Extreme value charts and analysis of means based on half logistic distribution

Abstract

Purpose

The purpose of this paper is to examine extreme value charts and analyse means based on half logistic distribution.

Design/methodology/approach

Variable control charts with subgroup observations based on the extreme values at each subgroup are constructed without specially going to any subgroup statistic. The control chart constants depend on the probability model of the extreme order statistic of each subgroup and the size of the subgroup. Accordingly the proposed chart is normal as extreme value chart. As a by‐product the technique of analysis of means for a skewed population is exemplated through half logistic distribution and extreme value control charts. The results are illustrated by examples on live data.

Findings

H.L.D is found to be better test for the data of the three examples, ANOM gave a larger (complete) homogeneity of data than those of Ott.

Research limitations/implications

Supposing arithmetic means of k subgroups of size “n” each drawn from a half logistic model. If these subgroup means are used to develop control charts to assess whether the population from which these subgroups are drawn is operating with admissible quality variations. Depending on the basic population model, we may use the control chart constants developed by the authors or the popular Shewart constants given in any SQC text book. Generally the authors say that the process is in control if all the subgroup means fall within the control limits. Otherwise it is said that the process lacks control.

Originality/value

Half logistic distribution is a better model, exhibiting significant linear relation between sample and population quantiles.

Citation

Rao Boyapati, S. and Kantam, R.R.L. (2012), "Extreme value charts and analysis of means based on half logistic distribution", International Journal of Quality & Reliability Management, Vol. 29 No. 5, pp. 501-511. https://doi.org/10.1108/02656711211230490