A Fuzzy Approach to Availability Assessment of Dual Operative and Dual Warm Standby Units subjected to Partial Failure and Imperfect Repair Mechanism

This paper presents a comprehensive fuzzy reliability and availability analysis of a machinery system consisting of two active operating units and two warm standby units. The model incorporates several realistic degradation mechanisms like partial failure effects, system reboot (restart) after minor faults, partial repair rate (where repaired units return in degraded operating state), and common cause shock failure affecting multiple units simultaneously. Classical crisp parameters are replaced by triangular fuzzy numbers to capture inherent uncertainty in failure and repair rate data. The state-space model is formulated and solved analytically to derive system reliability R(t), Mean Time to System Failure (MTTF), and steady-state availability. Sensitivity analysis using α-cut technique reveals how system performance indices vary with key fuzzy parameters. Numerical results demonstrate that partial failures and common cause shocks significantly degrade system availability, whereas warm standby units and rebooting mechanisms offer substantial improvement. The findings provide a decision-support framework for maintenance engineers in industrial environments where data imprecision is unavoidable.