Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions

Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results failure due the accumulated damage. In statistics, asymmetric distribution, commonly used for describing fatigue life of materials, Birnbaum–Saunders (BS) distribution. This distribution can be transform normal symmetrical. Furthermore, variance examine dispersion data. However, comparing variances two independent samples that follow BS distributions has not previously been reported. To accomplish this, we propose methods providing confidence interval ratio based on generalized fiducial (GFCI), Bayesian credible (BCI), highest posterior density (HPD) intervals prior with partial information (HPD-PI) proper known hyperparameters (HPD-KH). A Monte Carlo simulation study was carried out efficacies terms their coverage probabilities average lengths. The indicate HPD-PI performed satisfactorily all sample sizes investigated. illustrate proposed real data, they were also applied 6061-T6 aluminum coupon fatigue-life datasets.