiraoka, H., Ueno, T., Kato, K., Ookawa, H., Arita, M., Nanjo, K., Kawaharada, H., Part Agent Advice for Promoting Reuse of the Part Based on Life Cycle Information, 20th CIRP International Conference on Life Cycle Engineering; 2013, 335-340. [3] Borriello, G., RFID: Tagging the World, Communications of the ACM; 2005, 44/9:34–37. [4] Nanjo, K., Yamamori, Y., Kato, K., Ookawa, H., Kawaharada, H., Hiraoka, H., Part Agent That Proposes Maintenance Actions for a Part Considering Its Life Cycle, The 11th Global Conference on Sustainable Manufacturing; 2013, 235-240. [5] Kondo, S., Masui, K., Mishima, N.,Matsumoto, M., Total performance analysis of product life cycle considering the uncertainties in product-use stage ˈ Advances in Life Cycle Engineering for Sustainable Manufacturing Businesses; 2008, 371-376ˊ [6] Jensen, F, An Introduction to Bayesian networks, University College London Press; 1996.
Appendix㸸 㸸A brief explanation of Bayesian network Predicting failures of a part is an important function of the part agent to support the effective reuse of the part. However, it is also a difficult issue due to its probabilistic nature, as well as its dependency on the level of usage by the consumer and on environmental conditions. To deal with this problem, we have applied an estimation method based on a Bayesian network. A Bayesian network is a directed acyclic graph representing causality relationships among events with a
conditional probability table for each event node. It is a probabilistic model that is used for the prediction of uncertain events, decision-making, and failure diagnostics. Probabilities of nodes are calculated by giving evidence information to observable nodes and by propagating probabilities via the network structure based on conditional tables of nodes [6]. Fig 11 shows a simple example of a causal network with conditional probability tables. The graphic shown in the left of the figure depicts that the probabilities of event A and C affect the occurrence of event B. The probability of an event B that varies with the occurrence (shown as 0 and 1 in the table) of events A and C is called the conditional probability, and this is summarized in the conditional probability table in the right of Fig 11.
Fig 11. Example of Bayesian network with conditional probability table.
The probability that event A occurs after event B occurred is obtained by Bayes' theorem shown in equation (5).
ሺܣȁܤሻ ൌ
ሺȁሻሺሻ ሺሻ
(5)
Where P (A) is the prior probability of the occurrence of event A before the occurrence of event B, and P (A | B) is the posterior probability of the occurrence of event A after the occurrence of event B. You can estimate the probability of the occurrence of event A when you know event B occurred based on the prior probability of event A or P (A) and the conditional probability P (B|A). We represent probabilistic causal relationships between failures of a part and their factors using this Bayesian network in order to obtain the probability of the failures.
ScienceDirect Procedia CIRP 29 (2015) 692 – 697
The 22nd CIRP conference on Life Cycle Engineering
Maintenance decisions of part agent based on failure probability of a part using Bayesian estimation Keisuke Nanjoa,*, Yuki Yamamoria, Yumihito Yokokia, Yuta Sakamotoa , Hiroyuki Hiraokaa a
Department of Precision Mechanics, Chuo University, 1-13-27 Kasuga, Bunkyoku, Tokyo, Japan * Tel.: +81-3-3817-1711; fax: +81-3-3817-1711. E-mail address: [email protected]
Abstract To realize effective reuse of mechanical parts for the development of a sustainable society, it is essential to manage individual parts over their entire life cycle. For that purpose, we are developing a part agent system using network agents. This paper describes a method for a part agent to predict possible states of its corresponding part in the near future. Bayesian network is applied to estimate a failure probability of the part and a simple deterioration model is applied to evaluate properties of the part. Initial results are shown on a life cycle simulation of the developed part agent. © 2015 The Authors. Published by Elsevier B.V.access article under the CC BY-NC-ND license © 2015 Published by Elsevier B.V. This is an open Peer-review under responsibility of the International Scientific Committee of the Conference “22nd CIRP conference on Life Cycle (http://creativecommons.org/licenses/by-nc-nd/4.0/). Engineering. Peer-review under responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering Keywords: Part agent ; Bayesian estimation ; Life cycle
1. Introduction To realize effective part reuse for the development of a sustainable society [1], it is essential to manage individual parts with different reuse history over their entire life cycle. Manufacturers that need the quantity and quality of available used parts for reuse-based production have difficulties to predict such information due to the uncontrollable and unpredictable diversity of user behavior. On the other hand, product users also have difficulties to carry out appropriate maintenance on many and various parts in their products. Based on these considerations, we propose a scheme whereby a part “manages” itself and supports user maintenance activities. For this purpose, we are developing network agents that are programmed to follow their real-life counterpart parts throughout their life cycle. We refer to this network agent as a “part agent” [2]. A part agent provides users with appropriate advices on the reuse of its part and promotes the circulation of reused parts. Predictions of failures and deterioration are required for part agents to generate appropriate advices on reuse of part. However, in spite of many researches, failures of individual
