Absolute Deviation-Based Control Charts for Monitoring Mean of Weibull Distribution With Type-I Censoring

Abstract

This article presents deviation based exponentially weighted moving average control charts to monitor type-I censored data. Due to practical applications, this study considers Weibull distribution to assess the performance of the proposed memory-type control charts. The censored observations are replaced with the conditional expected value (CEV), conditional median (CM), and conditional standard deviation (CSD) to assess the performance of the charts. Various shifts, smoothing weights, and censoring rates are used to compare the effectiveness of different conditional measures. Besides average run length, the standard deviation of the run length is also used to compare different deviation based charts. In addition to a comprehensive simulation study, two real data sets (industrial thermostat and melt index experiments) are also discussed to illustrate the practical applications of the proposed charts.

Keywords

• Absolute deviation
• EWMA
• DEWMA
• Weibull distribution
• conditional expected value
• conditional median