Four-parameter beta distribution estimation and skewness test

Ronald G. McGarvey, Enrique Del Castillo, Tom M. Cavalier, El-amine Lehtihet

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Sequential tolerance control (STC) is a tolerance control methodology used in discrete parts manufacturing. Recently, an adaptive sphere-fitting method for STC (ASF-STC) was developed to account for potential skewness in manufacturing operations' distributions, a factor not considered in conventional STC. ASF-STC offers significant improvements over conventional STC when such skewness exists. The direction of skewness of an operations' distribution is a necessary input to ASF-STC. Thus, a novel approach to determining the skewness of a distribution for small sample sizes is presented here. ASF-STC has an additional requirement of distribution information for each operation. The beta distribution is an ideal candidate here, as it is very flexible in shape. The literature on four-parameter beta estimation is very limited, and their performance for small sample sizes is poor. STC was designed for low-volume production, thus the estimation for small sample sizes is necessary here. This study presents a heuristic, based on the method of moments estimates for a beta distribution, that estimates the four parameters for a beta distribution with small sample size. Several computational results are provided to compare this heuristic to the best-known procedure, with the heuristic found to perform better for the test problems considered.

Original languageEnglish (US)
Pages (from-to)395-402
Number of pages8
JournalQuality and Reliability Engineering International
Issue number5
StatePublished - Sep 2002

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


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