part are difficult to foresee mainly because of their probabilistic nature. Hence, we propose application of Bayesian estimation to overcome this problem. A part agent combines the foreseen probability of failure with the value, cost and environment load estimated using a simple deterioration model, and creates advices based on the predicted near-future state of the part in its life cycle. In this paper, we propose a function of part agent that gives the consumer advice on the reuse of its corresponding part considering the future state in the life cycle. This paper describes how the part agent creates the advice based on the probability of failures of the part estimated using a Bayesian network as well as various properties based on predicted deterioration of the part. First, the concept of part agent is described in the next section. Then, the mechanism of part agent to create advice on the reuse of part is explained in section 3. In section 4, a life cycle simulation conducted to evaluate the mechanism is described with some initial results. The paper is concluded in section 5.
2212-8271 © 2015 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering doi:10.1016/j.procir.2015.02.204
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Keisuke Nanjo et al. / Procedia CIRP 29 (2015) 692 – 697
2. Conceptual scheme of the part agent A part agent manages all information about its corresponding part throughout its life cycle. The proposal assumes the spread of networks and high-precision RFID technology [3]. A part agent is generated at the manufacturing phase of core parts, when an RFID tag is attached to its corresponding part. The part agent identifies the ID of the RFID tag during the part’s life cycle, tracking the part through the network. We chose an RFID tag for identification because RFIDs have a higher resistance to smudge or discoloration than printed bar codes during the long period of a part’s life cycle. Fig 1 shows the conceptual scheme of the part agent. The part agent communicates with various functions within the network and collects the information needed to manage its corresponding part such as product design information, predicted deterioration of parts, logistic information, or market information. It also communicates with local functions on-site, such as sensory functions that detect the state of the part, storage functions for individual part data, and management and control functions of the product. Communication is established using information agents that are subordinate network agents generated by the part agents.
of the part with the operations of its user and the current status of the part, as explained in 3.3. The other is the simulated state of the part, including its environmental load, value, and cost. These values are estimated for every life cycle stage in the near future using the current status of the part and information about its deterioration, as described in 3.4. Possibility of failures is also taken into consideration in the estimation of life cycle stage.
Fig.2 Framework of part agent for advice generation.
3.2. Expansion of life cycle model for estimation of future states of part
Fig.1 Conceptual scheme of the part agent.
3. Agent advice based on life cycle information using a Bayesian network 3.1. Framework of the part agent Fig.2 shows a basic framework for a part agent to advise its user based on the life cycle model of a part. At each time step, the part agent predicts possible states of the part in the near future, and evaluates those options in order to give advice to the user [4]. A part agent expands the life cycle to evaluate each optional expanded life cycle path for several time steps in the future as described in 3.2. We developed the evaluation to be based on two kinds of information. One is the possibility of failures. Considering its probabilistic nature, we applied a Bayesian network for the failure model that relates the failure
Fig 3 illustrates an example of expansion where a life cycle of a part shown on the left is expanded into an expanded life cycle model with a tree structure shown on the right. The expanded life cycle represents possible changes in the life cycle of the part over time. An expanded life cycle path represents a transfer from an expanded life cycle stage to another stage in one time step. Each expanded stage has values required or generated there for the step, such as cost, environmental load, and value. Probability is assigned to each expanded life cycle path. It represents a probability that the part agent takes that path and is estimated considering the probability of failures of the part.
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Keisuke Nanjo et al. / Procedia CIRP 29 (2015) 692 – 697 Fig.3 Expansion of life cycle model.
