Statistical inference of the generalized process capability index for the discrete lindley distribution

Area of Science:

• Industrial Engineering
• Statistical Quality Control
• Reliability Engineering

Background:

• Process capability (PC) indices are crucial for evaluating manufacturing process performance.
• Existing PC indices are primarily designed for continuous processes, leaving a gap for discrete applications.
• The discrete Lindley distribution is a relevant model for certain discrete processes.

Purpose of the Study:

• To introduce a novel generalized process capability (PC) index for discrete processes.
• To develop and evaluate estimation methods for this new discrete generalized PC index.
• To explore interval estimation techniques for enhanced process performance assessment.

Main Methods:

• Development of a new generalized PC index formula for discrete distributions.
• Application of estimation methods, including maximum likelihood, for the discrete generalized PC index.
• Utilization of non-parametric bootstrap methods (standard, percentile, student, bias-corrected percentile) for interval estimation.

Main Results:

• The study successfully defined a new generalized PC index for discrete processes.
• Simulation results indicated that maximum likelihood and bias-corrected percentile bootstrap methods provided superior performance.
• Bootstrap methods offered valuable interval estimates, complementing point estimates.

Conclusions:

• The proposed generalized PC index effectively addresses the need for assessing discrete process capabilities.
• The maximum likelihood and bias-corrected percentile bootstrap methods are recommended for practical application.
• The findings are validated through real-world case studies, demonstrating practical utility.