Estimation of mixture Maxwell parameters and its possible industrial application

Problem statement The conventional methods of monitoring a process sometimes provide misleading results when the population consists of two or more subpopulations. Mixture distribution may provide better performance in this circumstance. Objective To establish a control chart named Mixture Maxwell Cumulative Quantity (MMCQ) control chart for two components Maxwell mixture distribution. This chart may be implemented to monitor non-conforming items in this process. Method For estimating the parameters, the Expectation-Maximization (EM) algorithm has been used. To measure performance and for comparison, the average run length (ARL) has been used. Results We compared this MMCQ control chart with MCQ control chart where MMCQ chart performs better as compared to MCQ chart. Performance of the chart was measured using run length and detection properties. Conclusion As one of non-normal skewed distributions, Maxwell distribution is studied to model control charts. To monitor time between events for processes with Maxwell subpopulations, the behavior of the control chart based on two components mixture Maxwell distribution were examined.