A comparative analysis of mean charts assuming Weibull and generalized exponential distributions

Abstract

This study discusses Shewhart control charts to monitor the mean of non-normally distributed data using extensive Monte Carlo simulations. In particular, Weibull, exponential, and generalized exponential distributions are used to conduct a systematic study. Different parameters settings are considered to evaluate the effectiveness of the Shewhart charts based on the normal approximation. The results show significant differences between the charts using generalized exponential and Weibull distributions. In particular, the generalized exponential distribution based chart achieves the desired average run length of 370 with a single threshold value across a wide range of shape parameter combinations. On the other hand, the Weibull distribution requires different threshold values depending on its shape parameter. These findings highlight the significance of the two most commonly used distributions in reliability studies and their impact on control chart performance.

Keywords

• Average run length
• Generalized exponential distribution
• Mean chart
• Statistical process monitoring
• Weibull distribution