For stably normal processes with one-sided specification limits, capability indices CPU and CPL have been used to provide numerical measures on production yield assurance. Statistical properties of the estimators of CPU and CPL have been investigated extensively for cases with a single sample. It is shown that for multiple samples, the uniformly minimum-variance unbiased estimators of CPU and CPL 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 CPU and CPL. 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.