The majority of quality control charts are employed for normally distributed data. In reality this assumption is not always valid. This paper aims to consider an alternative the truncated normal.
Having derived integral equations for the average run length (ARL), a key measure of the performance of a control chart, approximate solutions are derived using Gaussian quadrature.
Polynomials closely approximating the ARL for the three most popular control charts, using their usual parameterization, are obtained.
An obvious extension is to other distributions and hopefully this work will encourage real world applications.
These charts are widely applicable within engineering, finance, medicine, environmental statistics, and many other fields. These problems are typically said to fall in the domain of risk management. It is hoped that this paper will add to the body of practitioners already employing this technique.
Control charts are widely employed, however applications are usually restricted to the normal distribution. This is the first time it has been applied to the truncated normal distribution and original polynomials derived for the ARL.
