研究目的
To investigate the efficiency of Gini’s mean difference (GMD) as a measure of variability in two commonly used process capability indices (PCIs), i.e., Cp and Cpk, and to compare the performance of GMD-based PCIs and Pearn and Chen quantile-based PCIs under low, moderate, and high asymmetry using Weibull distribution.
研究成果
The study concludes that GMD-based PCIs perform better than quantile-based PCIs under low and moderate asymmetry levels, providing lower bias and mean square error (MSE). For high asymmetry, GMD-based PCIs are more robust and give higher values, indicating better process capability. The bias corrected percentile bootstrap (BCPB) method is recommended for constructing confidence intervals for both Cp and Cpk using GMD-based estimators.
研究不足
The study is limited to Weibull distribution for evaluating the performance of GMD-based and quantile-based PCIs. The effectiveness of these methods for other non-normal distributions is not explored.
1：Experimental Design and Method Selection:
The study uses Gini’s mean difference (GMD) as a measure of variability in process capability indices (PCIs) Cp and Cpk. It compares the performance of GMD-based PCIs with Pearn and Chen quantile-based PCIs under different levels of asymmetry using Weibull distribution.
2：Sample Selection and Data Sources:
Data sets of size n = 25,50,75 and 100 are generated using each asymmetric level of Weibull distribution.
3：List of Experimental Equipment and Materials:
Not explicitly mentioned in the paper.
4：Experimental Procedures and Operational Workflow:
The study involves simulation to evaluate the performance of GMD-based and quantile-based PCIs under low, moderate, and high asymmetry levels. Nonparametric bootstrap confidence intervals are calculated for both methods.
5：Data Analysis Methods:
The performance of the PCIs is evaluated based on mean square error (MSE) and coverage probabilities of bootstrap confidence intervals.
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