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Statistical Method of Control of Changes when Operating Engineering Systems Statistical Method of Control of Changes when Operating Engineering Systems Statistical Method of Control of Changes when Operating Engineering Systems Statistical Method of Control of Changes when Operating Engineering Statistical Method of Control of Changes when Operating Engineering Systems Systems
Elena L. Gordeeva* Elena L. Gordeeva* Nataliya Mokrova** Elena Elena L. L.V.Gordeeva* Gordeeva* Nataliya Mokrova** Elena L.V. Gordeeva* Snezhana V. Atoyan*** Nataliya V. Mokrova** Nataliya V. Mokrova** Snezhana V. Atoyan*** Nataliya V. Mokrova** Snezhana V. V. Atoyan*** Atoyan*** Snezhana * D.Mendeleev University of Chemical Technology of Russia , Moscow, Snezhana V. Atoyan*** * D.Mendeleev University of Chemical Technology of Russia , Moscow, Russia, (e-mail:
[email protected]) ** D.Mendeleev University of Chemical Technology D.Mendeleev University Chemical Technology of of Russia Russia ,, Moscow, Moscow, Russia, (e-mail:of * D.Mendeleev University
[email protected]) Chemical Technology of Russia , Moscow, Russia, Russia, (e-mail: (e-mail:
[email protected])
[email protected]) Russia,State (e-mail:
[email protected]) ** Moscow University of Civil Engineering, Moscow, ** Moscow State University Russia, (e-mail:
[email protected]) ** Moscow Moscow State State University University of of Civil Civil Engineering, Engineering, Moscow, Moscow, ** of Civil Engineering, Moscow, Russia, (e-mail:
[email protected]) ** MoscowRussia, State University of Civil Engineering, Moscow, (e-mail:
[email protected])
[email protected]) Russia, (e-mail: Russia,
[email protected]) *** Moscow State(e-mail: University of Management, Moscow, *** Moscow State University of Management, Moscow, Russia, (e-mail:
[email protected]) *** Moscow State University of *** Moscow State University of Management, Management, Moscow, Moscow, Russia, (e-mail:
[email protected]) *** Moscow State University of Management, Moscow, Russia, (e-mail:
[email protected]) Russia, (e-mail:
[email protected]) Russia, (e-mail:
[email protected]) Abstract: This paper explores an approach to monitoring the location of objects during installation and Abstract: This paper explores an approach to monitoring location ofofobjects during installation operation of engineering systems. We presented a statisticalthe management processes based on the useand of Abstract: This paper an to the location during installation and Abstract: This paper explores explores an approach approach to monitoring monitoring the location of ofofobjects objects during installation and operation of engineering systems. We presented a statistical management processes based on the use of Abstract: This paper explores an approach to the monitoring the location ofofobjects during installation and control charts. This could serve to control technological state of foundations, communications, operation of engineering systems. We presented a statistical management processes based on the use operationcharts. of engineering systems. presentedthe a statistical management processes based on the use of of control This could serve We to control technological state ofof foundations, communications, operation of engineering systems. We presented a statistical management of processes based on the use of automation systems, and others fall intothe construction state zone of conditionscommunications, of constrained control charts. This serve to technological foundations, control charts. This could could serve that to control control thethe technological state ofunder foundations, communications, automation systems, and others that fall into the construction zone under conditions of constrained control charts. This could serve to control the technological state of foundations, communications, development. We proposed an algorithm constructing control zone chartsunder for monitoring from automation systems, and that into the conditions of automation systems, and others others that fall fallfor into the construction construction conditions deviations of constrained constrained development. We proposed an algorithm constructing control zone chartsunder for monitoring deviations from automation systems, others thatadjustment. fallfor into the zone under conditions of constrained design parameters thatand require timely In construction the analysis and construction of algorithms, we from have development. We proposed an algorithm for constructing control charts for monitoring deviations development. We proposed an algorithm for constructing control charts for monitoring deviations from design parameters that require timely adjustment. In the analysis and construction of algorithms, we have development. We proposed an algorithm for constructing control charts for monitoring deviations from taken into account features of the processes in construction, the main one being the change in the state of