Providing comprehensive control chart for monitoring of linear and nonlinear profiles using functional data analysis.

Document Type: research paper

Authors

1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran

Abstract

Considering profiles as functional variables, two control charts are proposed for their monitoring in phase II. Due to its conformity with the nature of real-world profiles, applying functional model leads to proposed control charts obtained through functional data analysis techniques with desired features. These include simplicity in calculation and possibility of using them for different profiles such as linear and non-linear (even in the presence of complex within-profile Autocorrelation forms). These features distinguish the functional model from the regression models common in profile monitoring. Simulated computer simulations show that, in different states, the proposed control charts have a lower average run length than other methods, which indicates the desired performance of the proposed functional approach. Morevere, in some non-linear cases with complex autocorrelation, other methods completely fail, and only the proposed control charts are able to detect the occurring deviation, and even in these cases, the average run length of these control charts is highly desirable.

Keywords


Article Title [Persian]

ارائه نمودار کنترلی فراگیر برای مانیتورینگ پروفایل‌های خطی و غیرخطی با استفاده از آنالیز داده‌های تابعی

Authors [Persian]

  • مهراب بحری 1
  • عبداله هادی وینچه 2
1 گروه مهندسی صنایع، دانشکده فنی و مهندسی، دانشگاه آزاد اسلامی، واحد علوم و تحقیقات، تهران، ایران
2 گروه ریاضی، دانشکده علوم،دانشگاه آزاد اسلامی، واحد اصفهان (خوراسگان)، اصفهان، ایران
Abstract [Persian]

در این مقاله پروفایل‌ها به عنوان متغیرهای تابعی در نظر گرفته شده و دو نمودار کنترلی برای مانیتورینگ آن‌ها در فاز II پیشنهاد شده است. به‌کارگیری مدل تابعی به دلیل منطبق بودن بر ماهیت پروفایل‌ها در دنیای واقعی، باعث می‌شود که نمودارهای کنترلی پیشنهادی که به کمک تکنیک‌های آنالیز داده‌های تابعی بدست آمده، دارای ویژگی‌های مطلوبی باشند از جمله: سادگی محاسباتی، قابلیت بکارگیری یکسان برای پروفایل‌های گوناگون (خطی و غیرخطی در شکل‌های مختلف) و پذیرش شکل‌های پیچیده خودهمبستگی درون پروفایلی. این ویژگی‌ها متمایز کننده مدل تابعی نسبت به مدل‌های رگرسیونی است که در پروفایل مانیتورینگ متداول‌اند. شبیه‌سازی کامپیوتری انجام شده نشان می‌دهد که در حالت‌های مختلف نمودارهای کنترلی پیشنهادی نسبت به سایر روش‌ها متوسط طول دنباله کوتاه‌تری دارند که نشان دهنده عملکرد مطلوب رویکرد تابعی اتخاذ شده است؛ بعلاوه این که در تعدادی از حالات غیرخطی با خودهمبستگی پیچیده، سایر روش‌ها به کلی از کار افتاده و تنها نمودارهای کنترلی پیشنهادی این تحقیق قادر به تشخیص انحراف بوجود آمده هستند و حتی در این حالات نیز متوسط طول دنباله این نمودارهای کنترلی بسیار مطلوب می‌باشد.

Keywords [Persian]

  • پروفایل مانیتورینگ
  • آنالیز داده‌های تابعی
  • نمودارهای کنترلی
  • کنترل فرآیند آماری
  • فاز II
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