Normalization of the origin-shifted exponential distribution for control chart construction

Shih-Chou Kao

Journal of Applied Statistics, 2010, vol. 37, issue 7, 1067-1087

Abstract: This study demonstrates that a location parameter of an exponential distribution significantly influences normalization of the exponential. The Kullback-Leibler information number is shown to be an appropriate index for measuring data normality using a location parameter. Control charts based on probability limits and transformation are compared for known and estimated location parameters. The probabilities of type II error (β-risks) and average run length (ARL) without a location parameter indicate an ability to detect an out-of-control signal of an individual chart using a power transformation similar to using probability limits. The β-risks and ARL of control charts with an estimated location parameter deviate significantly from their theoretical values when a small sample size of n≤50 is used. Therefore, without taking into account of the existence of a location parameter, the control charts result in inaccurate detection of an out-of-control signal regardless of whether a power or natural logarithmic transformation is used. The effects of a location parameter should be eliminated before transformation. Two examples are presented to illustrate these findings.

Keywords: location parameter; exponential distribution; power transformation; natural logarithmic transformation; Kullback-Leibler information number (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1080/02664760802571333

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