طراحی آماری- اقتصادی دو هدفه‌ی نمودارهای کنترل X ̅ با توزیع مکانیزم شکست پارتو

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

نمودارهای کنترل در تجزیه و تحلیل و کنترل فرآیندهای تولید کاربرد زیادی دارند تا کیفیتی رضایت بخش، کافی، قابل اعتماد و اقتصادی تولید کنند. تعیین بهینه‌ی پارامترهای نمودار یک موضوع مهم برای مهندسین کیفیت جهت بهبود فرآیندها است. در این مقاله، طراحی آماری‌- اقتصادی نمودار کنترل X ̅ تحت مدل شوک پارتو بر اساس طراحی دو هدفه ارائه شده، که در آن با اعمال محدودیت بر خطای نوع اول، هزینه به عنوان هدف اقتصادی و خطای نوع دوم به عنوان هدف آماری در نظر گرفته شده و سپس بر اساس جبهه‌ی پارتو، جواب‌های بهینه انتخاب شده‌است. در نهایت از طریق یک مثال کاربردی، مزایای رویکرد پیشنهادی با تهیه فهرستی از راه‌حل‌های بهینه و نمایش‌های گرافیکی نشان داده شده‌است

کلیدواژه‌ها


عنوان مقاله [English]

Double Objective Economic - Statistical Design under Pareto Shock models

نویسندگان [English]

  • Salimeh Sadat Aghili 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]

The technique of control charts to monitor process behavior is one of the basic tools of statistical process control. Process changes can be divided into two main categories: common (random) cause, which is a fundamental feature of any process, and cause (definable) deviation, the occurrence of which is an unusual disorder that must be eliminated in order for the process to reverse. The main purpose of using management control charts is to separate these two different sources.Control charts are widely used in the analysis and control of production processes to produce satisfactory, sufficient, reliable and economical quality. Optimizing chart parameters is an important issue for quality engineers to improve processes. In this paper, the economic statistical design of the X ̅ control chart under the Pareto shock model based on the double objective design is presented. Actually by applying restrictions on the first type of error, the cost as the economic objective and the second type of error as the statistical objective is considered and then the optimal solutions are selected based on the Pareto front. Finally, through a practical example, the advantages of the proposed approach are shown by preparing a list of optimal solutions and graphical representations.

کلیدواژه‌ها [English]

  • Economic- Statistical design
  • X ̅ control chart
  • Double- objective design
  • Pareto distribution
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