Generalized Fiducial Inference for Accelerated Life Tests With Failure-Free Life Based on Three-Parameter Weibull Distribution

Assessing the lifetime of products or materials effectively is essential for formulating maintenance strategies and warranty policies. With advancements in engineering technology, high-reliability, long-lifetime products are becoming increasingly common. To quickly obtain lifetime data for such products, constant-stress accelerated life tests (CSALT) have been widely employed. The failure-free life (FFL) characterizes the early stage during which these products experience no failures, and the three-parameter Weibull distribution (TPWD) models FFL through its threshold parameter. However, the effect of acceleration on the threshold parameter has not been adequately investigated, particularly in terms of modeling and estimation. To solve the above problem, first, we introduce a modeling approach based on the LCEM and fatigue theory, which accounts for the acceleration of the threshold parameter in CSALT. Applied to TPWD, the resulting model is referred to as CSALT-TPWD. Then, we examine the nonregular problem in the maximum likelihood estimation of CSALT-TPWD. Next, generalized fiducial inference is employed to provide both point and interval estimates. Furthermore, to enhance the sampling efficiency of the posterior distribution, a Hadamard-based ℓ ² norm prior is proposed. Theoretical analysis confirms that this prior accelerates computation compared to other commonly used norms, while preserving the value of the traditional ℓ ² norm prior. Finally, numerical simulations and real case analysis demonstrate that the proposed method captures the characteristics of FFL effectively.