Robustness Evaluation of the Process Capability Index C (Profile) for a Simple Linear Profile under Various Error Distributions

This study investigates the robustness of the C" (Profile) for SLPs when the normality assumption of error terms is violated. We use extensive simulations to assess how non-normal errors, such as those from a skewed gamma distribution and a heavy-tailed t-distribution, affect the performance index, evaluated via the absolute percentage error (APE) criterion. The results of simulation studies reveal that while the index shows sensitivity to non-normality at small sample sizes (m ≤۵۰), its performance becomes increasingly robust as sample size grows (m≥ ۱۰۰). Our findings reveal significant differences in estimation accuracy across error terms distribution types, with non-normal distributions requiring approximately double the sample size to achieve comparable APE to normal distributions. These insights offer practical valuable guidance for quality control professionals applying profile capability analysis in industrial settings where the assumption of normality is often untenable.

کلیدواژه ها:

Statistical Process Control ، Simple Linear Profile (SLP) ، Non-normality ، Process Capability Index (PCI) ، Absolute Percentage Error (APE) ، ANOVA