Estimation of mixture Maxwell parameters and its possible industrial application

- Mixture Maxwell distribution has been proposed along with control chart application.
- The EM algorithm has been used for parameter estimation.
- Proposed chart performs better than control chart for regular Maxwell distribution.
- To monitor a process with subpopulations, this distribution could be used.

Problem statementThe 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.ObjectiveTo 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.MethodFor 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.ResultsWe 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.ConclusionAs 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.