A control chart for the lognormal standard deviation

Abstract

Among the statistical process control techniques, the control chart has been proven to be effective in process monitoring. The Shewhart S-chart is one of the most commonly used control charts for monitoring the process variability based on the assumption that the distribution of the quality characteristic to be monitored is normal. However, in real applications, many process distributions may follow a positively skewed distribution such as the lognormal distribution. In this study, a control chart for monitoring the standard deviation of a lognormal distribution is presented. The simulation results show that the proposed chart is more effective than the existing charts when the true value of the scale parameter of the lognormal distribution is large. A real example is used to demonstrate how the proposed chart can be applied in practice.