Abstract
Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. In practice, process capability index Cpk is a popular means to assess target-the-best type quality performance. Normal distribution is an important assumption in process capability analysis. In product quality testing experiments, the experimenter may not always be in a position to observe the quality data of all the products (or items) put on test. Therefore, censored samples may arise in practice. Moreover, observations with coarse scales; measurement error that is not quantified accurately. Therefore, imprecise data also may arise in practice. Our study purposes to utilize the process capability index Cpk in assessing the quality performance of products more generally and accurately. A new approach of analyzing normal, censored and imprecise data is proposed in our study. The new approach will apply a fuzzy statistical estimator of Cpk to develop a new fuzzy statistical hypothesis testing procedure under the normal distribution with the type II right censored sample, imprecise data and large sample. The new fuzzy statistical hypothesis testing procedure can handle normal, censored, imprecise and large sample quality data. Moreover, the purchasers can then employ the new fuzzy statistical hypothesis testing procedure to determine whether the quality performance of products adheres to the required level. The manufactures also can utilize the new fuzzy statistical hypothesis testing procedure to enhance product process capability.