Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair

Abstract

Abstract This paper develops simultaneous confidence bands using computer intensive methods based on resampling, for the expected discounted warranty costs in coherent systems under physical minimal repair, that is, when the system is observed at its components level and only the component that causes the fault is minimally repaired. For this purpose, it is shown that, under the framework of the Martingale processes and the central limit resampling theorem (CLRT) over stochastic processes, the discounted warranty cost processes satisfy the conditions set by the central limit resampling theorem (CLRT). Additionally, a simulation study is performed on the most relevant variables, such that the finite sample features of the proposed bands may be assessed, based on their actual coverage probabilities. The results in the considered scenarios show that resampling-based simultaneous confidence bands have coverage probabilities that are close to the nominal coverage. In particular, the agreement is good when there are 100 systems or more where a large number of resamples are used for the approximation.

Keywords

• Central Limit Theorem
• Coverage Probability
• Point Process
• Resampling
• Semimartingales
• Weak Convergence