Sample size determination for production yield estimation with multiple independent process characteristics

Ya Chen Hsu*, W.l. Pearn, Ya Fei Chuang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Capability measure for processes yield with single characteristic has been investigated extensively, but is still comparatively neglected for processes with multiple characteristics. Wu and Pearn [Wu, C.W., Pearn, W.L., 2005. Measuring manufacturing capability for couplers and wavelength division multiplexers (WDM). International Journal of Advanced Manufacturing Technology 25(5/6), 533-541] proposed a capability index for multiple characteristics called CPUT, which provides an exact measure on process yield for multiple characteristics with each characteristic normally distributed. However, the exact sampling distribution of CPUT (multiple characteristics) is analytically intractable. In this paper, we apply the bootstrap method for calculating the lower confidence bounds of the index CPUT, and determine the sample size for a specified estimation accuracy. In order to obtain a desired estimation quality assurance, the sample size determination is essential as it provides the accuracy of the lower bound obtained from the bootstrap method. For convenience of applications, we tabulate the sample size required for various designated accuracy for the engineers/practitioners to use. A real-world example from manufacturing process with multiple characteristics is investigated to illustrate the applicability of the proposed approach.

Original languageEnglish
Pages (from-to)968-978
Number of pages11
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - 1 Aug 2009


  • Bootstrap resampling
  • Estimation accuracy
  • Lower confidence bound
  • Multiple characteristics
  • Process capability indices
  • Sample size determination

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