Control Charts for Monitoring the Lognormal Mean and Standard Deviation

Abstract

The Shewhart X-bar- 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-bar- and S-charts for jointly monitoring the lognormal mean and the standard deviation. The simulation results show that the combined lognormal X-bar- 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-bar- and S-charts can be applied in practice. ? Keywords：Average run length; Lognormal distribution; Phase II monitoring; S-chart; X-bar-chart.