Economic statistical design of the VP X¯ control charts for monitoring a process under non-normality

Recent studies proved that variable parameters (VP) X¯ control charts not only detect process mean shifts quicker than the classical X¯ control chart but also have better economic properties. While most papers in control chart design assume that process data are normally distributed this may not be true in practice. In this paper, we investigate the economic statistical design of the VP X¯ control chart when the underlying process distribution is non-normal. Here, we use the Burr distribution as a model of the process quality variable distribution because of its flexibility in terms of being able to model many distributions including the normal. We illustrate the design procedure and perform a sensitivity analysis on the process and cost parameters based upon the degrees of skewness and kurtosis of the population using an industrial application.