Reliability Analysis of a k-out -of-n:G System with Preventive Maintenance, Irrepairable Component Failures, and Spare Replenishment Policies

This paper investigates a k−out-of−n : G system consist- ing of identically distributed components subject to exponential fail- ure. Failed components are assumed to be irreparable and are replaced through a spare replenishment mechanism. Preventive maintenance is initiated either when the number of failed components reaches a prede- termined threshold L(k < L < n) or after an Erlang-distributed inspec- tion interval. During each preventive maintenance epoch, components exhibiting minor degradation are identified and arranged in a queue in a descending order of maintenance urgency. Additionally, when the num- ber of failed components reaches a lower threshold M, (k < M < L), a replenishment order for n− k +1 spare components is triggered. A single repair facility is assumed, where the repairman attends to components whenever the maintenance queue is non-empty and takes a vacation once all queued maintenance tasks are completed. The proposed model pro- vides a comprehensive framework for analyzing system reliability and supports effective maintenance and spare inventory planning in complex engineering systems.