A new multi-objective optimization model for preventive maintenance and replacement scheduling of multi-component systems

In this article, a new multi-objective optimization model is developed to determine the optimal preventive maintenance and replacement schedules in a repairable and maintainable multi-component system. In this model, the planning horizon is divided into discrete and equally-sized periods in which three possible actions must be planned for each component, namely maintenance, replacement, or do nothing. The objective is to determine a plan of actions for each component in the system while minimizing the total cost and maximizing overall system reliability simultaneously over the planning horizon. Because of the complexity, combinatorial and highly nonlinear structure of the mathematical model, two metaheuristic solution methods, generational genetic algorithm, and a simulated annealing are applied to tackle the problem. The Pareto optimal solutions that provide good tradeoffs between the total cost and the overall reliability of the system can be obtained by the solution approach. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.     

A Bayesian perspective on age replacement with minimal repair

In this article, a Bayesian approach is developed for determining an optimal age replacement policy with minimal repair. By incorporating minimal repair, planned replacement, and unplanned replacement, the mathematical formulas of the expected cost per unit time are obtained for two cases – the infinite-horizon case and the one-replacement-cycle case. For each case, we show that there exists a unique and finite optimal age for replacement under some reasonable conditions. When the failure density is Weibull with uncertain parameters, a Bayesian approach is established to formally express and update the uncertain parameters for determining an optimal age replacement policy. Further, various special cases are discussed in detail. Finally, a numerical example is given.     

Finite-horizon equipment replacement analysis

The optimal solution to the infinite-horizon equipment replacement problem with stationary costs is to continually replace an asset at its economic life. The economic life is the age that minimizes the Equivalent Annual Cost (EAC), which includes purchase, operating and maintenance costs less salvage values. We explore the question of whether this is a good policy for the finite-horizon problem, which occurs when companies only require an asset for a specified length of time, usually to fulfill a specific contract. We identify cases, according to capital costs, operating costs, and the interest rate, when this policy is good and when it deviates significantly from optimal. Furthermore, we provide a bound on the minimum number of times that an asset is retained at its economic life over a finite horizon. This is facilitated through a new dynamic-programming formulation to the problem based on the integer-knapsack problem with nonlinear costs. The bound can be derived from any feasible solution, although we provide a closed-form solution for the case of convex EAC values.     

Age replacement policy in the case of no data: the effect of Weibull parameter estimation

Age replacement is a common maintenance policy when wear-out failures occur, and it is characterised by periodic replacement of components. Data on time to failure (TTF), often modelled with the Weibull function, are necessary for estimating optimal replacement intervals to minimise the total maintenance costs. In many cases, such as new components, new machines or new installations, no TTF data are available, so the Weibull parameters and optimal replacement interval cannot be estimated. To overcome this problem, these parameters can be assessed from the experience of the maintenance engineers and technicians. The aim of this study is investigating the relationship between the error in parameter estimation and additional maintenance costs related to this error. Analysis of variance (ANOVA) and multifactorial analysis are carried out for investigating the influence of these estimations on the final costs. Economic decision maps are introduced for supporting maintenance engineering in defining the maintenance policy with minimal additional cost in the case of no data being available. The analysis shows that, when no data are available, the application of the age replacement policy can result in a global saving of more than 50% compared with corrective maintenance.     

An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon

It is difficult to find the optimal solution of the sequential age replacement policy for a finite-time horizon. This paper presents an accurate approximation to find an approximate optimal solution of the sequential replacement policy. The proposed approximation is computationally simple and suitable for any failure distribution. Their accuracy is illustrated by two examples. Based on the approximate solution, an approximate estimate for the total cost is derived.     

Optimal periodic replacement for a deteriorating production system with inspection and minimal repair

Here we discuss an inspection policy model for a deteriorating production system with minimal repair. A minimal repair is resorted to as and when the system is found to be in a failed state during an inspection unless it is apre-set overhaul/replacement time in which case the system is overhauled or replaced. Using a dynamic programming formulation, and assuming that the cost of minimal repair is a non-decreasing function of age, we arrive at the optimal inspection time that maximizes the profit per unit time for a given overhaul/replacement time. The procedure is then extended to determine the optimal periodic overhaul/replacement time and the corresponding optimal number of inspections and their schedule.     