3.3. Estimation of failure probability based on user’s operations and state of part
described in 4.3. Note that electronic tags are not considered in the simulation. Initial results of the simulation are shown in 4.4 with discussions. 4.1. Simulation process
Failures of parts occur depending on their usage environment such as temperature, as well as their usage levels such as frequency and intensity. However, the quantitative relationship between the occurrence of failure and those factors cannot be clearly determined due to its probabilistic nature. To deal with this problem, a Bayesian network is employed to capture the causal effects of various factors on the failure of parts. See Appendix for a brief explanation of Bayesian network. As we consider that failures are mainly affected by the state of part and the user's operations, we provide part agents with capabilities to collect sensory data on the status of the part and the user's operations. Prior probabilities of the Bayesian network are derived from the collected information. 3.4. Evaluation of value, cost and environment load based on deterioration Various models are required for part agents to evaluate appropriate maintenance actions. They include; a value model that represents changes to the value of the part; a cost model that represents the required cost for the part; an environmental load model that represents the environment load put on the part; and a user model that represents a user's behavior in relation to the part. As we consider these models are mainly based on the deterioration, a deterioration model of the part is also required to represent how the part deteriorates. We developed these models though they are still very simple ones as described in 4. Based on these models, the total performance index (TPI) [5] is derived for the evaluation of a stage. TPI provides a proper evaluation of the performance of a part throughout its life cycle by balancing its value, environmental load and costs and is given in the following equation (1).
ܶܲ ܫൌ
௩௨ ξ௦௧ൈ௩௧ௗ
A simple life cycle, shown in Fig 4, is defined for the simulation consisting of five stages that are 'produce' stage, 'sell' stage, 'use' stage, 'repair' stage, and 'dispose' stage. Paths connecting these stages for one time step are also defined. They are 'produce to sell,' 'sell to use,' 'use to repair,' 'repair to use,' 'use to dispose.' Note that paths representing staying in the same stage are also defined, that are 'produce to produce,' 'sell to sell,' 'use to use,' and 'repair to repair,' though they are not shown in Fig.4. Fig 5 shows an expanded life cycle generated from the simple life cycle in Fig 4 when the part is in the 'use' stage. The part agent calculates expected value, cost, environmental value and TPI for each candidate stage. It takes the path to the stage with the best expectation that is the highest TPI in this simulation. This evaluation may be changed according to the user’s preference, for example, lowest cost instead of highest TPI.
Fig.4 A simple life cycle model.
(1)
A large TPI indicates that the value is high compared to the environmental load and cost. The expected TPI of the stage is calculated using equation (1) based on the expectations of value, cost and environmental load. A part agent then propose to the user a choice of life cycle with the highest expected TPI. 4. Life cycle simulation We developed a simulation for maintenance decisions of part agent based on the scheme described in 3. A part agent evaluates its maintained part based on the estimation of probabilities and proposes maintenance actions for the part based on the result. Life cycle model is expanded as described in 4.1 for each step in the simulation. Failure is estimated as described in 4.2 and properties of the part are calculated as
Fig.5 Expanded life cycle model.
4.2. Estimation of failure probability using Bayesian network Bayesian estimation is used to estimate the possibility of failure of the part based on the operational history of its user and the current status of the part. Probability of the life cycle path to the repair stage is defined based on the result of this estimation. Note that the probability to disposal stage is fixed in this simulation. As an example, Fig 6 illustrates our method of simulation. Circles represent the stages and squares represent the paths. A symbol shown in a circle, such as u1, denotes expected value of the stage calculated by the simulation. A symbol in a square, such as Pu1, denotes the probability of the path. Probability of failure of the part derived from Bayesian network is used to determine the probability of the path.
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Dotted arrows starting from ‘Start’ stage show the current options for the part agent. Using these estimated values and taking into account the probabilities of the corresponding paths, the total expected value for all the branches starting ‘Use1’ stage is calculated as shown in the following equation (2). ݁݁ݑ݈ܽݒ݀݁ݐܿ݁ݔሺܷͳ݁ݏሻ ൌ ͳݑ ሺ ʹݑൈ ܲ ʹݑ ʹݎൈ ܲ ʹݎ ݀ʹ ൈ ܲ݀ʹሻ (2) Similarly, expected values of ‘Repair1’ and ‘Dispose1’ are calculated. Part agent then selects next life cycle stage based on expectations calculated by their expected values and the probabilities of paths to those stages that are derived from probability of failure of the part using Bayesian estimation. Fig.7 Representation of causal relations
Prior probabilities on operations with a low probability of 0.10 and high probability of 0.90 are provided for Users 1 to 8, as shown in Table 1. A calculation is made with conditional probabilities provided as shown in Fig 8. Table 1. Prior probability for the operation of users. User 1 User 2 User 3 User 4 User 5 User 6 User 7 User 8
P(Op1)
P(Op2)
P(Op3)
0.10 0.10 0.10 0.10 0.90 0.90 0.90 0.90
0.10 0.10 0.90 0.90 0.10 0.10 0.90 0.90
0.10 0.90 0.10 0.90 0.10 0.90 0.10 0.90
Fig.6 Example of the value of life cycle path.
