Average run lengths of control charts for monitoring observations from a Burr distribution

Purpose – The majority of quality control charts are employed for normally distributed data. In reality this assumption is not always valid, as an alternative the Burr distribution is considered here. Design/methodology/approach – Having previously derived integral equations for the average run length, a key measure of the performance of a control chart, approximate solutions are derived using Gaussian quadrature. Findings – Polynomials closely approximating the average run length for the three most popular control charts, using their usual parameterisation, are obtained. Research limitations/implications – This is an extension of the Burr distribution which is noted for its ability to fit numerous scenarios. Practical implications – 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. Originality/value – 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 Burr distribution and original polynomials derived for the average run length.