Estimating process yield based on Spk for multiple samples

W.l. Pearn*, Ya Ching Cheng

*Corresponding author for this work

Research output: Contribution to journalArticle

19 Scopus citations


Boyles (1994) proposed a process measurement called Spk, which provides an exact measure on the process yieldfor normal processes. Lee et al. (2002) considered an asymptoticdistribution 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 Ŝ́pk of Spk under multiple samples and find that for the same Spk, the variance of Ŝ́pk 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 Ŝ́pk for assurance purposes. To assess the normally approximated distribution of Ŝ́pk, we simulate with 10000 replications to generate 10000 estimates of Ŝ́pk, 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.

Original languageEnglish
Pages (from-to)49-64
Number of pages16
JournalInternational Journal of Production Research
Issue number1
StatePublished - 1 Jan 2007


  • Multiple samples
  • Process capability
  • Process yield

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