Signed log-likelihood ratio test for the scale parameter of Poisson Inverse Weibull distribution with the development...

Area of Science:

• Statistics
• Reliability Engineering
• Survival Analysis

Background:

• The Poisson Inverse Weibull (PIW) distribution provides a flexible model for system failure times.
• Hypothesis testing for parameters in complex distributions is crucial for accurate reliability analysis.

Purpose of the Study:

• Introduce and evaluate the signed log-likelihood ratio test (SLRT) for the scale parameter of the PIW distribution.
• Compare the performance of SLRT against the asymptotic normality of maximum likelihood estimators (ANMLE) test.

Main Methods:

• Simulation studies were conducted to assess Type I error rates and empirical power.
• The SLRT's performance was evaluated across various sample sizes and parameter configurations.
• A web application, PIW4LIFETIME, was developed for practical implementation.

Main Results:

• SLRT consistently maintained Type I error rates within the acceptable range (0.04-0.06) at a 0.05 significance level.
• SLRT demonstrated superior empirical power compared to ANMLE, particularly in small samples (n=10, 15).
• ANMLE was often conservative and showed lower power in small samples, though its power approached SLRT's with larger sample sizes.

Conclusions:

• The SLRT is a robust and reliable method for hypothesis testing in the PIW distribution, outperforming ANMLE, especially with limited data.
• The developed PIW4LIFETIME web application facilitates practical application of the SLRT for analyzing system failure data.
• The study highlights the SLRT's effectiveness and the utility of the PIW distribution in reliability engineering.