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Combined X-bar and CRL Charts for the Gamma Process

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  • C. Sim

Abstract

This paper (i) discusses the combined $\bar x$ and conforming run length (CRL) charts under the assumption that the quality characteristic under study follows a Gamma(ν, γ, ß) distribution with known parameters ν, γ and ß, (ii) examines the performance of the combined $\bar x$ and CRL charts for the Exp(γ, ß) process, when its parameters γ and ß are unknown and must be estimated from preliminary samples taken during the trial period, and (iii) obtains the adjusted control limits of the combined $\bar x$ and CRL charts that have a specified in-control average run length value for samples taken from the Exp(γ, β) process with unknown parameters. Studies of the average run lengths reveal that the combined $\bar x$ and CRL charts outperform the Shewhart $\bar x$ chart with either asymmetric probability limits or 3-sigma control limits. Copyright Physica-Verlag 2003

Suggested Citation

  • C. Sim, 2003. "Combined X-bar and CRL Charts for the Gamma Process," Computational Statistics, Springer, vol. 18(3), pages 547-563, September.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:3:p:547-563
    DOI: 10.1007/BF03354616
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