Inference on the triple modular redundancy system based on exponential distribution under type-I hybrid step-stress model with type-II censoring

This research introduces a novel hybrid model for the step-stress accelerated life test in which the stress transitions from a low level to a high level following a certain number of failures or a pre-determined time, whichever comes first. The stress is applied to the triple modular redundancy system, in which each device has a lifetime subjecting to the exponential distribution. This hybrid model significantly reduces testing time under a designated stress level. The test study also examines a simple step-stress testing scenario, concluding based on the type-II censoring scheme. Stress elevation follows the tampered hazard rate model. To estimate the reliability of the triple modular redundancy system and its mean time to failure, point and interval estimates for relevant parameters are determined using maximum likelihood and maximum product of spacings methods. Additionally, optimal timing for raising applied stress is explored, through two different approaches. The effectiveness of estimation methods is examined through the analysis of real-world data and Monte Carlo simulations. While both estimation methods yield convergent results, the maximum likelihood method proves to be more accurate, especially in the case of small sample sizes.