Abstract
In case of an ordinal process (
) involving three ordered categories, always the following condition holds:
where
and
are the proportion of items in the first and third categories respectively. Using this fact, Pal and Gauri (Citation2019) defined a measure called process area of proportions (
) aiming to evaluate capability of a process with ordinal responses. In this article, the statistical distribution of the sample estimate of process area of proportion (
) is studied in details using simulations. It is found that
approximately follows Gamma (
) distribution, where
and
are functions of
and
(sample size). Control charts are designed based on the Gamma approximation (GA) as well as empirical distribution (ED) of
and performances of these charts are evaluated based on simulation studies. The monitoring statistic (
) takes care of the fact that an ordinal process cannot be considered out-of-control if
and/or
shifts in favorable directions, and therefore, the proposed GA-based chart does not give false out–out-control signal when
and/or
shifts in favorable directions.
Acknowledgments
We are sincerely grateful to the referees for their valuable comments which have helped in improving the overall clarity and readability of this article.