Availability Maximization and Cost Study in Multi-State Systems

The paper presents a method for determining an optimal loading in series-parallel systems. The optimal loading is aimed at achieving the greatest possible expected system availability subject to required demand constraint. Then the corresponding system cost is deduced. We consider that system cost is a combination of downtime cost (loss of productivity), and repair cost (supposed proportional to repair time). The former is affected by a penalty value which reflects the importance of downtime cost with respect to repair cost. The model takes into account the relationship between the element failure rate and its corresponding load (element capacity). The universal generating function model is used to assess the performance distribution of the entire system and the system availability (knowing the probability of each performance level). Then, the unavailability and the repair time are estimated in order to study the system cost. The optimization is done for different values of required demand. The effect of required demand on the system availability and system cost is studied. The optimization technique is based on the genetic algorithm in order to determine the optimal load distribution. An illustrative example is presented.