Reliability Assessment for Small-Sample Accelerated Life Tests with Normal Distribution

A significant challenge in the accelerated life test (ALT) is the reliance on large sample sizes and multiple stress levels, which results in high costs and long test durations. To address this issue, this paper develops a new reliability assessment method for small-sample ALTs with normal distribution (or lognormal distribution) and censoring. This method enables a high-confidence evaluation of the percentile lifetime (reliable lifetime) under normal operating stress level using censored data from only two accelerated stress levels. Firstly, a relationship is established between the percentile lifetime at normal stress level and the distribution parameters at accelerated stress levels. Subsequently, an initial estimate of the percentile lifetime is obtained from failure data, and its confidence is then refined using a Bayesian update with the nonfailures. Finally, an exact one-sided lower confidence limit (LCL) for the percentile lifetime and reliability is determined. This paper derives an analytical formula for LCLs under Type-II censoring scenarios and further extend the method to accommodate Type-I censored and general incomplete data. The Monte Carlo simulations and case studies show that, the proposed methods significantly reduce the required sample size and testing duration while offering superior theoretical rigor and accuracy than the conventional methods.