Assessing process incapability when collecting data from multiple batches

Process capability indices have been widely used in industry to measure the ability of firms to meet quality specifications. The Cpp$ {C_{pp}} $ index not only can directly reflect the process incapability, but also provides more information regarding process inaccuracy and imprecision than other indices. Therefore, it can help contract manufacturers to better understand their processes for improving quality performance. In real applications, the sampling data are often collected from multiple batches. Based on this condition, this study proposes an alternate method to assess the true Cpp$ {C_{pp}} $ value. The concept of generalised pivotal quantity is used, and the generalised confidence interval is derived to estimate Cpp$ {C_{pp}} $. Furthermore, we provide simulations to compare the performances of our proposed method with an existing method. The results show that the empirical confidences of the two methods are affected by the degree of process departure. Therefore, practitioners can select the appropriate one to assess the process capability, depending on the degree of process departure.