Power of the (x̄, s) control chart based on the log-likelihood ratio statistic

Kyouko Watakabe, Ikuo Arizono

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Recently, Kanagawa et al. have proposed a new control chart, based on the estimator of Kullback-Leibler information, which enables the user to monitor both changes of the mean and the variance simultaneously for normally distributed characteristics. This control chart, called the (x̄, s) control chart, is designed in conformity with the probability limit method, that is, the control limit is derived from specifying the probability of the first kind of error. However, they have not referred to the power by using this control chart to detect a departure of the process from the null population, i.e., in-control state. Therefore, we consider the power of the (x̄, s) control chart presented by Kanagawa et al. in this article. In the process, we identify the estimator of Kullback-Leibler information as the log-likelihood ratio statistic for the in-control state. Then, we first derive the cumulant generating function of the log-likelihood ratio statistic. Furthermore, we develop some approximations for the distribution of the log-likelihood ratio statistic, and we investigate the power of the (x̄, s) control chart.

Original languageEnglish
Pages (from-to)928-951
Number of pages24
JournalNaval Research Logistics
Volume46
Issue number8
DOIs
Publication statusPublished - Dec 1999
Externally publishedYes

Fingerprint

Log-likelihood Ratio
Likelihood Ratio Statistic
Control Charts
Statistics
Kullback-Leibler Information
Estimator
Cumulants
Generating Function
Null
Control charts
Likelihood ratio statistic
Monitor
Approximation

ASJC Scopus subject areas

  • Management Science and Operations Research

Cite this

Power of the (x̄, s) control chart based on the log-likelihood ratio statistic. / Watakabe, Kyouko; Arizono, Ikuo.

In: Naval Research Logistics, Vol. 46, No. 8, 12.1999, p. 928-951.

Research output: Contribution to journalArticle

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