Reliability and Profit Analysis of a Five-Subsystem Hybrid Series-Parallel System with Gumbel–Hougaard Copula Repair, Cold Standby, and Dual Environmental Failure Rates

Abstract

This work offers a reliability framework for a five-subsystem hybrid series-parallel system representing smart factory monitoring infrastructure under heat and vibration stressors. A central programmable logic controller (1-out-of-1), pressure and temperature sensors (2-out-of-5), wireless communication units (2-out-of-4), solar power modules (3-out-of-6), and a cold standby database server (1-out-of-2) are connected in series. Unit failures are modeled using exponential distributions with component-specific failure rates and two environmental failure rates for thermal stress (α6) and vibration stress (α7) which go beyond the single-parameter models used in prior research. Repair of degraded states is governed by general distributions. The Gumbel–Hougaard copula family deals with total failure states, permitting positive repair time dependence due to common maintenance resources and environmental recovery. The state probabilities are obtained in closed form by using Laplace transforms and the supplementary variable method. Those state probabilities are used to find system availability, reliability, MTTF, sensitivity, indices and profit for three cases: copula-based repair, general distribution repair and a reduction technique with parameter ρ. Numerical analysis reveals steady state availability of 96.80%when using copula repair, and 99.35% when using the reduction technique (ρ = 0.2). Sensitivity analysis reveals that the solar power module subsystem is the main cause of MTTF degradation, however cost analysis reveals that proactive quality enhancement is more profitable than reactive repair options at all maintenance expenditure levels.