Reliability Analysis and Statistical Fitting for the Transmuted Weibull Model in R

Abstract

Accelerated life testing is a fundamental practice in reliability engineering, allowing the evaluation of component or device performance over extended lifetimes impractical to encounter during design. This study delves into the application of the transmuted Weibull distribution to model lifetime data, showcasing its versatility in real-world scenarios. The evaluation includes critical metrics such as Akaike’s information criterion (AIC), Bayesian information criterion (BIC), coefficient of determination, and standard error for distribution comparison. Utilizing Maximum Likelihood Estimation (MLE) for parameter estimation, a simulation study is conducted with varying sample sizes, and the R programming language is employed for in-depth analysis. Real data analysis involves comparing the Transmuted Weibull (twd) model with other models using goodness-of-fit criteria. Maximum Likelihood Estimates (MLEs) are obtained, and the likelihood ratio test demonstrates the (twd) model's superior alignment with the data. The study concludes with the simplicity of producing Quick Fit plots for analysis using R software. The presented approach provides a comprehensive understanding of reliability characteristics, combining theoretical insights with practical applications and numerical analyses