Statistical Inferences for the Lifetime Performance Index of the Products with the Gompertz Distribution under Censored Samples

Abstract

Manufacturers often apply process capability indices in the quality control. This study constructs statistical analysis methods of assessing the lifetime performance index of Gompertz products under progressively type II right censored samples. The maximum likelihood estimator of the index is inferred by data transformation and then utilized to develop a hypothesis testing procedure and a confidence interval to assess product performance. We also give one example and some Monte Carlo simulations to assess the behavior of the testing procedure and confidence interval. The results show that our proposed method can effectively evaluate whether the lifetime of products meet the requirement.

Keywords:

• Gompertz distribution
• Lifetime performance index
• Maximum likelihood estimator
• Monte Carlo simulation
• Progressively type II right censored sample

Mathematics Subject Classification:

• Primary 62P30
• Secondary 62N03