Parametric inference on partially accelerated life testing for the inverted Kumaraswamy distribution based on Type-II...

Area of Science:

• Reliability Engineering
• Statistical Inference
• Accelerated Life Testing

Background:

• Estimating product lifetime under stress is crucial for reliability.
• Traditional life testing can be time-consuming and expensive.
• Accelerated life testing (ALT) methods reduce testing time by applying higher stress levels.

Purpose of the Study:

• To develop estimation methods for step-stress partially accelerated life tests (SS-PALT) with Type-II progressively censored data.
• To model product lifetimes using the two-parameter inverted Kumaraswamy distribution.
• To compare the performance of Maximum Likelihood Estimation (MLE) and Bayesian estimation techniques.

Main Methods:

• Utilizing Type-II progressive censoring for efficient data collection.
• Calculating numerical Maximum Likelihood Estimates (MLEs) for unknown parameters.
• Constructing asymptotic interval estimates based on MLE properties.
• Applying Bayesian inference with symmetric and asymmetric loss functions.
• Employing Lindley's approximation and Markov Chain Monte Carlo (MCMC) for Bayes estimates.
• Calculating Highest Posterior Density (HPD) credible intervals.

Main Results:

• Numerical MLEs were computed for model parameters.
• Asymptotic confidence intervals were derived.
• Bayesian estimates were obtained using Lindley's approximation and MCMC.
• HPD credible intervals provided uncertainty quantification for parameters.
• The study demonstrated practical application through a real-world example.

Conclusions:

• Both MLE and Bayesian methods provide viable approaches for parameter estimation in SS-PALT.
• The inverted Kumaraswamy distribution is suitable for modeling lifetimes under these conditions.
• Progressive censoring enhances the efficiency of life testing experiments.
• The proposed methods offer robust tools for reliability assessment in engineering applications.