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Two-sided variable inspection plans for arbitrary continuous populations with unknown distribution

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Abstract

The ordinary variable inspection plans rely on the normality of the underlying populations. However, this assumption is vague or even not satisfied. Moreover, ordinary variable sampling plans are sensitive against deviations from the distribution assumption. Nonconforming items occur in the tails of the distribution. They can be approximated by a generalized Pareto distribution (GPD). We investigate several estimates of their parameters according to their usefulness not only for the GPD, but also for arbitrary continuous distributions. The likelihood moment estimates (LMEs) of Zhang (Aust N Z J Stat 49:69–77, 2007) and the Bayesian estimate (ZSE) of Zhang and Stephens (Technometrics 51:316–325, 2009) turn out to be the best for our purpose. Then, we use these parameter estimates to estimate the fraction defective. The asymptotic normality of the LME (cf. Zhang 2007) and that of the fraction defective are used to construct the sampling plan. The difference to the sampling plans constructed in Kössler (Allg Stat Arch 83:416–433, 1999; in: Steland, Rafajlowicz, Szajowski (eds) Stochastic models, statistics, and their applications, Springer, Heidelberg, pp 93–100, 2015) is that we now use the new parameter estimates. Moreover, in contrast to the aforementioned papers, we now also consider two-sided specification limits. An industrial example illustrates the method.

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Acknowledgements

The authors like to thank the referees for their valuable comments that lead to an improvement of the presentation.

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Authors and Affiliations

  1. Department of Computer Science, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489, Berlin, Germany

    Wolfgang Kössler & Janine Ott

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  1. Wolfgang Kössler
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  2. Janine Ott
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Correspondence to Wolfgang Kössler.

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Kössler, W., Ott, J. Two-sided variable inspection plans for arbitrary continuous populations with unknown distribution. AStA Adv Stat Anal 103, 437–452 (2019). https://doi.org/10.1007/s10182-018-00338-w

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  • DOI: https://doi.org/10.1007/s10182-018-00338-w

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