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Individual and Moving Ratio Charts for Weibull Processes

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Stochastic Orders in Reliability and Risk

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 208))

Abstract

This chapter proposes methods for monitoring Weibull processes when data collection is restricted to one observation per sampling period. Because the Weibull distribution is an asymmetric distribution, it is not appropriate to apply normal-based individual and moving range charts to Weibull data. A transformation of Weibull to approximate normality prior to applying normal-based methods has been suggested in the literature. This chapter studies the run length properties of and the difficulties encountered with this approach. As an alternative, this chapter proposes combined individual and moving range charts for monitoring changes in either the Weibull scale or shape parameter. A method for computing the average run length ARL is discussed, and control limits are presented for ARL-unbiased charts. The proposed method is applied to a Weibull data set.

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Authors and Affiliations

  1. Department of Mathematics, Washington State University, Pullman, WA, 99164-3113, USA

    Francis Pascual

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  1. Francis Pascual
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Correspondence to Francis Pascual .

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Editors and Affiliations

  1. Dept. Mathematics, Washington State University, Lighty 370, Pullman, 99164, Washington, USA

    Haijun Li

  2. Xiamen University, Xiamen, 361000, China, People's Republic

    Xiaohu Li

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Pascual, F. (2013). Individual and Moving Ratio Charts for Weibull Processes. In: Li, H., Li, X. (eds) Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics(), vol 208. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6892-9_17

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