Quantile-based reliability comparison of products: Applied to Log-normal distribution

Abstract

In this paper, reliability comparison indices are developed for log-normally distributed populations. In this regard, three indices are proposed for reliability comparison of products respectively in earlier, later, and entire stages of their lifetime. These indices are based on the confidence interval of difference between quantiles of two independent lognormal distributions. Therefore, we apply a generalized confidence interval (GCIN), and a method of variance estimates recovery (MOVER) to construct confidence intervals for difference between quantiles. The coverage probability and average length of the proposed approaches are compared through Monte Carlo simulations. The proposed indices and interval estimation methods are applied to a real world case study to show their application and performance in life data analysis.

Keywords:

• Reliability comparison
• log-normal distribution
• confidence interval
• quantile
• coverage probability
• generalized confidence interval

Notes

1 Uniformly Minimum-Variance Unbiased

2 Earlier Stage Reliability

3 Later Stage Reliability

4 Entire Stage Reliability