طراحی آماری اقتصادی بهینه‌ی نمودارهای کنترلی وصفی سازوار کامل برای پایش عدم انطباق‌ها

نوع مقاله: مقاله پژوهشی

نویسندگان

1 کارشناس ارشد ، دانشگاه علامه طباطبایی، گروه آمار،تهران، ایران

2 استاد، گروه آمار، دانشگاه علامه طباطبائی، تهران، ایران

چکیده

نمودار کنترلی c به طور گسترده برای پایش فرایندهایی که در آن‌ها کیفیت هر قلم تولیدی توسط تعداد عدم انطباق‌های موجود در آن مشخص می‌شود به کار می‌رود. تحقیق‌های اخیر مزایای به کارگیری طرح‌های سازوار به جای طرح‌های ایستا در هنگام پایش چنین فرایندهایی را تایید کرده است. در این مقاله، ما یک طرح سازوار کامل برای نمودارهای کنترلی c ارائه می‌دهیم که در آن همه‌ی پارامترهای طراحی (اندازه نمونه، بازه نمونه‌گیری، حد کنترلی) بر مبنای جدیدترین اطلاعات حاصل از فرایند بین دو مقدار تغییر می‌کنند. طرح پیشنهادی با استفاده از رویکرد آماری اقتصادی مدل‌بندی می‌گردد. مدل هزینه با به کار گیری رویکرد زنجیر مارکوف پایه‌ریزی می‌شود. ما با استفاده از مثال‌های عددی عملکرد مدل‌های پیشنهادی را مورد بررسی قرار داده و کارایی آن‌ها را با طرح‌های دیگر مقایسه می‌کنیم. همچنین با استفاده از روش‌های طراحی آزمایش‌ها و تحلیل رگرسیونی یک تحلیل حساسیت نیز به منظور بررسی اثرات پارامترهای مدل بر روی جواب های بهینه‌ی طراحی آماری اقتصادی انجام می‌شود.

