Reliability estimation under cyclic accelerated life-testing based on scale family of distributions

The Norris–Landzberg model is extensively used to model crack growth due to thermal cyclic stress, taking into account a more realistic set of factors compared to the Coffin–Manson model. Despite its merits, the Norris–Landzberg model faces challenges when used with multiple linear regression without distributional assumptions, potentially leading to unsatisfactory statistical outcomes. To counter this, in this work, we assume a general scale distribution family, ensuring that the least squares method yields the best linear unbiased estimator (BLUE) of model parameters. We integrate the Kaplan–Meier estimator with accelerated failure time modeling to develop a semi-parametric reliability assessment methodology. We then discuss the properties and advantages of this methodology compared with the traditional maximum likelihood estimation (MLE). It provides the best fit for parameters and the reliability function in small sample situations when the true distribution is unknown. We also have proposed an optimal design procedure. Finally, an illustrative example is presented, demonstrating the model's effectiveness and the inferential results developed from our approach.