Simulation of an integrated age replacement and spare provisioning policy using SLAM

This paper presents a SLAM simulation model for determining a jointly optimal age replacement and spare part provisioning policy. The policy, referred to as a stocking policy, is formulated by combining age replacement policy with a continuous review (s, S) type inventory policy, where s is the stock reorder level and S is the maximum stock level. The optimal values of the decision variables are obtained by minimizing the total cost of replacement and inventory. The simulation procedure outlined in the paper can be used to model any operating situation having either a single item or a number of identical items. Results from a number of case problems specifically constructed by 5-factor second order rotatory design have been presented and the effects of different cost elements, item failure characteristics and lead time characteristics have been highlighted. For all case problems, optimal (s, S) policies to support the Barlow-Proschan age policy have also been determined. Simulation results clearly indicate the separate optimizations of replacement and spare provisioning policies do not ensure global optimality when total system cost has to be minimized.     

Cost-Variability-Sensitive Preventive Maintenance Considering Management Risk

Traditional preventive maintenance policies, such as age replacement, periodic replacement under minimal repair, and replacement policy N, are all studied based on the expected cost criteria without considering the management risk due to the cost variability. As a result, these policies could be significantly beyond the anticipated maintenance budget allocation and lead to crisis. In order to solve this problem, a new analysis methodology is proposed in this paper to consider the effects of both cost expectation and cost variability on the optimal maintenance policy. A new concept of the long-run variance of the cost is defined to represent the maintenance management risk, and then the objective function is revised accordingly to achieve an optimal cost-variability-sensitive maintenance policy. Based on the proposed framework, three traditional preventive maintenance policies have been reinvestigated and the effect of the variability sensitivity on the optimal policies is further analyzed, which reveals general management insights and explicates the search bound of the optimal solution. An example is given to illustrate the importance and the effectiveness of the proposed methodology. Compared with the traditional optimal maintenance policy, the numerical solution shows that the proposed variability-sensitive optimal policies can significantly reduce the maintenance management risk with only a small increase in the expected cost.     

Optimal age replacement scheduling for a random work system with random lead time

System maintenance and spare parts are two closely related logistics activities since maintenance generates the demand for spare parts. Most studies on integrated models of preventive replacement and inventory of spare parts have focused on age replacement scheduling, while random replacement policy, which is sensible and necessary in practice, is rarely discussed and applied. The purpose of this paper is to present a generalised age replacement policy for a system which works at random time and considers random lead time for replacement delivery. To model an imperfect maintenance action, we consider that the system undergoes minimal repairs at minor failures and corrective replacements at catastrophic failures. Before catastrophic failures, the system is replaced preventively at age T or at the completion of a working time, whichever occurs first. The main objective is to determine an optimal schedule of age replacement that minimises the mean cost rate function of the system in a finite time horizon. The existence and uniqueness of optimal replacement policy are derived analytically and computed numerically. It can be seen that the proposed model is a generalisation of the previous works in maintenance theory.     

Optimal machining conditions and buffer space size for the two-stage case

This paper presents a model for calculating optimal cutting speeds and tool replacement policies for both operations of a two-stage machining problem when the unit cost is minimized or the profit rate is maximized. The tool life is assumed to be a stochastic variable and penalty costs are imposed for tool failures during production. The optimal size of buffer space between the two machines is also calculated analytically. It is shown that the unit cost increases as the tool variability and/or the penalty cost increase. The cutting speeds and tool replacement policies on both operations depend strongly on the tool variability and the penalty cost. The cutting speeds differ from those determined independently for each operation. Finally, the optimal buffer space size is the one necessary to keep the critical machine running when there is a tool change on the non-critical machine, and its optimal size can be calculated analytically.