Parametric inference of the process capability index for exponentiated exponential distribution.

Area of Science:

• Industrial Engineering
• Statistical Quality Control
• Reliability Engineering

Background:

• Process Capability Indices (PCIs) are vital for evaluating product quality and manufacturing process performance.
• The PCI C, based on the proportion of conformance, is versatile, applying to various distributions (normal, non-normal, continuous, discrete).
• Accurate estimation of PCI C is essential for effective quality management.

Purpose of the Study:

• To estimate the PCI C for processes following exponentiated exponential and generalized Rayleigh distributions.
• To compare the performance of five classical estimation methods regarding bias and Mean Squared Error (MSE).
• To construct and evaluate five Bootstrap Confidence Interval (BCI) methods for PCI C using Monte Carlo simulations.

Main Methods:

• Estimation of PCI C using five classical methods for exponentiated exponential distribution.
• Performance evaluation of estimators via bias and MSE through simulation.
• Construction of five BCIs for PCI C.
• Comparison of BCIs based on average width and coverage probabilities via simulation.
• Net Sensitivity (NS) analysis for PCI C.
• Application to electronic, food, and failure time industry data sets.

Main Results:

• Comparison of classical estimators revealed varying performance based on bias and MSE.
• Bootstrap confidence intervals demonstrated differences in average width and coverage probabilities.
• The study illustrates the practical application of the methods using real-world data.
• PCI C was successfully developed for generalized Rayleigh distribution.

Conclusions:

• The study provides a comprehensive comparison of estimation methods and BCIs for PCI C.
• The findings aid in selecting appropriate methods for quality assessment in diverse industrial settings.
• The developed methods enhance the reliability of process capability analysis for non-standard distributions.