Approximate Bayesian Computation for a Dual-Failure-Modes Models and Its Application to Failure Times Data

In this study, comprehensive approximate Bayesian computation (ABC) technique is explored, and develop for an innovative model. We practically demonstrate approximate Bayesian computation (ABC)-Gibbs scheme using Kolmogorov-Smirnov as distance function; this method is a simulation-based scheme, which the explicit formulation of the likelihood function is not required, hence, suitable for a complex model or big data, where the “accept-reject” mechanism is required for the posterior computation. The proposed ABC-Gibbs algorithm presents a remarkable computational efficiency and accuracy in simulation studies and practice. Additionally, we utilize an adaptable Weibull related lifetime distribution for the purpose of testing the proposed algorithm. The model was designed for the analysis of complex systems exhibiting bathtub-shaped failure rate, and its termed as the two-parameter-modified-Weibull-Chen (TMWC). Some vital reliability characteristics of the TMWC are derived, applied and thoroughly discussed. The TMWC model show its significance within reliability frameworks, notably presenting a bathtub-shaped failure rate with an extended-flat-region, presenting a distinctive burn-in and wear-out periods. Extensive simulation studies were conducted to evaluate the performance of ABC-Gibbs on TMWC. Results showed that incorporating the KS distance metric lead to significant improvement; as we decreases the tolerance threshold, the ABC posterior converges more accurately to the true posterior, though with a lower acceptance rate. Finally, a practical study involving the modeling of two failure datasets with a bathtub failure rate is presented-namely, the failure times of thirty devices, and the failure times of dielectric insulation in a generator armature. This study confirms the practical efficiency of the TMWC model and the ABC-Gibbs methodology in reliability engineering.