DOI: 10.1515/eqc-2025-0055 ISSN: 2367-2390
Control Chart for Mean Under OPPE Model
Sandipan Maiti, Subhradev Sen Abstract
The control limits for the
X
¯
{\bar{X}}
-control chart are derived under the assumption that the quality characteristic follows the one-parameter polynomial exponential (OPPE) family of distributions. The probability distribution of the subgroup means under the OPPE model is derived, along with its mean and variance, to construct the control limits of the chart. The control limits for the exponential, Lindley, and Sujatha distributions (particular cases of the OPPE distribution) have been demonstrated. The performance of the proposed control chart in terms of average run length (ARL) has been described, along with an illustration. Two real-life data sets and a synthetic data set have been analysed to demonstrate the proposed chart, and its ARLs are compared. It was found that the performance is better for certain OPPE distributions.