پايش فرايندهاي چندمشخصه‌ي وصفي و متغير با استفاده از شيوه‌ي بوت‌استرپ

Monitoring Multivariate-attribute Processes Based on the Bootstrap Technique

در برخي موارد كيفيت يك محصول يا فرايند، به‌وسيله‌ي تركيبي از مشخصه‌هاي كيفي متغير و وصفي هم‌بسته بازنمايي مي‌شود. تاكنون تحقيقات چنداني در زمينه‌ي پايش اين‌‌گونه فرايندها صورت نگرفته است. در اين نوشتار دو روش براي پايش همزمان مشخصه‌هاي كيفي وصفي و متغير با استفاده از شيوه‌ي بوت‌استرپ ارايه شده است. ابتدا روشي براي تعيين فاصله‌ي اطمينان همزمان براي مشخصه‌هاي كيفي وصفي و متغير پيشنهاد شده است. سپس، از اين فاصله‌‎ي اطمينان به‌عنوان حدود كنترل براي پايش مشخصه‌هاي كيفي استفاده شده است. در ادامه، روش پيشنهادي به‌منظور طراحي چندين نمودار كنترل ميانگين متحرك موزون نمايي توسعه داده شده است. روش‌هاي پيشنهادي، ضمن كشف وضعيت خارج از كنترل، قادر به تشخيص عامل انحراف در فرايند نيز هستند. نتايج نشان مي دهد كه احتمال خطاي نوع اول روش‌هاي پيشنهادي در اغلب موارد، و به‌ويژه در مقادير كم‌تر خطاي نوع اول، به مقدار اسمي نزديك‌تر است.

Nowadays, in many production and service environment, the quality of a product or process is represented by two or more quality characteristics. Therefore, multivariate and multi-attribute control charts have been widely developed by many authors, separately. Sometimes, the quality of a product or a process is represented by correlated variables and attribute quality characteristics. For example, in plastic manufacturing companies, the number of defects in one product, as an attribute, has a correlation with the weight of the product, as a variable quality characteristic. To the best of our knowledge, there is no method to monitor this type of quality characteristic. Note that monitoring correlated variables and attribute quality characteristics separately, without considering the correlation structure, leads to increasing the overall probability of Type I error in the control chart. An appropriate approach in designing control charts is defining confidence limits. There are some methods to determine confidence limits for correlated random data, such as described by Bonferoni (Hayter and Tsui, 1994) and Sidak (1967). But, the first method requires large samples, which lead to less application, and the second has a weakness in neglecting the correlation between quality characteristics. In this paper, we propose two methods to monitor multivariate-attribute processes, based on the bootstrap technique (Jhun et al. 2007), which has none of the drawbacks of the mentioned methods (Bonferoni and Sidak). In the first method, new confidence limits for multivariate-attribute quality characteristics are presented by using the bootstrap technique. In the second method, the bootstrap technique is used to determine confidence limits for EWMA control statistics, which are used for correlated attribute and variable quality characteristics. Finally, these confidence limits are used to monitor the process. Based on the signal rule, whenever each control chart signals, the process will be out-of-control and the corresponding quality characteristic is introduced as the source of variation. This research is performed in Phase II, thus, it is assumed that the distributions of quality characteristics are known based on Phase I analyses. The obtained results confirms the efficiency of the proposed method compared to the traditional method based on the accuracy of probability of Type I error, especially under small values of Type I error probability.