Journal of Quality Engineering and Management

Statistical-economic design of X ̅ control diagram for correlated data under generalized shock and Weibull models

Document Type : Original Article

Authors

Saeedreza Rafiee
Mohammad Bamenimoghadam

Department of Statistics, Faculty of Mathematical and Computer Sciences, Allameh Tabatabai University

Abstract
One of the most important tools for statistical process control is the control chart. The construction of control diagrams is achieved by determining the design parameters of the sample size, sampling distance and coefficient of control limits. Statistical-economic design is the best way to determine these parameters by considering statistical properties and cost. Statistical design - Economics Control charts require a distribution for the process failure mechanism. The most popular distributions in the analysis of the failure mechanism of the exponential distribution process are gamma and Weibull. Recently, a new distribution called generalized exponential distribution has been added to conventional distributions in data life analysis and process failure mechanisms. If the failure mechanism data follows this distribution, the use of other distributions will give users misleading and inaccurate results. On the other hand, a fundamental assumption in most control charts is the independence of process-related observations; But in practice we have situations with correlated data. As a result, it is of particular importance to identify control charts that can be used to control such data.In this paper, statistical-economic design of control charts with correlated data under generalized shockwave and Weibull models and by providing a numerical example , We show their application. We have applied a sensitivity analysis to investigate the effect of changing the controlled properties of the first type error rate, power and correlation coefficient. The results show that this type of control charts have undesirable statistical properties and the limitation on the first type of error has a significant effect on determining the average cost per unit time and design parameters. Also, the correlation coefficient is indirectly related to the sample size and sampling distance and is directly related to the average cost per unit time.

Keywords

Statistical-economic design
Generalized shock model
Weibull shock model
Correlated data
[1] Shewhart, W. A. (1931). Economic control of quality of manufactured product. ASQ Quality Press.
[2] Girshick, M. A., & Rubin, H. (1952). A Bayes approach to a quality control model. The Annals of mathematical statistics, 114-125.
[3] Duncan, A. J. (1956). The economic design of  charts used to maintain current control of a process. Journal of the American Statistical Association,51(274), 228-242.
[4] Saniga, E. M. (1989). Economic statistical control-chart designs with an application to  and R charts. Technometrics, 31(3), 313-320.
[5] Banerjee, P. K., & Rahim, M. A. (1987). The economic design of control charts: a renewal theory approach. Engineering Optimization+ A35, 12(1), 63-73.
[6] Banerjee, P. K., & Rahim, M. A. (1988). Economic Design of –Control Charts Under Weibull Shock Models. Technometrics, 30(4), 407-414.
[7] Zhang, G., & Berardi, V. (1997). Economic statistical design of  control charts for systems with Weibull in-control times. Computers & industrial engineering, 32(3), 575-586.
[8] Al-Oraini, H. A., & Rahim, M. A. (2002). Economic statistical design of  control charts for systems with Gamma (λ,2) in-control times. Computers & industrial engineering, 43(3), 645-654.
[9] Gupta, R. D., & Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics,41(2), 173-188.
[10] Aghabeig, D., & Moghadam, M. B. (2014). Economic design of -control charts under generalized exponential shock models with uniform sampling intervals. European Online Journal of Natural and Social Sciences, 2(3 (s)), pp-1540.
[11] رفیعی، سعیدرضا، آهنی، نازنین، نادری، محمدحسین و بامنی‌مقدم، محمد (1394). طراحی آماری- اقتصادی نمودار کنترلی   تحت مدل شوک نمایی تعمیم‌یافته، نشریه مهندسی و مدیریت کیفیت، زمستان، جلد 5، شماره 4.
[12] Heydari, A. A., Moghadam, M. B. & Eskandari, F. (2016). An extension of Banerjee and Rahim model in economic and economic statistical designs for multivariate quality characteristics under Burr XII distribution, Communications in Statistics - Theory and Methods, 46:16, 7855-7871.
[13] Heydari, A. A., Moghadam, M. B. & Eskandari, F. (2017). Economic statistical design of the T2 control chart under the Weibull shock model with multiple assignable causes, Journal of Statistical Computation and Simulation, 88:1, 1-27.
[14] Neuhardt, J.B. (1987). Effects of correlated sub-samples in statistical process control. IIE Transactions, Vol.19,No, 2, pp208–214.
[15] Yang, K., Hancock, W.M. (1990) Statistical quality control for correlated samples. International Journal of Production Research, Vol.28, No, 3, pp595–608.
[16] Chou, C.Y., Chen, C.H., Liu, H.R. (2001) Economic design of X charts for non-normally data. International Journal of Production Research, Vol.39, No.9, pp1931-1941.
[17] Liu, H.R., Chou, C.Y., Chen, C.H. (2002). Minimum-loss design of X-bar charts for correlated data. Journal of Loss Prevention in the Process Industries, Vol.15, pp 405–411.
[18] Chen, F. L., & Yeh, L. L. (2010, July). Economic statistical design of x-bar control charts for correlated data and Gamma failure mechanism with genetic algorithm. In Computers and Industrial Engineering (CIE), 2010 40th International Conference on (pp. 1-6). IEEE.
Journal of Quality Engineering and Management
Volume 7, Issue 3
Autumn 2017
Pages 200-207

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