| dc.description.abstract | Process yield is a reasonable approach used in industry for assessing process performance. There is also another and more common approach to measuring and communicating the assessment of process performance, called process capability indices. Process capability indices have been used widely in the industry to provide a numerical measure to determine whether a process is capable of producing items within the established specification limits present by the customer or designer. Among various capability indices, companies use capability indices to measure process improvement or to compare the processes of vendors and internal suppliers continue to rely heavily on Cpk index. Since the estimator of Cpk index is a random variable with a corresponding distribution, simply reporting from the sample data and then making a conclusion on whether the process is considered capable is not reliable. In practice, process information about process characteristics is often derived from multiple samples rather than from one single sample, particularly, when a daily-based production control plan is implemented for monitoring process stability. Applications in real situation, the production may require multiple supplies with different quality levels on each single shipment of the raw materials or components, or the raw materials or components from supply with unequal performance level on each period. Therefore, the common assumption that the process mean stay as a constant may not be satisfied in real situations. In this dissertation, There are four various standard deviation estimators are substituted for the process standard deviation, including the un-pooled sample standard deviation, the pooled sample standard deviation, the average of the subsample standard deviation and the average of the subsample range. The concrete contributions of this dissertation are threefold. The first is to investigate the distributional and inferential properties of the estimators of Cpk index based on un-pooled and pooled standard deviation estimators. The second is to investigate the asymptotic distributions of these estimators of Cpk index for arbitrary population under fairly general conditions of regularity, assuming that the fourth central moment exists. The third is to ensure the performance assessment reliable, the theory of testing hypothesis using the sampling distributions of these estimators of Cpk index are implemented, which is provided the critical values required for making decisions. Following Hamaker’s approximation, the testing procedures can be adequately derived from normal approximations while avoiding more complicated distributions. By further applying a two-point adjustment, equations to determine the critical values and to estimate the sample sizes necessary to achieve the recommended minimal value for Cpk index are provided. We then develop a step- by-step procedure for testing Cpk index. Practitioners can use the procedure to assess whether their processes meet the quality requirement. | en_US |