Reliability optimization for series systems under uncertain component failure rates in the design phase

We develop an optimization model to determine the reliability design of critical components in a serial system. The system is under a service contract, and a penalty cost has to be paid by the OEM when the total system down time exceeds a predetermined level, which complicates the evaluation of the expected cost under a given reliability design. Furthermore, in the design phase for each critical component, all possible designs are subject to uncertain component failure rates. Considering the computational intractability of evaluating the system performance, we develop approximate evaluation methods which take the system uncertainty into account. Numerical results show that the method which includes randomness in the number of failures, failure rates and repair times leads to efficient and accurate evaluations and to close-to-optimal design decisions when used in an enumeration procedure for the optimization problem. We also show that ignoring these three types of uncertainty may result in bad design decisions.