design parameters that require timely adjustment. In and of algorithms, we have design parameters that require timely adjustment. In the the analysis analysis and construction construction ofchange algorithms, we have taken into account features of the processes in construction, the main one being the in the state design parameters that require timely adjustment. In the analysis and construction of algorithms, we have the construction object at the stages of the life cycle. taken into into account account features features of of the the processes processes in in construction, construction, the the main main one one being being the the change change in in the the state state of of taken of the construction object at the stages of the life cycle. taken into account features ofstages the processes in cycle. construction, the main one being the change in the state of the construction object at the of the life the construction object at the stages of the life cycle. Β© 2019, IFAC (International of Automatic Hosting by Elsevier All rights reserved. Keywords: statistical monitoring of systems, control chartsLtd. of individual values, life the construction objectcontrol, at theFederation stages of the lifeengineering cycle.Control) Keywords: statistical control, monitoring of engineering systems, control charts of individual values, life cycle management of construction. Keywords: statistical control, monitoring of engineering systems, control charts of individual values, life life statistical control, monitoring of engineering systems, control charts of individual values, Keywords: cycle management of construction. Keywords: statistical control, monitoring of engineering systems, control charts of individual values, life cycle management of construction. cycle management of construction. cycle management of construction. A necessary condition for the implementation of monitoring 1. INTRODUCTION A necessary condition for the implementation of monitoring the location ofcondition technological objects is the presence of current 1. INTRODUCTION A for implementation of A necessary necessary for the the implementation of monitoring monitoring 1. INTRODUCTION the location ofcondition technological objects is the presence of current INTRODUCTION necessary condition forwhich the implementation ofasmonitoring estimates of their values, can be obtained a of The task of quality1. control of technological processes and A the location of technological objects is the presence ofresult current 1. INTRODUCTION the location technological objects is the presence current of of their values, which can be obtained as aof of The task of quality control of technological processes and estimates the location of technological objects is the presence ofresult current either direct measurements with a flow meter or assessing the engineering systems based on the current control using control estimates of their values, which can be obtained as a result of The task of quality control of technological processes and estimates of measurements their values, which be obtained as a resultthe of The task ofsystems quality based control and either direct with can a flow meter or assessing engineering on of thetechnological current controlprocesses using control estimates of measurements their values, which can be obtained as a methods resultthe of The task of quality control of technological processes and current values of qualitative indicators by statistical charts was present since the 60s of the last century [1]. Control either direct with a flow meter or assessing engineering systems based on the current control using control either direct measurements with a flow meter or assessing the engineering systems based on theofcurrent control using control current values of qualitative indicators by statistical methods charts was present since the 60s the last century [1]. Control either direct measurements with a flow meter or assessing the engineering systems based on the current control using control from measured values of other quantities with monitoring of charts are used to monitor ongoing processes by finding and current values values of of qualitative qualitative indicators indicators by by statistical statistical methods methods was present present since since the the 60s 60s of of the the last last century century [1]. [1]. Control Control from charts was current measured values of other quantities with monitoring of charts are used to monitor ongoing processes by finding and current values of qualitative indicators by statistical methods charts was present since the 60s of the last century [1]. Control the obtained estimates from rare laboratory measurements. correcting problems as they occur. They help determining the from measured values of other quantities with monitoring charts are are used used to to monitor monitor ongoing ongoing processes processes by by finding finding and and the measuredestimates values offrom otherrare quantities