Monitoring Dispersion in Non-Normal Processes with Unknown Parameters

The article presents an analysis of dispersion control charts commonly used in process monitoring, namely R,S and S_p charts. These charts are utilized to track the variation (σ) in non-normal distributions, which is frequently encountered in real-world scenarios. The research also focuses on situations where the process's in-control dispersion is un- known and control limits are estimated based on preliminary Phase I data. Moreover, the study investigates the performance of the proposed dispersion monitoring scheme by comparing it with existing methods, employing the probability of signal as a performance metric. The efficacy of the proposed approach is further demonstrated through the examination of two medical datasets, showcasing its practical application. The adjusted constants proposed in this work are more generalized and result in the correct decision regarding the actual state of control. The IC robustness comes at the cost of a deterioration (increase) in the unconditional OOCARL, but this effect is negligible for large values of m or significant changes in variability. When applying these limits, prior knowledge of the underlying distribution is crucial, which poses a practical limitation on the proposed strategy.