طراحی آماری- اقتصادی نمودار کنترل بیزی مبتنی بر توزیع پیشگو برای مشاهدات انفرادی با توزیع مشخصه‌ی کیفی نمایی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه آزاد اسلامی واحد علوم و تحقیقات تهران، گروه آمار ، تهران، ایران

2 استادیار، دانشگاه آزاد اسلامی واحد قزوین، گروه ریاضی، قزوین، ایران

3 دانشگاه بوعلی سینا، دانشکده ی علوم پایه، گروه آمار، همدان، ایران

چکیده

در این مقاله، طراحی آماری- اقتصادی نمودار کنترل بیزی مبتنی بر توزیع پیشگو برای مشاهدات انفرادی از توزیع مشخصه‌ی کیفی نمایی ارائه شده است. در انجام این کار، دو نوع توزیع پیشین مزدوج و توزیع جفریز در نظر گرفته شده و بر اساس توزیع مشاهدات در فاز اول، توزیع پیشگو تعیین شده است. سپس با استفاده از مدل اقتصادی لورنزن و وانس، یک طرح آماری- اقتصادی برای داده‌ها به‌دست‌ آمده است. پارامترهای طراحی بهینه (فاصله‌ی نمونه‌گیری، اندازه‌ی نمونه و حدود کنترل) با استفاده از الگوریتم ژنتیک تعیین شده و تجزیه و تحلیل حساسیت برای مقادیر مختلف پارامترهای مدل انجام گرفته است. نتایج این رویکرد با نتایج مدل کلاسیک مقایسه شده است. بر اساس نتایج، این روش نسبت به روش کلاسیک مؤثرتر است

کلیدواژه‌ها

عنوان مقاله [English]

Economic-statistical design of Bayesian control chart based on the predictive distribution for individual observations with an exponential qualitative characteristic distribution

نویسندگان [English]

  • Razieh Seirani 1
  • Mohsen Torabian 2
  • Mohammad Hassan Behzad 1
  • Asghar Seif 3
1 Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3 Department of statistics, Bu-Ali Sina University, Hamedan, Iran
چکیده [English]

In this article with title "Economic-statistical design of Bayesian control chart based on the predictive distribution for individual observations with an exponential qualitative characteristic distribution" the economic-statistical design of the Bayesian control chart based on the predictive distribution for individual observations of the exponential qualitative characteristic distribution is presented. In doing this, two types of the conjugate prior distribution and Jeffrey’s distribution are considered, and based on the distribution of observations in phase I, the predictive distribution is determined. Then, using the economic model of Lorenzen and Vance, an economic-statistical design was obtained for the data. Optimal design parameters (sampling distance, sample size, and control limits) were determined using a genetic algorithm and sensitivity analysis was performed for different values of model parameters. The results of this approach have been compared with the results of the classical model. The results show that this method is more effective than the classical method

کلیدواژه‌ها [English]

  • Bayesian control chart
  • prior distribution
  • predictive distribution
  • economic-statistical design (ESD)
  • genetic algorithm (GA)

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نشریه علمی پژوهشی مهندسی و مدیریت کیفیت
دوره 12، شماره 2
شهریور 1401
صفحه 153-169

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