يك رويكرد كنترل تطبيقي جديد براي پايش پروفايل‌هاي خطي چندگانه

A Novel Adaptive Control Approach for Monitoring Multiple Linear Profiles

در سال‌هاي اخير پايش پروفايل‌‌ها، كه در آن كيفيت محصول يا عملكرد فرايند به‌وسيله‌ي رابطه‌ي رگرسيوني بين يك متغير پاسخ و يك يا چند متغير مستقل توصيف مي‌شود، مورد توجه محققين قرار گرفته است. اين رابطه در پروفايل‌ها انواع مختلفي دارد ــ نظير رگرسيون خطي ساده، رگرسيون خطي چندگانه، رگرسيون غيرخطي و رگرسيون مبتني بر مدل‌هاي خطي تعميم‌يافته ــ كه براي پايش آنها روش‌هايي ارايه شده است. از سوي ديگر، محققين روش‌هاي تطبيقي مختلفي براي بهبود عملكرد نمودارهاي كنترل در كشف شيفت‌هاي پديد آمده در پارامترهاي مدل به كار گرفته‌اند. در اين نوشتار نيز به‌طور خاص بر نمودار كنترل ميانگين متحرك موزون نمايي چندمتغيره (MEWMA) براي پايش پروفايل‌هاي خطي چندگانه متمركز شده و با تطبيقي‌‌كردن ضريب هموارسازي عملكرد روش را بهبود بخشيده‌ايم. اين بهبود از طريق مطالعات شبيه‌سازي و مقايسه‌ي معيار متوسط طول دنباله در قالب دو مثال نشان داده شده است.

Statistical process control (SPC) is widely used in different industries to create high quality products through reducing the variability in processes. Among all SPC tools, the control chart is a powerful tool usually used by quality engineers. It can detect shifts in process parameters by distinguishing between common causes and special causes of variations. Quality characteristics can be univariate or multivariate and can be monitored by corresponding univariate or multivariate control charts. However, in some practical situations, the quality of a process or product is better characterized by a relationship between a response variable and one or more explanatory variables, which is usually referred to as a profile. In recent years, profile monitoring has been considered by many researchers and different applications of profile monitoring, such as calibration, are discussed in different papers. Different types of profile include simple linear regression, multiple linear and polynomial regression, nonlinear regression and logistic regression. Several methods are proposed in the literature of profile monitoring to monitor different types of profiles in both phases I and II. In phase I, one checks the stability of a process, while, in phase II, the aim is to detect shifts in the process parameters as quickly as possible. On the other hand, a variety of adaptive methods have been proposed by different researchers to improve the performance of control charts to detect small to large shifts in the process parameters quickly. When the adaptive control charts are applied, one or more design parameters vary during the production process, based on recent data obtained from the process. This paper proposes the use of an adaptive control chart for monitoring multiple linear regression profiles, and is focused on the proposed multivariate exponentially weighted moving average (MEWMA) control chart by Zou et al. [7] for monitoring general linear profiles. The proposed method improves the performance of the MEWMA control chart using an adaptive smoothing constant. This improvement is shown through simulation studies and comparison of an average run length criterion. The results show that in simple and multiple linear profiles, performance of the proposed method is better than the MEWMA method by Zou et al. [7] in the medium to large shifts considered in this paper.