پایش فرآیندهای پواسن صفرآماسیده به کمک نمودار کنترل جمع تجمعی مبتنی بر مدل

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی صنایع، دانشکده فنی و مهندسی، دانشگاه آزاد اسلامی واحد تهران شمال.

2 گروه مهندسی صنایع، دانشگاه آزاد اسلامی واحد تهران شمال.

3 دانشکده مهندسی صنایع، دانشگاه صنعتی خواجه نصیرالدین طوسی

چکیده

در این مقاله سه رویکرد به منظور پایش فرآیندهای مبتنی بر توزیع پواسن صفرآماسیده ارائه شده‌است. رویکرد اول بر مبنای توزیع پواسن صفر آماسیده کلاسیک موجود در ادبیات، رویکرد دوم بر مبنای مدل رگرسیونی مخاطره متناسب با هدف تاثیر حضور متغیرهای قابل اندازه‌گیری و رویکرد سوم به منظور لحاظ کردن هم‌زمان تاثیر متغیرهای قابل اندازه‌گیری و متغیرهای غیر قابل اندازه‌گیری با تلفیق مدل رگرسیونی مخاطره متناسب و مدل شکنندگی، می‌باشد. رویکرد های دوم و سوم مبتنی بر مدل مخاطره متناسب و مدل تلفیقی از مهم‌ترین نوآوری‌های مقاله‌ی حاضر می‌باشد که تاکنون به آن پرداخته نشده‌است. عملکرد نمودارهای کنترل با اعمال شیفت به طور جداگانه و هم‌-زمان در دو پارامتر توزیع پواسن صفرآماسیده بررسی شده‌است. مطالعات شبیه‌سازی، دلالت بر برتری نمودار کنترل جمع تجمعی با لحاظ کردن هم‌زمان تاثیر متغیرهای قابل اندازه‌گیری و غیرقابل اندازه‌گیری دارد. همچنین، عملکرد نمودارهای کنترل پیشنهادی در یک مطالعه موردی در کارخانه چاپ لیبل بررسی شده‌است.

کلیدواژه‌ها

عنوان مقاله [English]

Monitoring Zero-inflated Poisson Processes based on Model-based Cumulative Sum(CUSUM)

نویسندگان [English]

  • Elham Keyvani 1
  • Shervin Asadzadeh 2
  • Yaser Samimi 3
1 Department of Industrial Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran
2 Department of Industrial Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran
3 Department of Industrial Engineering, K. N. Toosi University of Technology
چکیده [English]

In this article, three monitoring approaches using cumulative sum (CUSUM) control charts in phase two for zero inflated poisson-based processes are presented. The first approach is based on the zero inflated poisson distribution, the second on, a proportional hazard regression model, and the third integrates a proportional hazard (PH) regression model and a frailty model to consider both measurable and unmeasurable covariates. The performance of all three control charts was evaluated separately and simultaneously by applying shifts to both parameters of the zero inflated poisson distribution. Extensive simulation studies were conducted to evaluate the performance of these monitoring methods in terms of the average run length (ARL) of the control charts. The proposed cumulative sum control chart with simultaneous consideration of measurable and unmeasurable variables showed superior performance. Finally, a real case study in a label printing factory has been provided to show the effectiveness of the proposed control chart.

کلیدواژه‌ها [English]

  • Zero inflated Poisson distribution
  • Frailty regression model
  • Proportional hazard regression model
  • Cumulative sum control chart
  • Influential variables

