تلفیق رهیافت زیان تاگوچی در طراحی آماری اقتصادی نمودار کنترلX ̅ با به‌‌کارگیری یک تابع زیان نامتقارن

نوع مقاله : مقاله پژوهشی

نویسندگان

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

2 استادیار، دانشگاه بوعلی سینا، دانشکده علوم پایه، گروه آمار، همدان، ایران

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

4 دانشگاه علامه طباطبایی

چکیده

نمودارهای کنترل، یکی از مهم‌ترین ابزارها برای ارزیابی عملکرد و پایش فرایند هستند. در طراحی کلاسیک نمودار کنترل، هزینه­ی کیفیت به این­که مشخصه­ی کیفیت درون یا بیرون حدود کنترل قرار گیرد بستگی دارد. استفاده از تابع زیان در طراحی نمودارهای کنترل، به­عنوان براورد کننده ‌ی هزینه­ی تولید محصولات معیوب، به ارزیابی جامع­تر و تصمیم­های بهتر در مدیریت کمک شایانی می­کند، بنا بر این در این مقاله به تلفیق تابع زیان و طراحی آماری اقتصادی نمودار کنترل  پرداخته می­شود. توابع زیانی که تا کنون در این زمینه مورد استفاده قرار گرفته‌اند توابعی متقارن بوده­اند، اما در بسیاری از مواقع بیش براورد کردن و یا کم براورد کردن مقدار ایده­ال برای مشخصه­ی کیفیت زیان­های یکسانی را ایجاد نمی­­کند. لذا این مقاله برای اولین بار در ادبیات موضوع طراحی نمودارهای کنترل، از تابع زیان نامتقارن لاینکس استفاده می‌کند. با استفاده از یک مثال کاربردی، عملکرد توابع زیان درجه دوم، خطی، نمایی و لاینکس مقایسه شده است. نتیجه‌ی این مقایسه­ها نشان داد تابع زیان لاینکس، کم‌ترین مقدار هزینه را در طراحی آماری- اقتصادی نمودار کنترل  نسبت به سایر توابع زیان به خود اختصاص می­دهد.

کلیدواژه‌ها


عنوان مقاله [English]

Integrating the Taguchi Loss Approach into the Economic Statistical Design of the X ̅ Control Chart Using an Asymmetric Loss Function

نویسندگان [English]

  • mitra abdolmohamadi 1
  • Asghar seif 2
  • Mohahammad Hosain behzadi 3
  • Mohammad bamenimoghadam 4
1 Islamic Azad University, Science and Research Branch, Department of Statistics, Tehran, Iran
2 Assistant Professor, Bu Ali Sina University, Faculty of Basic Sciences, Department of Statistics, Hamedan, Iran
3 Associate Professor, Islamic Azad University, Science and Research Branch, Department of Statistics, Tehran, Iran
4 Allameh Tabatabaei University
چکیده [English]

Control charts are one of the most important tools for evaluating process performance and monitoring. In the classic design of a control chart, the cost of quality depends on whether the quality characteristic is inside or outside the control. The use of loss function in the design of control charts, as an estimator of the cost of production of defective products, contributes to a more comprehensive assessment and better management decisions. Therefore, in this article, the combination of loss function and economic statistical design of control charts. The loss functions used so far in this field have been symmetric functions, but in many cases overestimating or underestimating the ideal value for a quality characteristic does not produce the same losses. Therefore, for the first time in the literature on the design of control charts, this paper uses the asymmetric loss function of Linux. Using a practical example, the performance of quadratic, linear, exponential and linear loss functions are compared. The result of these comparisons showed that the Linex loss function has the lowest cost in statistical-economic design of the control chart compared to other loss functions.

کلیدواژه‌ها [English]

  • Control chart
  • Statistical-economic design
  • Taguchi loss approach
  • Genetic Algorithm
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