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.

Acknowledgements

The authors thank the anonymous referees for careful reading of the manuscript and for constructive comments that significantly improved the paper. Research was supported in part by the National Science Council, Taiwan, ROC, Grant No. NSC 91-2218-E-230-005.