Assessing the lifetime performance index with Lomax distribution based on progressive type I interval censored sample

Area of Science:

• Industrial Engineering
• Statistical Quality Control
• Reliability Engineering

Background:

• The lifetime performance index (LPI) is crucial for evaluating larger-the-better quality characteristics in manufacturing.
• Accurate LPI estimation is vital for ensuring products meet desired lifetime performance levels.

Purpose of the Study:

• To develop a robust method for estimating the LPI using the Lomax distribution.
• To establish hypothesis testing procedures for product quality assessment based on LPI.

Main Methods:

• Maximum Likelihood Estimation (MLE) for LPI under progressive type I interval censoring.
• Delta method for constructing asymptotic confidence intervals for LPI.
• Hypothesis testing procedures for LPI with a given lower specification limit and known scale parameter.

Main Results:

• The study derives the MLE for the LPI with two unknown parameters in the Lomax distribution.
• Asymptotic confidence intervals for the LPI are developed using the delta method.
• Effective hypothesis testing procedures are established for quality inspection.

Conclusions:

• The proposed methods provide efficient and implementable algorithms for assessing product lifetime performance.
• The developed techniques enhance quality control in manufacturing by offering reliable LPI estimation and hypothesis testing.
• The study validates the proposed inspection procedures with a real-world manufacturing example.