withmeasurements. monitoring of of charts obtained laboratory the from correcting problems as they occur. They help determining from measured valuesthe offrom other quantities withmeasurements. monitoring of charts arerange used to monitor ongoing processes by finding and The article [8] notes limitations of using control charts, expected of process results, to analyse the patterns of the obtained estimates rare laboratory correcting problems as they occur. They help determining the the obtained estimates from rare laboratory measurements. correcting problems as they occur. They help determining the article [8]estimates notes thefrom limitations of using measurements. control charts, expected range of process to analyse the patternsthe of The the obtained rare laboratory correcting problems aswell theyasresults, occur. They help determining which are explained by solving the problem of intra-laboratory process variation, as to identify specific problems of The article [8] notes the limitations of using control charts, expected range of process results, to analyse the patterns The article [8] notesbythe limitations of using control charts, expectedvariation, range of as process to analyse theproblems patterns of of which are explained solving the problem ofthe intra-laboratory process well asresults, to identify specific article [8]the notes the limitations of and using control charts, expected range of as process results, to analyse theproblems patterns of of The monitoring of accuracy of analyzers use of control the process in order towell make fundamental changes [2]. which are explained by solving the problem of intra-laboratory process variation, as to identify specific which are explained by solving the problem of intra-laboratory process variation, as well as to identify specific problems of monitoring of the accuracy of analyzers and the use of control the process in orderastowell make changesproblems [2]. are explained byindustries solving the problem ofthe intra-laboratory process variation, asfundamental to identify specific of which charts only in discrete due to the features prescribed, monitoring of the accuracy of analyzers and use of control the process in order to make fundamental changes [2]. monitoring of discrete the accuracy of analyzers and the useprescribed, of control the process in ordercontrol to makeisfundamental changes [2]. only in industries due to the features When statistical used to monitor quality in charts monitoring ofin the accuracy of analyzers and the use of control the process in ordercontrol to makeisfundamental changes [2]. for example, GOST R 50779.45-2002, GOST Rprescribed, 50779.42charts only in discrete industries due to the features When statistical used to monitor quality in for charts only in discrete industries due to the features prescribed, example, in GOST R 50779.45-2002, GOST R 50779.42construction, it collects statistics on production parameters or When statistical control is used to monitor quality in charts only in discrete industries due to the features prescribed, 99 (ISO 825891). for example, example, in in GOST GOST R R 50779.45-2002, 50779.45-2002, GOST GOST R R 50779.4250779.42When statistical control is used to monitor quality or in 99 construction, it collects statistics on production parameters 8258-in91). When control is used to monitor quality in for (ISO the statestatistical of engineering systems inon a special way,parameters which allows construction, it statistics production or example, GOST R 50779.45-2002, GOST R 50779.4299 (ISO 825891). construction, it collects collects systems statisticsin on production parameters or for the state of engineering a special way, which allows 99 (ISO 825891). construction, it collectsbased statistics on production parameters or The basis of the development of control charts lies in the making scientifically conclusions about their quality, the of systems in way, which allows 99 (ISO 825891).development the state state scientifically of engineering engineeringbased systems in aa special specialabout way, their whichquality, allows The basis of the of control charts lies in the making conclusions the state of engineering systems in a special way, which allows known distribution laws, meaning that you can build trends in the state of production systems and, ultimately, the The basis of the of charts lies in making scientifically scientifically based based conclusions conclusions about about their their quality, quality, known The basis of the development development of control control chartscan liesbuild in the theaa making distribution laws, meaning that you trends in the state of production systems and, ultimately, the The basis ofinterval the development of control charts lies in thea making scientifically based conclusions about theirthat quality, confidence for the expectation (ππ ) of the sample quality of products or services [3]. One should note such known distribution laws, meaning that you can build trends in the state of production systems and, ultimately, the ππ known distribution laws, that(ππyou can build a trends inofthe state of systems and, ultimately, the confidence interval for the meaning expectation quality products orproduction services [3]. One should note that such of the sample ππ ππ )) average distribution laws, meaning that you can build trends inofcan the state of production systems and, ultimately, the known average (π₯π₯Μ
