The Bootstrap S-chart for Process Variability: an Alternative to Mad Chart

In statistical process control, the control charts are the most powerful tools for assessing the process behaviour. The Shewhart S chart is a standard tool for determining process variability. Similar to S chart, the chart based on Median Absolute Deviation from the sample median namely MAD estimator is also considered robust for both normal and non-normal processes. As ̅ and are considered unbiased estimators of so the process standard deviation can be estimated but the true standard deviation cannot be found because only one specific sample is considered. Under the remarkable properties of bootstrap methods, we have proposed bootstrap S chart through which the true process standard deviation can be estimated. The performance of proposed chart is estimated on the basis of in-control average run length, coverage probability and confidence width. As a result the proposed chart has performed better than the traditional S and MAD charts under the assumption of normality. The simulation study based on monte-carlo runs is conducted for the purpose and the application on a practical data set is also discussed to justify the findings.