توسعه‌ي نمودار كنترل تطبيقي با فاصله‌ي نمونه‌گيري متغير براي پايش پروفايل‌هاي خطي ساده

Developing VSI Control Chart for Monitoring Simple Linear Profiles

در اين مطالعه يك نمودار كنترل تطبيقي با فاصله‌ي نمونه‌گيري متغير براي پايش پروفايل‌هاي خطي ساده كه توسط يك رابطه‌ي خطي بين يك متغير پاسخ و يك متغير مستقل توصيف مي‌شود، توسعه داده مي‏شود. در اين نوشتار از 3 نمودار كنترل ميانگين متحرك موزون نمايي ( ) با فواصل نمونه‌گيري متغير (VSI) براي پايش پروفايل‌هاي خطي ساده استفاده شده است. عملكرد نمودار كنترل پيشنهادي با استفاده از متوسط زمان تا هشدار تعديل شده (AATS) اندازه‌گيري مي‌شود كه براي محاسبه‌ي آن از رويكرد زنجيره‌ي ماركوف استفاده شده است. با استفاده از يك مثال عددي عملكرد نمودار كنترل VSI پيشنهادي با نمودار كنترل با فاصله‌ي نمونه‌گيري ثابت (FSI) مقايسه، و نشان داده شده كه سرعت كشف تغيير در نمودارهاي كنترل ((VSI نسبت به نمودارهاي (FSI) بيشتر است.

Control charts are used to monitor the variation of productions and processes. They can detect an out-of-control signal when an assignable cause is occurred. Recently, many researchers have investigated different types of profiles. Simple linear profile is one of the most important types of profiles, which has many applications in industry, especially in calibration. The simple linear profile is characterized by a relationship between a response variable and one explanatory variable. Monitoring simple linear profiles in both phases I and II is well studied in the literature. In phase I, the parameters are unknown and are estimated by historical dataset while the process parameters are known in phase II and the main aim is detecting assignable causes as quickly as possible. One of the most popular methods in phase II monitoring of the simple linear profile is scheme. In the scheme, three EWMA control charts are used to monitor the regression parameters of the simple linear profile, including intercept, slope and standard deviation- separately. In this paper, we specifically concentrate on phase II monitoring of the simple linear profiles through scheme. Since the third statistic in the scheme does not follow any specific distribution, we first propose an EWMA control chart for monitoring the standard deviation instead of the third control chart used in the scheme. Then, a variable sampling interval (VSI) method is proposed to improve the performance of the modified control chart. In the VSI procedure, the sampling interval for the next sample depends on the current sample situation on the control chart and it varies over time. The performance of the proposed VSI control chart is evaluated in terms of the adjusted average time to signal (AATS) obtained by a Markov chain approach. A numerical example is provided to demonstrate the effectiveness of the proposed adaptive control chart. The results show that the VSI control chart is more effective than the FSI control chart.