کلیدواژه‌ها


 [1] Reynolds, MR J. r., Amin, R. W., Arnold J. C. and Nachlas J. A. (1988).  Charts with variable sampling    intervals, Technometrics, 30:181-192
[2] Reynolds MR J. r. and Arnold J. C. (1989). Optimal Shewhart control charts with variable sampling intervals between samples, Sequential Analysis, 8:51-77.
[3] Reynolds MR J. r. (1995). Evaluating properties of variable sampling interval control charts, Sequential Analysis, 14:59-97.
[4] Reynolds MR J. r. (1989). Optimal variable       sampling interval control charts, Sequential       Analysis,8:361-379
[5] Runger G. C. and Montgomery D. C. (1993). Adaptive sampling enhancements for Shewhart control charts, IIE Transactions, 25:41-51.
[6] Daudin J. J. (1992). Double sampling  charts, Journal of Quality Technology, 24:78-87.
[7] Prabhu, S. S., Runger G. C. and Keats J. B. (1993).  chart with adaptive sample sizes, International Journal of Production Research, 31:2895-2909.
[8] Costa, A. F. B. (1994).  charts with variable  sampling size, Journal of Quality Technology,
pp, 155-163.
[9] Zimmer, L. S., Montgomery D. C. and Runger G. C. (1998). Evaluation of a three-state adaptive sample size  control chart, International Journal of Production Research, 36:733-743.
[10] Prabhu, S. S., Montgomery D. C. and Runger G. C. (1994). A combined adaptive sample size and sampling interval  control scheme, Journal of Quality Technology, 26:164-176.
[11] Costa, A. F. B. (1997).  charts with variable sample size and sampling intervals, Journal of Quality Technology, 29:197-204.
[12] Reynolds MR J. r. and Arnold J. C. (2001). EWMA control charts with variable sample sizes and variable sampling intervals, IIE Transactions, 33:511-530.
[13] Wu, Z., Zhang S. and Wang P. H. (2007). A CUSUM scheme with variable sample sizes and sampling intervals for monitoring the process mean and variance, Quality and Reliability Engineering International, 23:157–170.
[14] Mahadik S. B. (2013). Variable sample size and sampling interval  charts with runs rules for switching between sample sizes and sampling interval lengths, Quality and Reliability Engineering International, 29(1):63-76.
[15] Mahadik S. B. (2013).  Charts with Variable Sample Size, Sampling Interval, and Warning Limits, Quality Reliability Engineering International, 29(4):535-544.
[16] Costa A. F. B. (1999).  charts with variable parameters. Journal of Quality Technology,
 31:408-416.
[17] De Magalhaes, M. S., Epprecht E. K. and Costa A. F. B. (2001). Economic design of a VP  control chart, International Journal of Production Economics, 74:191–200.
[18] Chen Y. K. (2007). Adaptive sampling enhancement of Hotelling’s T2 control charts. European Journal of Operational Research
 178:841-857.
[19] Lin Y. C. (2009). The Variable Parameters  Control Charts for Monitoring Auto-correlated Processes, Communications in Statistics - Simulation and Computation 38:729-749.
[20] Faraz, A., Heuchenne, C., Saniga E. and Costa A. F. B. (2014). Double-objective economic statistical design of the VP T2 control chart: Wald's identity approach, Journal of
Statistical Computation and Simulation,
 84(10):2123-2137.
[21] Duncan A. J. (1956). The economic design of  charts used to maintain current control of a process, Journal of American Statistical Association, 51:228-242.
[22] Goel, A. L., Jain S. D. and Wu S. M. (1968). An algorithm for the determination of the design of  charts based on Duncan’s model, Journal of the American Statistical Association, 63, pp, 304-320.
[23] Knappenberger H. A. and Grandage A. H. (1969). Minimum cost quality control tests, IIE Transactions 1:24–32.
[24] Gibra I. N. (1971). Economically optimal determination of the parameters of an  control chart, Management Science, 17:635–646.
[25] Montgomery D. C. (1980). The economic design of control charts: a review and literature survey, Journal of Quality Technology, 12:75-87.
[26] Lorenzen T. J. and Vance L. C. 1986. “The economic design of control charts: A unified approach.” Technometrics 28:3-11.
[27] Costa A. F. B. and Rahim M. A. (2001). Economic design of X charts with variable parameters: The Markov chain approach, Journal of Applied statistics, 28:875–885.
[28] Saniga E. M. (1989). Economic statistical control chart designs with an application to  and R charts, Technometrics, 31:313-320.
[29] McWilliams T. P. (1994). Economic, statistical, and economic-statistical  chart designs, Journal of Quality Technology, 26:227-238.
[30] Montgomery, D. C., Torng, J. C. C., Cochran J. K. and Lawrence F. P. (1995). Statistically Constrained Economic Design of the EWMA Control Chart, Journal of Quality Technology, 27:250–256.
[31] Molnau, W., Montgomery D. C. and Runger G. (2001). statistically constrained economic design of the MEWMA control chart. Quality and Reliability Engineering International, 17:39–49.
[32] Heydari A.A., Bameni Moghadam M. and 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,DOI:10.1080/03610926.2016.1140782
[33] Rafiey S.R., Ghaderi M.M., and Bameni Moghadam M. (2016), A Generalized Version of Banerjee and Rahim Model In Economic and Economic Statistical Designs of Multivariate Control Charts under Generalized Exponential Shock Model, Communications in Statistics - Theory and Methods. DOI:10.1080/03610926.2016.1171354
[34] Katebi, M., Seif A. and Faraz A. (2016). Economic and Economic-Statistical designs of the T2 control charts with SVSSI samplingscheme. Communications in Statistics - Theory and Methods. 46 (20):10149-10165, DOI:10.1080/03610926.2016.1231823.
[35] Calabrese J. M. (1995). Bayesian process control for attributes. Management Science 41:637–645.
[36] Vaughan T. S. (1993). Variable sampling interval np process control chart, Communication in Statistics-Theory and Methods, 22(1):147–167.
[37] Porteus E. L. and Angelus A. (1997). Opportunities for improved statistical process control, Management Science, 43:1214–1228.
[38] Epprecht E. K. and Costa A. F. B. (2001). Adaptive sample size control charts for attributes, Quality Engineering, 13(3):465–473.
[39] Luo H. and Wu Z. (2002). Optimal np control charts with variable sample sizes or variable sampling intervals, Economic Quality Control,
 17(1):39–61.
[40] Wu Z. and Luo H. (2004). Optimal design of the adaptive sample size and sampling interval np control chart, Quality and Reliability Engineering International, 20:553-570.
[41] Epprecht, E. K., Costa A. F. B. and Mendes F. C. T. (2003). Adaptive control charts for attributes, IIE Transactions, 35(6):567–582.
[42] Epprecht, E. K., Simões B. F. T. and Mendes F. C. T. (2010). A variable sampling interval EWMA chart for attributes, International Journal of Advanced Manufactured Technology,
 49:281–292.
[43] Chiu W. K. (1975). Economic Design of Attribute Control Charts. Technometrics,
 17:81–87.
[44] Duncan, A. J. (1978). The Economic Design of p Charts to Maintain Current Control of a Process: Some Numerical Results, Technometrics, 20:235–243.
[45] Saniga, E. M., Davis, D. J. and McWilliams T. P. (1995). Economic, statistical, and economic-statistical design of attribute charts, Journal of Quality Technology, 27:56-73
[46] Kooli I. and Limam M. (2011). Economic design of an attribute np control chart using a variable sample size, Sequential Analysis, 30:145–159. DOI: 10.1080/07474946.2011.563703.
[47] Katebi, M., Pourtaheri R. and Moghadam M. B. (2016). Economic and economic statistical designs for three-level control charts, Journal of Statistical Computation and Simulation,
 86:1463-1478.
[48] Brook, D., Evans D. A. (1972). An approach to the probability distribution of CUSUM run length, Biometrika 59:539–549.
[49] Mahadik S. B. and Shirke D. T. (2009). A special variable sample size and sampling interval X chart, Communications in Statistics-Theory and Methods, 38:1284–1299.
[50] Niaki, S. T. A., Ershadi M. J. and Malaki M. (2010). Economic and economic statistical designs of MEWMA control charts-a hybrid Taguchi loss, Markov chain and genetic algorithm approach, International journal of advanced manufactured technology,
 48:283-296.
[51] Chen Y. K. (2009). Economic design of T2 control charts with the VSSI sampling scheme, Quality and Quantity 43:109-122.