The power of the (x̄, s) control chart based on the log‐likelihood ratio statistic

Kyouko Watakabe and Ikuo Arizono

Naval Research Logistics (NRL), 1999, vol. 46, issue 8, 928-951

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 (¯x, 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. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 928–951, 1999

Date: 1999
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1002/(SICI)1520-6750(199912)46:83.0.CO;2-R

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:46:y:1999:i:8:p:928-951

Access Statistics for this article

More articles in Naval Research Logistics (NRL) from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().