) , and vice versa β for the sample of thea methods be used to control deviations from the standard confidence interval for the expectation (ππ of the sample quality products or services [3]. One should note that such ππ confidence interval for the expectation (ππ ) of the sample quality of products or services [3]. One should note that such ππ ),interval and vice β for the sample methods be used control[3]. deviations fromnote the that standard (π₯π₯Μ
of the confidence forversa the expectation (ππππ ) average of the sample quality ofcan products or to services One should such average indicators throughout the life cycle stage infrom the construction known expectation (1): (π₯π₯Μ
versa average methods be control deviations the average (π₯π₯Μ
)),, and and vice vice versa β β for for the the sample sample average of of the the methods can can be used used to to control deviations from the standard standard average (1): indicators throughout the life cycle stage in the construction known expectation averageexpectation (π₯π₯Μ
), and vice versa β for the sample average of the methods can be used to control deviations from the standard known industry. indicators throughout the life cycle stage in the construction (1): + β) indicators throughout the life cycle stage in the construction known expectation (1): industry. ππ(π₯π₯Μ
βexpectation πΏπΏ + < ππππ <(1): π₯π₯Μ
+ πΏπΏ β indicators throughout the life cycle stage in the construction known industry. ππ(π₯π₯Μ
β πΏπΏ + < π₯π₯Μ
+ πΏπΏ β industry. ππ β + < ππππ β) = ππ(βπΏπΏ π₯π₯Μ
< + β ππ(π₯π₯Μ
β πΏπΏ < ππ < + πΏπΏ industry. + β ππ 2. TASKS OF THE STATISTICAL ANALYSIS OF π₯π₯Μ
β) )) ππ(π₯π₯Μ
β +πΏπΏ ++ < ππ < + πΏπΏ = ππ(βπΏπΏ β π₯π₯Μ
< β ππ (1) < ππ πΏπΏ ππππ< > β) ππ 2. TASKS OF THE STATISTICAL ANALYSIS OF ππ(π₯π₯Μ
β +πΏπΏ + < ππ π₯π₯Μ
< + πΏπΏ ππ(πΏπΏ > π₯π₯Μ
β βπΏπΏ ππ + β = ππ(βπΏπΏ < ππ β π₯π₯Μ
πΏπΏ ππ (1) β ππ ENGINEERING SYSTEMS ++ β) )) β = ππ(βπΏπΏ < ππ β π₯π₯Μ
< πΏπΏ 2. TASKS OF THE STATISTICAL ANALYSIS OF > π₯π₯Μ
β ππ > βπΏπΏ ππ(πΏπΏ β ππ = + 2. TASKS OF THE STATISTICAL ANALYSIS OF ππ (1) + β ππ ) ENGINEERING SYSTEMS = ππ(βπΏπΏ < ππ β π₯π₯Μ
< πΏπΏ ) = πΎπΎ. ππ(ππ + π₯π₯Μ
πΏπΏ + < ππ β)) πΏπΏ β (1) πππππ₯π₯Μ
= β > ππ > 2. TASKS OF THE STATISTICAL ANALYSIS OF = ππ(πΏπΏ ENGINEERING SYSTEMS ππ(πΏπΏ + > β> > βπΏπΏ βπΏπΏππππ β (1) = ππ(ππ + π₯π₯Μ
πΏπΏ + >ππ π₯π₯Μ
ππππ < ππ πΏπΏ β = πΎπΎ. +ππ ββ ENGINEERING SYSTEMS ) ππ > + β ππ ) = ππ(πΏπΏ π₯π₯Μ
β ππ > βπΏπΏ Statistical evaluation of errors in the implementation of control ππ < ππππ β πΏπΏ β ) + > π₯π₯Μ
= ππ(ππ + πΏπΏ = πΎπΎ. ENGINEERING SYSTEMS ππ ) = ππ(ππ + πΏπΏ > π₯π₯Μ
< ππ β πΏπΏ = πΎπΎ. Statistical evaluation of errors in the implementation of control The + β ππ ππ expected value of the monitored parameter of the ) = πΎπΎ. = ππ(ππ > π₯π₯Μ
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can note a violation of the specified requirements to the technological process. In the case of an unknown distribution law, we use Chebyshev's inequality [9], further investigating the process and preliminary estimating the value of the variance. Methods for its assessment are based on the theory of point estimates [10]. The control chart shows the changes in the monitored parameter, taking into account the previously applied control limits (tolerance limits) in accordance with the limits of the confidence interval. In this case, the control consists in plotting statistical data on the chart and making a decision on intervention in the technological process. The process is considered to be statistically controlled, as long as the analyzed values lie within the control limits. When the controlled value goes beyond these limits, the operation of the engineering system should be suspended for reconfiguration or changeover of equipment. Preparatory work requires, in order to determine the tolerance limits, not only the knowledge ππ, but also the sample sizes for Ni control, and the confidence level Ξ³ (or the level of significance β the error probability Ξ± = 1 β Ξ³). If the hypothesis of any particular distribution law is used, then it must be verified using the Pearson Ο2 test. For the volumes of control samples, Ni is always assigned the same small odd number N (5 or 7), which will simplify calculations of the mean and determination of the median and range. In practice, βconvenientβ for the applicable law of the distribution of the number is accepted as a confidence probability: for a normal law: 0.9973 (from rule 3 ππ), 0.99 or 0.95, for Chebyshev's inequality 0.89 (from rule 3 ππ).
