A MC‐PSO approach to the failure probability evaluation of risky plant components: The maintenance design

A mandatory feature of the risky plants is the high reliability obtained through a careful engineering design joined with a well planned maintenance program. This latter aims at decreasing the wear thus rejuvenating the component age as if it had operated for a shorter time. The variable appearing in the failure distribution which rules the failures is then switched from chronological time to age and the (few) observed failures always occur during the early age of the component, i.e. from the lower tail of the true unknown distribution. Correspondingly, a first guess distribution based on the observed failures is strongly biased towards lower ages. In the present paper, we firstly consider the problem of estimating the true failure probability and then we apply the results to a maintenance design. In order to recover the true distribution, we propound resorting to the Particle Swarm Optimization (PSO) technique joined with a Monte Carlo (MC) simulation. We assume that the failures obey a Weibull distribution and that a set of real data has been observed from which a reference distribution has been guessed. In the PSO approach a set of agents move within the space of the two Weibull parameters: in correspondence of each location of each agent the corresponding distribution is computed and a sequence of failures is Monte Carlo sampled. The distribution thereby estimated is compared with the reference one until a match is found. The true distribution is then that corresponding to the coordinates of the agent which realized the match. Knowledge of the true failure distribution allows us to optimize the maintenance design and also to correctly compute quantities of interest involving the plant economy and the safety.