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.
Highlights
When σ0 is small, which means that the data are more symmetric, the combined lognormal X- and S-charts are less effective than the combined Shewhart X- and S-charts and the combined median absolute deviation (MAD) X- and S-charts
We discuss the construction of three combined X- and S-charts for jointly monitoring the mean and the standard deviation of the lognormal distribution
The simulation studies show that the combined lognormal X- and S-charts have good performance when the underlying lognormal distribution is more skewed
Summary
Charts for Joint Monitoring of the Lognormal Mean and Standard. Hryniewicz, Fadel Megahed, Alejandro F Villaverde and Sergei D. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
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