MIXTURE‑DISTRIBUTION MAINTAINABILITY MODELLING TO CAPTURE TAIL‑RISK DOWNTIME IN CRITICAL MACHINERY

Abstract

Maintainability modelling for critical machinery (e.g., gas turbines, offshore drilling rigs, medical imaging systems, nuclear reactor coolant pumps) traditionally relies on standard probability distributions such as the lognormal or Weibull to represent repair time. However, these unimodal models often fail to account for tail-risk downtime—rare but excessively long repair events caused by cascading failures, specialized part unavailability, or non-routine troubleshooting. Such tail events, while low in probability, disproportionately contribute to operational losses, safety violations, and regulatory non-compliance. This paper introduces a Mixture-Distribution Maintainability (MDM) framework that explicitly captures tail-risk downtime by combining a primary component (representing routine, fast repairs) with a secondary, heavy-tailed component (representing rare, prolonged interventions). Using a finite mixture of two lognormal distributions—or a lognormal-Pareto composite—the model yields maintainability metrics (e.g., mean time to repair, maximum time to repair, and the 95th percentile repair time) that are robust to tail sensitivity. Through a case study on centrifugal compressor repair logs (N=1,200 records), we demonstrate that a single lognormal fit underestimates the 95th percentile repair time by 31% compared to the MDM approach. We further develop a Bayesian estimation procedure to handle sparse tail data and provide a decision rule for classifying high-risk repair modes. The proposed MDM framework enables reliability engineers to quantify tail risk, optimize spare parts inventory, and design maintenance policies that are resilient to extreme downtime events.