Abstract

Statistical Process Control (SPC) plays a vital role in monitoring and improving industrial processes. However, many quality characteristics, such as failure times, defect counts, waiting times, and repair durations, are strictly positive and highly skewed, violating the normality assumption underlying traditional Shewhart charts. The Xgamma distribution is a versatile and flexible mixture distribution suitable for modeling positive, right-skewed data in reliability, lifetime, and process monitoring studies, particularly when classical exponential or gamma models fail to adequately describe the tail behavior and variability. This study proposes an Individual (I) control chart based on Xgamma distribution, a suitable probability model capable of handling skewed and heavy-tailed data. A fourth-root transformation is employed to reduce skewness and achieve normality. Control limits are constructed using a percentile-based approach. The performance of the proposed chart is evaluated through a simulation study in terms of both in-control Average Run Length (ARL₀) and out-of-control Average Run Length (ARL₁). Simulation study results indicate that the proposed chart maintains the in-control ARL₀ while achieving smaller ARL₁ values under various shift magnitudes, demonstrating improved sensitivity to small and moderate process shifts compared with the exponential-based Individuals chart.

Keywords

Quality control, Statistical process control, Exponential distribution, Gamma distribution, Xgamma distribution, Control chart, Average run length.

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