Lower confidence bounds for C-PU and C-PL based on multiple samples with application to production yield assurance

Abstract

For stably normal processes with one-sided specification limits, capability indices C-PU and C-PL have been used to provide numerical measures on production yield assurance. Statistical properties of the estimators of C-PU and C-PL have been investigated extensively for cases with a single sample. It is shown that for multiple samples, the uniformly minimum-variance unbiased estimators of C-PU and C-PL are consistent and asymptotically efficient. Based on the uniformly minimum-variance unbiased estimators, an algorithm is developed with an efficient program using a direct search method to compute the lower confidence bounds for C-PU and C-PL. The lower confidence bounds convey critical information to the minimum capability of a process, providing a necessary yield assurance of production. The lower confidence bounds are tabulated for some commonly used capability requirement so that engineers/practitioners can use them for their in-plant applications. An example of a high-speed buffer amplifier is presented to illustrate the practicality of the approach to data collected from the factories for production yield assurance.