Condition-Monitoring-Based Reliability and Profit Optimization of PEM Electrolyser: A Multi-State Semi-Markov Approach with Derated Operation and Logistics Delay

Proton exchange membrane (PEM) water electrolysis is a key technology for converting renewable electricity into green hydrogen, and the availability of electrolyser stacks directly determines the hydrogen output and economics of such plants. This paper extends a previously reported ten-state semi-Markov reliability model of a PEM electrolyser into a twenty-state framework that better reflects field behaviour. The extension adds a derated, partial-output operating state for each of four degradation mechanisms (membrane, electrode, chemical and thermal), a spares-waiting state that separates logistics delay from active repair, a scheduled preventive-maintenance branch, and a rare catastrophic-shock branch, all treated as competing risks at the operative state. Closed-form steady-state expressions are derived for availability, mean time to system failure (MTSF) and maintenance-crew busy periods. A delta-method procedure converts sensitivity coefficients into a confidence interval on availability, and a profit function balances hydrogen revenue against inspection, derating, logistics and repair costs. Using plant rates from a pilot-scale electrolyser and literature-informed values for the new parameters, the model gives a steady-state availability of 0.8804 (95% CI: 0.778–0.983), a production-equivalent availability of 0.8856 that credits the output of derated states, an MTSF of about 5297 h and an illustrative net profit rate of $191.03/h after electricity cost. The results show that models omitting preventive maintenance and shock-type failures overstate electrolyser availability, with direct consequences for hydrogen supply planning and plant economics. Numerical Markov-chain solution and Monte Carlo simulation verify the closed-form results, and transient, sensitivity and operating-condition analyses identify membrane degradation as the mechanism whose maintenance matters most.