A Standard Deviation Control Chart for Marshall–Olkin Alpha Power Inverse Rayleigh Distribution

Abstract

The conventional SPC charts, including the Shewhart standard deviation chart, are prone to failure due to skewed or heavy-tailed data, resulting in false alarms and an inability to detect shifts in variability. The primary objective of this study is to develop a deviation control chart based on percentiles of the Marshall-Olkin Alpha Power Inverse Rayleigh Distribution (MOAPIRD) of non-normal processes. Empirical MOAPIRD percentiles are used to derive the control limits giving correct probability limits. The simulations of different parameters and sample sizes demonstrate that MOAPIRD chart can have a large average run length (ARL) and very low standard deviation of run length (SDRL) in most scenarios, it outperforms other techniques like the Shewhart and Inverse Rayleigh distribution charts. The chart is validated against real engine oil viscosity data which confirms the reliability of the chart which effectively accommodates skewness and heavy tails without spurious uncontrolled signals. The chart based on MOAPIRD is suggested when it is necessary to accurately monitor the variability of the processes in the unusual industrial settings.