مراجع

Mahmood, T., and Xie, M. (2019). Models and monitoring of zero-inflated processes: The past and current trends. Quality and Reliability Engineering International, 35(8), 2540-2557.
Xie, Y., Xie, M., and Goh, T. N. (2011). Two MEWMA charts for Gumbel's bivariate exponential distribution. Journal of Quality Technology, 43(1), 50-65.
Steiner, S. H., and MacKay, R. J. (2004). Effective monitoring of processes with part per million defective: A hard problem. In Frontiers in Statistical Quality Control 7, 140-149.
Keshavarz, M., and Asadzadeh, S. (2021). Phase II monitoring of survival times with categorical covariates. Quality and Reliability Engineering International, 37(2), 451-463.
Wen, H., Liu, L., and Yan, X. (2021). Regression-adjusted Poisson EWMA control chart. Quality and Reliability Engineering International, 37(5), 1956-1964.
Borror, C. M., Champ, C. W., and Rigdon, S. E. (1998). Poisson EWMA control charts. Journal of Quality Technology, 30(4), 352-361.
Jiang, W., Shu, L., and Tsui, K. L. (2011). Weighted CUSUM control charts for monitoring Poisson processes with varying sample sizes. Journal of Quality Technology, 43(4), 346-362.
Katemee, N., and Mayureesawan, T. (2012). Control charts for zero-inflated Poisson models. Applied Mathematical Sciences, 6(26), 2791-2803.
Fatahi, A. A., Noorossana, R., Dokouhaki, P., and Moghaddam, B. F. (2012). Zero inflated Poisson EWMA control chart for monitoring rare health-related events. Journal of Mechanics in Medicine and Biology, 12(4), 1250065.
Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34(1), 1-14.
Xie, M., & Goh, T. N. (1993). SPC of a near zero-defect process subject to random shocks. Quality and Reliability Engineering International, 9(2), 89-93.
Hu, Q., and Liu, L. (2021). Weighted score test based EWMA control charts for zero-inflated Poisson models. Computers & Industrial Engineering, 152.
Steiner, S. H., Cook, R. J., Farewell, V. T., and Treasure, T. (2000). Monitoring surgical performance using risk-adjusted cumulative sum charts. Biostatistics, 1(4), 441-452.
Yue, J., Lai, X., Liu, L., and Lai, P. B. (2017). A new VLAD-based control chart for detecting surgical outcomes. Statistics in Medicine, 36(28), 4540-4547.
Liu, L., Lai, X., Zhang, J., and Tsung, F. (2018). Online profile monitoring for surgical outcomes using a weighted score test. Journal of Quality Technology, 50(1), 88-97.
Megahed, F. M., Kensler, J. L., Bedair, K., and Woodall, W. H. (2011). A note on the ARL of two-sided Bernoulli-based CUSUM control charts. Journal of Quality Technology, 43(1), 43-49
Mahmood, T. (2020). Generalized linear model based monitoring methods for high-yield processes. Quality and Reliability Engineering International, 36(5), 1570-1591.
He, S., Huang, W., and Woodall, W. (2012). CUSUM charts for monitoring a zero-inflated Poisson process. Quality and Reliability Engineering International, 28(2), 181-192.
Mahmood, T., Balakrishnan, N., and Xie, M. (2021). The generalized linear model-based exponentially weighted moving average and cumulative sum charts for the monitoring of high-quality processes. Applied Stochastic Models in Business and Industry, 37(4), 703-724.
Tan, Y., Lai, X., Wang, J., Zhang, X., Zhu, X., Chong, K. Chan, PKS. & Tang, J. (2021). Risk-adjusted zero-inflated Poisson CUSUM charts for monitoring influenza surveillance data. BMC Medical Informatics and Decision Making, (21)2, 1-11.
Lai, X., Liu, R., Liu, L., Wang, J., Zhang, X., Zhu, X., & Chong, K. C. (2022). Residuals based EWMA control charts with risk adjustments for zero‐inflated Poisson models. Quality and Reliability Engineering International, 38(1), 283-303.
Lai, X., Lian, X., Jiyayin, W., and Chong, K. (2022). Generalized likelihood ratio based risk-adjusted control chart for zero-inflated Poisson process. Quality and Reliability Engineering International, 39(1), 363-381.
Asadzadeh, S., Aghaie, A., and Shahriari, H. (2014). Using frailty models to account for heterogeneity in multistage manufacturing and service processes. Quality & Quantity, 48, 593-604.
Wienke, A. (2011). Frailty Models in Survival Analysis. Boca Raton, FL: Taylor and Francis Group.
Asadzadeh, Sh., Torabi, A. (2018). Development of CUSUM and DEWMA control charts based on generalized linear regression models for monitoring cascade processes. Journal of Quality Engineering and Management, 7(2), 82-93 (In Persian).
نشریه علمی پژوهشی مهندسی و مدیریت کیفیت
دوره 12، شماره 4
اسفند 1401
صفحه 439-460

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