Robust process capability indices C_pm and C_pmk using Weibull process.

Area of Science:

• Industrial Engineering
• Statistical Quality Control
• Manufacturing Process Analysis

Background:

• Process Capability Indices (PCIs) assess manufacturing quality, typically assuming normal distributions.
• Non-normal processes necessitate robust PCIs, with limited research on third-generation methods.
• Existing robust PCIs often focus on first- and second-generation approaches.

Purpose of the Study:

• To evaluate dispersion measures (MAD, IQR, GMD) in third-generation PCIs for non-normal processes.
• To construct bootstrap confidence intervals (CIs) for these robust PCIs.
• To compare the efficacy of these methods against quantile-based PCIs under Weibull process asymmetry.

Main Methods:

• Simulation of Weibull processes with varying asymmetry.
• Evaluation of Median Absolute Deviation (MAD), Interquartile Range (IQR), and Gini's Mean Difference (GMD) as dispersion measures.
• Construction and comparison of bootstrap confidence intervals (BCPB, PB, PTB).

Main Results:

• Quantile-based PCIs are sensitive to high process asymmetry.
• IQR performed poorly across all sample sizes.
• GMD showed good performance under asymmetry but requires careful handling; MAD excelled in low/moderate asymmetry.
• Recommended CIs: BCPB for quantile-based, PB/PTB for MAD-based PCIs.

Conclusions:

• The GMD method is a viable option for third-generation PCIs in asymmetric non-normal processes.
• MAD-based PCIs are effective under low to moderate asymmetry.
• Appropriate confidence interval selection is crucial for robust PCI estimation in non-normal manufacturing scenarios.