Abdelhakim Khatab

Selective maintenance optimization when quality of imperfect maintenance actions are stochastic

Abstract This paper addresses the selective maintenance optimization problem in a multi-component system, carrying out several missions with scheduled inter-mission breaks. To improve the probability of the system successfully completing the next mission, maintenance is performed on the system׳s components during the break. Each component is assigned a list of eligible maintenance actions ranging from minimal repair, through intermediate imperfect maintenance actions, to replacement. The quality of a maintenance action is assumed to be stochastic, reflecting the degree of expertise of the repairman and the tools used to perform the maintenance action. This quality is thus treated as a random variable with an identified probability distribution. The selective maintenance problem aims thus at finding a cost-optimal subset of maintenance actions, to be performed on the system during the limited duration of the break, which guarantees that the pre-set minimum probability of successfully completing the next mission is attained. The fundamental constructs and the relevant parameters of this nonlinear and stochastic optimization problem are developed and thoroughly discussed. It is then put into practice for a series–parallel system and the added value of solving it as a stochastic problem is demonstrated on some test cases.

Availability optimisation for stochastic degrading systems under imperfect preventive maintenance

This paper deals with imperfect preventive maintenance (PM) optimisation problem. The system to be maintained is typically a production system assumed to be continuously monitored and subject to stochastic degradation. To assess such degradation, the proposed maintenance model takes into account both corrective maintenance (CM) and PM. The system undergoes PM whenever its reliability reaches an appropriate value, while CM is performed at system failure. After a given number of maintenance actions, the system is preventively replaced by a new one. Both CM as well as PM are considered imperfect, i.e. they bring the system to an operating state which lies between two extreme states, namely the as bad as old state and as good as new state. The imperfect effect of CM and PM is modelled on the basis of the hybrid hazard rate model. The objective of the proposed PM optimisation model consists on finding the optimal reliability threshold together with the optimal number of PM actions to maximise the average availability of the system. A mathematical model is then proposed. To solve this problem an algorithm is provided. A numerical example is presented to illustrate the proposed maintenance optimisation model.

Optimizing production and imperfect preventive maintenance planning׳s integration in failure-prone manufacturing systems

Abstract This paper investigates the issue of integrating production and maintenance planning in a failure-prone manufacturing system. It is assumed that the system׳s operating state is stochastically predictable, in terms of its operating age, and that it can accordingly be preventively maintained during preplanned periods. Preventive maintenance is assumed to be imperfect, that is when performed, it brings the manufacturing system to an operating state that lies between ‘as bad as old’ and ‘as good as new’. Only an overhauling of the system brings it to a ‘as good as new’ operating state again. A practical integrated production and preventive maintenance planning model, that takes into account the system׳s manufacturing capacity and its operational reliability state, is developed. The model is naturally formulated as a mixed-integer non-linear optimization problem, for which an extended mixed-integer linear reformulation is proposed. This reformulation, while it solves the proposed integrated planning problem to optimality, remains quite demanding in terms of computational time. A fix-and-optimize procedure, that takes advantage of some properties of the original model, is then proposed. The reformulation and the fix-and-optimize procedure are tested on some test instances adapted from those available in the literature. The results show that the proposed fix-and-optimize procedure performs quite well and opens new research direction for future improvements.

A condition-based maintenance policy for a production system under excessive environmental degradation

In this paper a condition-based maintenance model is proposed for a single-unit system of production of goods and services. The system is subject to random deterioration which impacts not only the product quality but also the environment. We assume that the environment degrades whenever a specific level of system deterioration is reached. The proposed maintenance model aims to assess the degradation in such a way to reduce the deterioration of the environment. To control this deterioration, inspections are performed and after which the system is preventively replaced or left as it is. Preventive replacement occurs whenever the level of the system degradation reaches a specific level threshold. The objective is to determine optimal inspection dates which minimize the average total cost per unit of time in the infinite horizon. Cost function is composed of inspection and maintenance costs in addition to a penalty cost due to environmental deterioration. The maintenance optimization model is formally derived. On the basis of Nelder–Mead method, inspection dates as optimal solutions are computed. A numerical example is provided to illustrate the proposed maintenance model.

