Control Charts for Joint Monitoring of the Lognormal Mean and Standard Deviation

Abstract

The Shewhart X¯- and S-charts are most commonly used for monitoring the process mean and variability based on the assumption of normality. However, many process distributions may follow a positively skewed distribution, such as the lognormal distribution. In this study, we discuss the construction of three combined X¯- and S-charts for jointly monitoring the lognormal mean and the standard deviation. The simulation results show that the combined lognormal X¯- and S-charts are more effective when the lognormal distribution is more skewed. A real example is used to demonstrate how the combined lognormal X¯- and S-charts can be applied in practice.