We have defined the causal network model of between parts and user as shown in Fig 7, to estimate the probability of failure of the part. The causal network model represents the causal relations among the occurrences of events. In the figure, events shown as white boxes represent input events, those in dark blue represent observable events, those in light blue represent unobservable events, and those in gray represent target events whose probability is yet to be estimated. We assume three operations 1 to 3 for the consumer’s operation, and two states 1 and 2 for the state of the part that are observable using sensors. Operations 1 to 3 affect the occurrences of defects 1 and 2. Defect 1 affects the occurrence of state 1, and defect 2 affects the occurrence of state 2. We assume that costly maintenance is required when defect 2 occurs.
Fig.8 Conditional probability tables.
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4.3. Evaluation of life cycle stages based on deterioration model To create a simulation to estimate the future state of a part, we assume that a part deteriorates with operational time. Our deterioration model of the part is shown in Fig 9. The performance of the part decreases with its operational time. When the part is repaired, some performance is recovered. In this simulation, it decreases 5 percent of initial performance for each step of use and is recovered for 40 percent within initial performance on repair. The properties of parts are updated in the stages for each time step as shown in Table 2. P denotes the current performance of the part and Pmax denotes its initial performance when it is newly produced. Note that we took a simple assumption where the cost and the environmental load depend on P and Pmax.
Fig 9. Deterioration model Table 2. Properties of stages. Value Produce Sell Use Repair Dispose
0 0 P 0 0
Cost
Environmental load
0 P 0.2×ܲ௫ 㸫0.1×P 0.5×ܲ௫ 0.2×ܲ௫
0 0.1×P 0.2×ܲ௫ 㸫0.1×P 0.2×ܲ௫ ܲ௫
ܲ ݎൌ ܲሺܯȁʹܦሻ ሺͲǤͳ ൈ
ܲ௫ െ ܲ ሻ െ ͲǤͲͷ ܲ௫
(4)
4.4. Simulation results To evaluate our method of prediction, simulation of a part agent was performed with eight users for 20 steps choosing an appropriate stage in each step. Fig 10 shows the average of TPI by performing this simulation for 10 times. The solid line represents the results of eight users, and the dotted line represents the results without Bayesian estimation. Longer use of part is observed with failure prediction. We consider, when the part is deteriorated, expectation for use gets higher with high expectation of repair anticipated in the next step than expectation of repair in this step. Total value of TPI in 20 steps for User 1, that is 121.2, is smaller than that without Bayesian estimation that is 140.0, because the failure of part is not simulated and failure probability does not affect TPI in this simulation. Differences in behaviors of part are observed among users, but they are little in quantity. In this simulation, deterioration is not taken into account in failure model represented with Bayesian network shown in Fig. 8. This makes probability Pr for transition to repair stage irrelevant to deterioration of the part, which leads to little difference of expectation of repair stage by the intensity of use. In this paper, we deal with failure model and deterioration model separately. However, their mutual relation should be considered in the next step of development. We will also propagate this method to the estimation of cost and environmental load too and investigate the effectiveness of our system in detail.
Table 3. Probabilities of paths. To From Produce Sell Use Repair Dispose
Produce
Sell
0.1
0.9 ͲǤ͵
Use
Repair
Dispose
ͲǤ Pu ͲǤͻ
Pr ͲǤͳ
0.05 1.0
Pr and Pu in Table 3, representing probabilities whether the part is repaired or not, are calculated by the following equations. Coefficient 0.1 multiplied to the term of the deterioration represents how the deterioration is emphasized in the decision and may depend on preference of the user. ܲ ݑൌ ͳǤͲ െ ሼܲሺܯȁʹܦሻ ൬ͲǤͳ ൈ
ܲ௫ െ ܲ ൰ሽ ܲ௫
(3)
Fig.10 Simulation result.