Hybrid hazard rate model for imperfect preventive maintenance of systems subject to random deterioration

This paper deals with imperfect preventive maintenance optimization problem. The system to be maintained is assumed to be subject to random deterioration. To reduce the risk of failures, the proposed maintenance model takes into account two type of maintenance actions, namely corrective maintenance (CM) and preventive maintenance (PM). The system undergoes PM whenever its reliability reaches an appropriate value, while CM is performed at system failure. After a given number of maintenance actions, the system is preventively replaced by a new one. Both CM as well as PM are considered imperfect, i.e. they bring the system to an operating state which lies between two extreme states, namely the as bad as old state and as good as new state. The imperfect effect of CM and PM is modeled on the basis of the hybrid hazard rate model. The objective of the proposed imperfect PM optimization model consists on finding the optimal reliability threshold together with the optimal number of PM actions to minimize the expected total maintenance and replacement cost per unit of time. A mathematical model is then proposed. To solve this problem an algorithm is provided. A numerical example is also given to illustrate the proposed maintenance model.

Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break. A list of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme.

Optimal selective maintenance decisions for large serial k-out-of-n: G systems under imperfect maintenance

Abstract The selective maintenance problem (SMP) arises in many large multicomponent systems which are operated for consecutive missions interspersed with finite breaks during which only a selected set of component repairs or replacements can be carried out due to limited time, budget, or resources. The problem is to decide which components and degree of repairs should be performed in order to guarantee a pre-specified performance level during the subsequent mission. Current SMP formulations in the literature are nonlinear, deal mainly with basic or series-parallel systems and mostly use heuristic methods to obtain solutions. This paper introduces the first SMP model for serial k-out-of-n systems. Two nonlinear formulations are developed, which can be used to solve the problem for small to moderate size k-out-of-n systems. For large k-out-of-n systems or complex reliability structures, we develop a new two-phase approach which transforms the problem into a multidimensional multiple-choice knapsack problem (MMKP). The new approach is shown to be efficient through multiple sets of numerical experiments.

Kernel estimator of maintenance optimization model for a stochastically degrading system under different operating environments

This paper investigates the preventive age replacement policy (ARP) for a system subject to random failures. Unlike most maintenance models in the literature, our model considers a system that is exploited under different operating environments each characterized by its own degree of severity. The system lifetimes follow a different distribution depending on the environment it is operating under. Furthermore, the system lifetimes distribution is assumed unknown and therefore estimated from field reliability data. The reliability of the system is calculated using two kernel estimators. This method offers the advantage of non-parametric estimation methods and completely determined by two parameters, namely the smoothing parameter and the kernel function. First, a probability maintenance cost model is derived and conditions under which an optimal preventive maintenance age exists are provided. Then, a statistical maintenance cost model is developed using two kernel estimators. The impact of the variability of the kernel smoothing parameter on the cost model is also investigated. Numerical experiments are provided to illustrate the proposed approach. Results obtained demonstrate the accuracy of the proposed statistical maintenance cost model.

Maintenance optimization of series-parallel systems operating missions with scheduled breaks

This paper addresses the selective maintenance optimization problem for a multi-mission series-parallel system. Such a system experiences several missions with breaks between successive missions. To improve the reliability of the system, preventive maintenance actions are performed during breaks. Each preventive maintenance action is characterized by its age reduction coefficient. The selective maintenance problem consists then in finding an optimal maintenance plan which minimizes the total maintenance cost while providing a given required system reliability level for each mission. The fundamental constructs and the relevant parameters of this decision-making problem are developed and discussed.

KRONECKER ALGEBRA FOR SERIES-PARALLEL MULTI-STATE SYSTEMS RELIABILITY EVALUATION

Multi-state systems (MSS) are systems whose stochastic degradation process is characterised by several performance levels varying from nominal functioning to complete failure. MSS arise naturally in many application areas. MSS reliability evaluation and estimation has received much attention from researchers and a wide range of papers dealing with MSS have been published. In this paper, an approach based on Kronecker algebra combined with stochastic processes is proposed to evaluate the reliability of a series–parallel MSS. The main advantage of the proposed approach is that the mathematical expressions of the MSS reliability indices are derived from data of individual elementary components without generating the whole, possibly huge, MSS state space. Furthermore, the approach is well formalised and easy to implement thanks to Kronecker algebra operators. Examples are given to illustrate the proposed approach.