Estimating process yield based on Spk for multiple samples

Boyles (1994) proposed a process measurement called Spk, which provides an exact measure on the process yield for normal processes. Lee et al. (2002) considered an asymptotic distribution for the natural estimator of Spk under a single sample. In this paper, we extend the results for the case of multiple samples. We first compare the yield index Spk with the most commonly used index, Cpk, and review some results of Spk under a single sample. Next, we derive the sampling distribution for the estimator of Spk under multiple samples and find that for the same Spk, the variance of would be largest when the process mean is on the centre of specification limits. We calculate the lower bounds for various commonly used quality requirements under the situation with the largest variance of for assurance purposes. To assess the normally approximated distribution of , we simulate with 10 000 replications to generate 10 000 estimates of , calculate their lower bounds, compare with the real (preset) Spk and check the actual type I error. We also compute how many sample sizes are required for the normal approximation to converge to Spk within a designated accuracy. Then, we present a real-world application of the one-cell rechargeable Li-ion battery packs, to illustrate how we apply the lower bounds to actual data collected from factories.