the connections between them, as well as the interaction of technological objects in the context of changing external factors. The mathematical description of the process of changing of the technical state of an engineering system consisting of a large number of structural elements, having a certain technological purpose, presents considerable difficulties. This is due to the fact that it is impossible to track all the essential parameters, and the process of changing of the performance of technical devices is characterized by uncertainty and randomness. Strictly following the control chart technology allows us to provide an acceptable level of current control, this type of statistical analysis can be attributed to high-tech and promising, due to the development, in particular, of methods of video monitoring of the position of objects, various types of pattern recognition, etc. This paper presents an example of using control charts for statistical analysis of the state of the engineering system in the area of travel of a bridge crane. Geodetic survey of engineering systems at the site of assembly and welding of a bridge crane rail was performed with a Sokkia FX-105 total station, with a verification certificate corresponding to the measurement period. During the survey, the magnitude of the ingress (in meters) of the engineering system (communications, foundation, etc.) was recorded in the crane travel zone. The results of the executive survey are partially shown in Figure 1.
In practice, a number of control charts are used for measurable and non-measurable features. Use the average chart π₯π₯Μ
; the chart of individual values xi β when the sample size is N = 1, the decision is made after going beyond 4 β 6 consecutive values; median chart π₯π₯Μ β based on an approximately normal distribution of the median; chart π₯π₯Μ
/π π β a combination of charts: for x and for s, which has control boundaries (2) 0 < s < (1 + 1
π’π’β ππ2β
β1 β ππ2β ) π π Μ
,
(2)
where π π Μ
= βππππ=1 π π ππ ; a chart π₯π₯Μ
/π
π
that is a combination of two ππ charts, a p chart β an average defect rate with control borders (3) ππ(1βππ)
ππ β π’π’πΌπΌ β
ππ
<
π₯π₯
ππ
< ππ + π’π’πΌπΌ β
ππ(1βππ) ππ
,
(3)
N is large enough, Np chart is a modification of p chart, a chart is c defects, failures distributed according to Poissonβs law, with control borders (4) c β uπΌπΌ βππ < π₯π₯ < c + uπΌπΌ βππ,
(4)
where c is the distribution parameter Poisson, chart u β generalization of chart c to the percentage of defects, failures. 3. EVALUATION OF ENGINEERING SYSTEMS The technical condition of engineering systems as a whole is a function of the performance of individual structural elements,
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Fig. 1. Executive survey of engineering systems.
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It is believed that the process goes out of control if the deviation value is beyond the control limits. We first build a chart (Fig. 3). Since all points are within control limits, there is a statistically controlled state and one can build a chart. On the chart, a single point (number 28) exceeds the upper control limit. This point must be analyzed for non-random reasons and, if confirmed, all points affected by these reasons should be excluded and the mean and the boundaries of the chart should be recalculated. This algorithm must be repeated until a statistically controlled state is reached.
Fig. 2. A fragment of the source data table. The data of the executive survey is summarized in the table in fig. 2 shows a part of this table. In this example, only one observation was obtained at each survey point; therefore, we use control charts of individual values.
The usage of control charts of individual values provides statistical control of the processes at the stages of the life cycle of construction. The proposed approaches and algorithms allow to identify changes in the parameters of processes and to make their adjustment in the case of fixing certain changes. Processes are maintained at a level that ensures that they meet certain requirements.
The control limits are calculated using the measure of variation, which is derived from sliding spans for two adjacent observations. Under the sliding dimension we mean the absolute value of the difference in measurements in successive pairs, i.e. the difference between the first and second measurement, then the second and third, etc. Based on the sliding span, the average sliding span π
π
is calculated, which is used to build control charts. Also, the total average ππΜΏ is calculated for all data. Central line for the middle ππΜΏ. Central line for swing: π
π
. The boundaries of regulation for the average: ππΜΏ Β± πΈπΈ2 π
π
. Lower π·π·3 π
π
and upper π·π·4 π
π
boundaries of regulation for scope πΈπΈ2 = 3βππ2 . The values of the constants for the calculation of the boundaries: π·π·3 = 0 (since ππ < 2), π·π·4 = 3,267, ππ2 = 1,128, [11].
