Testing Quality Assurance Using Process Capability Indices C_(PU) and C_(PL) Based on Several Groups of Samples with Unequal Sizes

摘要

For stably normal processes with one-sided specification limits, capability indices C_(PU) and C_(PL) have been used to provide numerical measures for product quality assurance from manufacturing perspective. Statistical properties of the estimators of C_(PU) and C_(PL) have been investigated extensively for cases with one single sample. In this paper, we consider testing product quality assurance for cases of several groups of samples with unequal sizes. We obtain the uniform minimum variance unbiased estimators (UMVUEs) of C_(PU) and C_(PL), and develop a powerful test for that purpose. We also implement Fortran programs to compute the p-values, critical values, for testing product quality assurance. A practical procedure using the UMVUEs is provided to assist the practitioners judging whether their processes are capable of reproducing reliable products. An example of voltage limiting amplifier (VLA) is presented to illustrate the practicality of our approach to actual data collected from the real-world applications.