5. Conclusion It is required for part agents to give users appropriate advices on maintenance in order to promote the reuse of parts. We proposed a function of part agent that gives the consumer advice on whether its corresponding part should be repaired or not considering the future state in the life cycle. The function creates the advice by calculating the expected future TPI of
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the part based on its deterioration and failure probability estimated by Bayesian network. A simulation of the system is made to evaluate its effectiveness and its first result is reported. We expect flexible maintenance will be achieved using part agents with this function for the cases where predetermined maintenance cannot be applied. The remaining issues and future prospects are communication among multiple part agents, creation of a more realistic deterioration model for parts and establishment of mutual relations between failure probability and deterioration. When multiple part agents are considered, the mutual P(B|A,C) A C effects among parts and part 0 1 agents should be dealt with, 0 0 p11 p21 including their appropriate communication. 0 1 p12 p22 Deterioration may vary 1 0 p13 p23 depending on the parts and its 1 1 p14 p24 environments. We need to create a deterioration model based on deterioration data of real parts. Relations among models including the model for failure estimation and the model for estimating deterioration should be developed for more precise and practical application. Acknowledgements This work was supported by JSPS KAKENHI Grant Number 24560165. References [1] Hauschild, M., Jeswiet, J., Alting, L., From Life Cycle Assessment to Sustainable Production: Status and Perspectives, Annals of CIRP; 2005, 54/2:535–555. [2] Hiraoka, H., Ueno, T., Kato, K., Ookawa, H., Arita, M., Nanjo, K., Kawaharada, H., Part Agent Advice for Promoting Reuse of the Part Based on Life Cycle Information, 20th CIRP International Conference on Life Cycle Engineering; 2013, 335-340. [3] Borriello, G., RFID: Tagging the World, Communications of the ACM; 2005, 44/9:34–37. [4] Nanjo, K., Yamamori, Y., Kato, K., Ookawa, H., Kawaharada, H., Hiraoka, H., Part Agent That Proposes Maintenance Actions for a Part Considering Its Life Cycle, The 11th Global Conference on Sustainable Manufacturing; 2013, 235-240. [5] Kondo, S., Masui, K., Mishima, N.,Matsumoto, M., Total performance analysis of product life cycle considering the uncertainties in product-use stage ˈ Advances in Life Cycle Engineering for Sustainable Manufacturing Businesses; 2008, 371-376ˊ [6] Jensen, F, An Introduction to Bayesian networks, University College London Press; 1996.
Appendix㸸 㸸A brief explanation of Bayesian network Predicting failures of a part is an important function of the part agent to support the effective reuse of the part. However, it is also a difficult issue due to its probabilistic nature, as well as its dependency on the level of usage by the consumer and on environmental conditions. To deal with this problem, we have applied an estimation method based on a Bayesian network. A Bayesian network is a directed acyclic graph representing causality relationships among events with a
conditional probability table for each event node. It is a probabilistic model that is used for the prediction of uncertain events, decision-making, and failure diagnostics. Probabilities of nodes are calculated by giving evidence information to observable nodes and by propagating probabilities via the network structure based on conditional tables of nodes [6]. Fig 11 shows a simple example of a causal network with conditional probability tables. The graphic shown in the left of the figure depicts that the probabilities of event A and C affect the occurrence of event B. The probability of an event B that varies with the occurrence (shown as 0 and 1 in the table) of events A and C is called the conditional probability, and this is summarized in the conditional probability table in the right of Fig 11.
Fig 11. Example of Bayesian network with conditional probability table.
The probability that event A occurs after event B occurred is obtained by Bayes' theorem shown in equation (5).
ሺܣȁܤሻ ൌ
ሺȁሻሺሻ ሺሻ
(5)
Where P (A) is the prior probability of the occurrence of event A before the occurrence of event B, and P (A | B) is the posterior probability of the occurrence of event A after the occurrence of event B. You can estimate the probability of the occurrence of event A when you know event B occurred based on the prior probability of event A or P (A) and the conditional probability P (B|A). We represent probabilistic causal relationships between failures of a part and their factors using this Bayesian network in order to obtain the probability of the failures.