In Fig. 3, a chart of individual values is shown ππ, a chart of individual values, and in Fig. 4 β a chart of sliding span π
π
.
Fig. 4. Sliding Chart. The technology of control charts is applicable, including on condition of a minimum of output parameters determining the state of engineering systems and consumer properties of products [12]. Control charts allow, from an economic point of view, to optimally control and control complex engineering systems. It should be particularly noted that all mathematically rigorous results in each specific case can be communicated to algorithms suitable for practical use [13, 14]. 4. CONCLUSIONS The conducted studies allow us to propose a statistical method for monitoring the state of engineering systems, which can be used along with the development of methods for monitoring and controlling random processes [15], the main purpose of which is to provide economical maintenance as per condition. Fig. 3. Chart of individual values ππ.
The proposed methods along with the process improvement strategy allow monitoring of engineering systems in order to determine the technical conditions and residual resource. At
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the same time, appropriate measures are taken at the stage of the life cycle even before the discovery of defects and damages, the occurrence of emergency situations and before the expiration of the survey period or the standard operation period. The complexities of the construction projects being erected give rise to tasks related to ensuring safe life in the conditions of a megalopolis, which is determined by the reliability of the buildings under construction, the influence of the construction objects on the already existing infrastructure, taking into account the changing operating conditions. Modern trends in construction, for example, the compaction of urban buildings, constrained construction sites, the saturation of utilities lead to the emergence and subsequent increase in the negative anthropogenic impact of construction on already constructed facilities located in adjacent areas. Of particular importance is the problem of monitoring of the technical condition of the engineering infrastructure in order to prevent the occurrence of emergency situations and the validity of the choice of a complex of engineering measures to prevent them. At the same time, the monitoring of engineering systems must be systematic and allow for the assessment of changes taking place on the basis of quantitative criteria. REFERENCES 1 Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke Jr. A Chronicle of Permutation Statistical Methods. Springer International Publishing, 2014. β 517 p. 2 Control Chart Rules and Interpretation. Dr. Bill McNeese. BPI CONSULTING, LLC. 2016. 3 GOST R 22.1.12-2005 Safety in emergency situations. Structured system of monitoring and management of engineering systems of buildings and structures. 4 Bray, J. H., and Maxwell, S. E. (1985). Multivariate analysis of variance, Sage, Newbury Park, CA. 5 Abdelgawad, M., and Fayek, A. (2012). Comprehensive hybrid framework for risk analysis in the construction industry using combined failure mode and effect analysis, fault trees, event trees, and fuzzy logic. J. Constr. Eng. Manage., P. 642β651. 6 Bahn, S. (2013). Workplace hazard identification and management: The case of an underground mining operation. Saf. Sci., 57(1), P. 129β137. 7 Rozenfeld, O., Sacks, R., Rosenfeld, Y., and Baum, H. (2010). Construction job safety analysis. Saf. Sci., 48(4), P. 491β498. 8 E.A. Grebenyuk. Application of methods of statistical analysis in the quality control system of products for the production of technological type. / Proceedings of the XII all-Russian meeting on management (VSPU-2014, Moscow). β M.: IPU Russian Academy of Sciences, 2014. P. 4915-4926. 9 Boards B.Ya., Yakovlev S.Ya. Modeling Systems: A textbook for universities. β M.: "High School", 1998. β 320 p. 10 Storm R. Theory of Probability. Mathematical statistics. Statistical quality control. β M.: Mir, 1970. β 368 p.
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11 GOST R 50779.42-99, Statistical methods. Shewhart control charts. 12 Ramesh Marasini, Nashwan Dawood. Innovative Managerial Control System (IMCS): An Application to the Precast Concrete Building Products Industry. Fraunhofer-Informationszentrum Raum und Bau IRB. 13 Barzilovich E.Yu. Optimally controlled random processes and their applications (theoretical basis for the operation of aircraft systems as they are). β Yegorievsk: EATK GA, 1996. β 299 p. 14 Variance sensitive adaptive threshold-based PCA method for fault detection with experimental application. Alkan Alkaya, Δ°lyas Eker, ISA Transactions 50 (2011). P. 287β 302. 15 GOST R 50779.45-2002, Statistical methods. Cumulative control charts. The main provisions.