EWMA control chart framework for efficient Maxwell quality characteristic monitoring: An application to the aerospace industry

Abstract

The Maxwell distribution is extensively employed in statistical modeling to analyze data, notably in the fields of chemistry, astrophysics, demography, actuarial sciences, economics, industry, and engineering. Recently, the application of the Maxwell data generating process (DGP) has focused extensively on the domain of statistical control charts. The $V$ chart and $V_{SQ}$ chart are often used to identify unexpected changes in the distributional shift of the Maxwell process. The $V_{SQ}$ chart offers considerably better performance than the V chart for detecting moderate to large shifts in the scale parameter. However, the $V_{SQ}$ chart adopts the fundamental structure of the Shewhart monitoring scheme and is insensitive to small alterations in the target parameter. We propose a new control chart, namely, the Maxwell exponentially weighted moving average (MXEWMA) chart, for improved monitoring of quality attributes that are assumed to conform to Maxwell data generation. The factors used to design the parameters of the proposed chart are computed at different false alarm probabilities and across various sample sizes. The effectiveness of the suggested scheme is considered in terms of the different features of the run length (RL) distribution, including the average, median and standard deviation. A comparative study of the MXEWMA chart with the existing $V_{SQ}$ chart was performed across various sample sizes. The comparative analysis showed that the MXEWMA chart is an effective alternative and performs well in detecting reasonably small shifts in the parameter. Simulated data are employed to describe the computational procedure of the MXEWMA scheme. The simulation analysis demonstrated that the MXEWMA chart outperforms the existing method in identifying slight changes in the studied parameters. A real dataset is also considered to support the theoretical part of the work.