Fuzzified imperfect repair redundant machine repair problems

The implication of machine repair problems in the continued functioning of real-time machining models keeps growing with the advent of technology for socioeconomic progression, mobility, security, and safety. The uninterrupted functioning of critical appliances, monitoring controllers, next-generation devices, workstations, and data exchange systems is expected whenever needed prompt. When active units fail, the results may be catastrophic, injury, or loss, leading to critical reliability challenges that must be resolved. This article aims to provide a comprehensive, state-of-the-art study for failure/repair/operation uncertainties and impreciseness in optimistic and pessimistic conditions. We consider the fault-tolerant machining system consisting of two-active units, a single-warm standby unit, and a single-repair facility in a fuzzy environment governing the involved imperfectness, vagueness, uncertainty. Switching the standby unit to the failed active unit is also subject to failure. The notion of imperfect repair makes the proposed model more insightful. A membership grade function of the reliability characteristics: mean time-to-failure and system availability are constructed to study uncertainties in-depth for the fault-tolerant redundant repairable system with switching failure and imperfect repair for well to poor design. The nonlinear parametric program technique converts the studied problem into a set of conventional problems. It is employed to compute the upper and lower bounds of the reliability characteristic based on the $$\gamma$$ γ -cut approach and Zadeh’s extension principle for extreme design constrained limits. Extensive numerical simulations are also performed for the different sets of governing parameters ranging from well-conditioned to ill-conditioned. The concluding remarks and future scopes are also included.