A constructive algorithm to maximize the useful life of a mechanical system subjected to ageing, with non-resuppliable spares parts

Abstract

In this paper, the focus is on mechanical systems that, like a ship or a submarine, perform risky missions and that must remain operating for the whole mission time. Missions take place far from the operational base and so, in case of failures, although repairs are possible, spares parts cannot be resupplied. Hence, given space constraints, the problem is to define the optimal set of spare parts that should be taken aboard, to maximize the probability to complete the mission. To solve this problem, we propose a constructive algorithm that generates the Pareto Optimal Frontier of all the non-dominated solutions, in terms of the system's reliability and of required space. At first, the algorithm is formulated in a generic way; next, it is contextualized to the common case of Weibull distributed failure times. In this condition, the underlying equations of the model cannot be solved in closed form and an approximated procedure is proposed and validated through extensive numerical simulation.

Hierarchical spline for time series prediction: An application to naval ship engine failure rate

“…So, defining the optimal set of spare parts is crucial for mission success. 2 For accurate prediction, several special features resulting from the navy's system should be noted. First of all, imbalances are observed in two categories of the data: age period and engine types.…”

“…Moreover, from a system point of view, overestimation induces unnecessary use of budget and even leads to inventory shortage for other ships. So, defining the optimal set of spare parts is crucial for mission success 2 …”

“…However, it had limits in determining the parameter. Zammori et al 2 tried to solve the problem of parameter estimation of Sherbrooke's 10 model by applying time series Weibull distribution. Other attempts such as Pareto‐optimal, Monte‐Carlo, 10 ARMA, and least‐squares logarithm 9 have been made to add the effect of stochastic factors to this distribution.…”

Hierarchical spline for time series forecasting: An application to Naval ship engine failure rate

“…However, it had limits in determining the parameter. Zammori et al (2020) tried to solve the problem of parameter estimation of Sherbrooke's (2006) model by applying time-series Weibull distribution. Other attempts such as Pareto-optimal, Monte-Carlo (Sherbrooke, 2006), ARMA, and least-squares logarithm (Wang and Yin, 2019) have been made to add the effect of stochastic factors to this distribution.…”

“…Moreover, from a system point of view, overestimation induces unnecessary use of budget and even lead to inventory shortage for other ships. So, defining the optimal set of spare parts is crucial for mission success (Zammori et al, 2020).…”