استفاده از شاخص ناكارايي Cpp در طراحي اقتصادي نمودار كنترل X با نمونه گيري دو مرحله اي

Using incapability index ?????? in economical design of double sampling ?X control chart analysis

شاخصهاي كارايي فرآيند، معيارهايي براي بررسي توانايي فرآيند جهت توليد محصولات منطبق با مشخصات فني ميباشند. شركتها اين شاخصها را براي ارزيابي عملكرد، جهت رقابت و سود بالا استفاده ميكنند. يكي از مهمترين شاخصها، شاخص ناكارايي Cpp است، كه اطلاعات بيشتري نسبت به ديگر شاخصها فراهم ميكند. همچنين كار كردن با آن ساده است، زيرا به شاخص نادرستي (Cia) و شاخص عدم دقت (Cip) قابل تجزيه است. از طرفي ديگر شاخص Cpp برمفهوم زيان كيفي تاگوچي بنا شده است كه مفهومي اقتصادي به همراه دارد. در اين مقاله، مدل هزينهي پاناگوس با اضافه كردن محدوديتهاي آماري اصلاح شده است و بهينه سازي پارامترهاي طرح نمودار كنترل X (تحت نمونهگيري دو مرحلهاي) توسط مدل اصلاح شده انجام ميشود. با استفاده از پارامترهاي بهينه شده، ميتوان يك حد كنترل بالا براي شاخص Cpp به دست آورد به طوري كه كارايي فرآيند را تحت كنترل قرار داد.

Process capability indices (PCIs) have been used to measure the ability of a process to decide how well the process meets the specification limits. These have been applied by companies to compete and lead markets by evaluating the quality and productivity performance. One of the most important PCIs is process incapability index (Cpp) which provides more process information than other process PCIs and is easily applied. This index can be used along with the indices of inaccuracy (Cia) and imprecision (Cip). Since the process capability index Cpm is based on the concept of Taguchiʹs quality loss, the process capability index Cpm already includes an economical concept. In this article, Panagosʹ cost model was modified by adding the statistical constraints to develop the design model of double sampling (DS) X ? control chart for the optimizaition of design parameters. By using the optimization parameters, one can obtain an upper control limit for Cpp index to control process capability. A numerical example was provided to illustrate the use of this model. A sensitivity analysis of the effects of model parameters and statistical constraints on the optimal design of DS X ? chart was also performed. From the sensitivity analysis, we can conclude for larger shift (?? ?3), a Shewhart X ? control chart will be preferred to a DS X ? control chart for process monitoring. In addition, by taking the sample sizes of two process states in to consideration, the economic-statistical design model can provide a more balanced sampling.