طراحی آماری- اقتصادی نمودار کنترلی EWMA برای پایش میانگین فرایند تحت نمونه-گیری مجموعه‌ی رتبه‌ای

نوع مقاله : مقاله پژوهشی

نویسندگان

1 پژوهشگر

2 تخصص: نمودارهای کنترلی، استنباط بیزی

3 استاد، دانشگاه علامه طباطبایی، گروه آمار، تهران، ایران

چکیده

اگر شناسایی تغییرات کوچک در فرایند تولید مد نظر باشد، نمودار کنترلی میانگین متحرک موزون نمایی (EWMA) جایگزین مناسبی برای نمودار کنترلی X ̅ است. در شرایطی که به‌‌علت محدودیت‌های اقتصادی نتوان نمونه بزرگ از جامعه استخراج کرد، طرح نمونه‌گیری تصادفی ساده (SRS) ممکن است از دقت کافی برخوردار نباشد، که در این صورت می‌توان از طرح نمونه‌گیری مجموعه‌ی رتبه‌‌ای (RSS) استفاده نمود. در این مقاله برای اولین بار طراحی اقتصادی و آماری- اقتصادی نمودار کنترلی EWMA تحت طرح RSS بررسی شده است. با ارائه‌ی نتایج‌ عددی، مزایای طراحی آماری-اقتصادی به طراحی اقتصادی نشان داده شده است. نتایج نشان می‌دهد که هزینه‌ها در طراحی آماری-اقتصادی نسبت به طراحی اقتصادی با اندک تغییری افزایش یافته است، اما به‌دلیل پایین بودن نرخ هشدار نادرست با اهداف کنترل کیفیت آماری هم‌راستا بوده و هم‌زمان با کاهش هزینه‌ها، کیفیت محصول را در سطح مطلوبی از خطا و توان بالا، کنترل می‌کند.

کلیدواژه‌ها


عنوان مقاله [English]

Statistical-economic design of EWMA control chart for monitoring the process average under ranking set sampling

نویسندگان [English]

  • Olia Rostmi 1
  • Rahmat Shojaei Aliabadi 2
  • Mohammad Bameni Moghadam 3
1 Department of Statistics, Allameh Tabatabaʼi University, Tehran, Iran,  
2      Phd Student, Department of Statistics, Allameh Tabatabaʼi University, Tehran, Iran,
3 Profesor, Department of Statistics, Allameh Tabatabaʼi University, Tehran, Iran,
چکیده [English]

 
 If the identification of small changes in the production process is intended, the Moving Averaging Control Chart (EWMA) is a good alternative to the X control chart. In situations where a large sample of the population cannot be extracted due to economic constraints, the Simple Random Sampling Scheme (SRS) may not be accurate enough, in which case the RSS can be used. Appeared. In this paper, for the first time, the economic and statistical-economic design of the EWMA control chart under the RSS design is reviewed. By presenting numerical results, the advantages of statistical-economic design over economic design are shown. The results show that costs in statistical-economic design have increased slightly compared to economic design, but due to the low false alarm rate are in line with statistical quality control objectives and at the same time reduce costs. , Controls the quality of the product at the desired level of error and high power. Keywords: Statistical-economic design, ranking set sampling, shock model. 

کلیدواژه‌ها [English]

  • Statistical-economic design
  • ranking set sampling
  • shock model
 
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