Optimal Age Replacement Policy Research Articles

A Net Present Value Analysis of Opportunity-Based Age Replacement Models in Discrete Time

Two important opportunistic age replacement models, under replacement first and last disciplines, are generalized in discrete time. The net present value (NPV) is applied to formulate the expected total costs. The priority of multiple replacement options is considered to classify the cost model with discounting into six cases. Since the NPV method accurately calculates the expected replacement costs over an infinite horizon in an unstable economic environment, we discuss some optimal opportunistic age replacement policies which minimize the expected total discounted costs over an infinite time horizon. Furthermore, we formulate a unified model under each discipline, merging six discrete time replacement models with probabilistic priority. Finally, a case study on optimal replacement first and last policies for pole air switches in a Japanese power company is presented.

Optimal opportunity-based age replacement policies in discrete time

Optimal opportunity-based age replacement policies in discrete time

Optimal age replacement policies of mission-oriented systems with discounting

The instability of global economic would affect us in many aspects. For some important mission-oriented systems, if the decision-makers does not make the adequate budget preventively, the systems could not undergo the maintenance in time and then unimaginable disasters would occur. Therefore, we firstly consider the discount rate of cost, and extend the age replacement policies of mission-oriented systems with discounting. To balance the maintainability and cost, the replacement first and replacement last are analyzed respectively. Furthermore, the effectiveness of the suggested policies are verified via the numerical examples. Finally, we illustrate the suggested policies in maintaining the electronic radar system of warning aircraft based on the assumed data. It can provide a better guidance for the engineers to maintain the mission-oriented systems when the economic is changed a lot.

Optimal Age-replacement Policy for Series Systems Considering Maintenance Time

Optimal Age-replacement Policy for Series Systems Considering Maintenance Time

Optimal age replacement policy for discrete time parallel systems

Optimal age replacement policy for discrete time parallel systems

Optimal maintenance policies for linear consecutive [formula omitted]-out-of-[formula omitted]:F systems susceptible to dependent failures

A linear consecutive k-out-of-n:F system is an ordered sequence of n-components that fails if and only if k consecutive components in positions i, (i+1), …, (i+k−1) fail. This modeling paradigm is suitable for several modern systems such as wireless communication, which may be unable to send messages if several adjacent transmission stations fail. Although these systems are susceptible to correlated and dependent failures from geospatial events such as extreme weather, only a handful of consecutive-k-out-of-n:F models in the literature assume failures are not statistically independent and even fewer consider maintenance of consecutive-k-out-of-n:F systems subject to dependent failures. To address this limitation, this paper develops a novel formulation of the linear consecutive-k-out-of-n:F model subject to dependent failures and derives maintenance models. A sequence of illustrative examples demonstrates the ability of the model to explicitly characterize the influence of dependence on several reliability measures and shows how the model enables the identification of optimal age replacement policies to minimize cost or maximize availability despite dependence.

Optimal age replacement policies for parallel systems with mission durations

The replacement time might be scheduled during the mission executing process if the conventional maintenance policies are adopted. The system may fall short of requirements and unimaginable losses or bad social impact would take place. Hence, as a vital role in maintaining engineering systems, the mission durations should be integrated in maintenance studies. In this paper, we firstly propose the age replacement policy for parallel systems with mission durations and derive the optimum number of units. To address the trade-off between the cost and maintainability, we consider the replacement time in maintenance and propose two policies, i.e., replacement first and replacement last. Then, the optimal policies of each replacement are discussed analytically. Numerical examples are discussed to demonstrate the effectiveness of the methodology derived by this paper. Finally, the suggested replacement policies are illustrated in maintaining the pumps of a cooling water system of a nuclear power plant based on the assumed data.

Optimal age replacement policies with multiple missions for multi-state systems

The mission duration plays a very vital role in maintaining engineering systems in reality. This paper considers the mission duration into the age replacement policies with multiple missions for multi-state systems (MSSs). We first introduce the MSS whose degradation process follows a non-homogenous continuous time Markov process. Then, the basic replacement policy is given, and the optimum number of missions is derived analytically and numerically. To address the trade-off between the cost and maintainability, we consider the replacement time in maintenance and propose two policies, i.e., replacement first and replacement last. The optimal policies of each replacement are discussed analytically. Numerical examples are proposed to verify the applicability of the methodology derived by this paper. Finally, the suggested replacement policies are illustrated in maintaining the coal transportation system in a power station based on the assumed data.

Determination of the Optimal Replacement Age for the Preventive Maintenance of Bearing Assemblies Involving Weibull Failure Probability Distribution Functions

This paper describes the determination of optimal replacement age for bearing systems with failure times described by Weibull distributions. Optimal age replacement policies are determined for bearing assemblies produced two different types of steel. The parameters of the Weibull probability distribution functions for the bearings were determined by non-linear least square analysis from published data on rolling contact fatigue lives. The resulting distribution functions are used as inputs into the standard expression for the maintenance cost of an age replacement policy and manipulated symbolically using the computer program Maple. These yields closed form expressions for the policy costs that invariably exhibit the well-known vase shape characteristic of these types of problems. The resulting expressions can then be easily used to determine the optimal replacement age of the bearing components. The problem of determining the optimal age replacement policy of bearing assembles consisting of independent components arranged in series is also examined. The effect on the optimal age replacement time of using the same type steel to manufacture all the components is compared with that of building the bearing assembly using components made with different steels. As expected, the results clearly show the increased superiority of the higher-quality steel components in the form of much longer optimal replacement ages. However, replacement policy efficiencies depend on replacement time in a complex fashion. Moreover, the results also suggest that building bearing assemblies combining high quality and low quality steel components may be wasteful. Overall, computer experimentation and examination of the behavior of cost functions using symbolic manipulation with Maple can produce useful guidelines for the design of optimal age replacement policies.

On optimal age replacement policy for a class of coherent systems

According to the well-known age replacement policy, the system is replaced preventively at time t or correctively at system failure, whichever occurs first. For a coherent system consisting of components having common failure time distribution which has increasing failure rate, we present necessary conditions for the existence of the unique optimal value which minimizes the mean cost rate. The conditions are mainly based on the signature which only depends on the system’s structure. The results are illustrated for linear and circular consecutive type systems.

A hybrid preventive maintenance model for systems with partially observable degradation

AbstractA new model of hybrid preventive maintenance of systems with partially observable degradation is developed. This model combines condition-based maintenance with age replacement maintenance in the proposed, specific way. A system, subject to a shock process, is replaced on failure or at some time ${T}_S$ if the number of shocks experienced by this time is greater than or equal to m or at time $T>{T}_S$ otherwise, whichever occurs first. Each shock increases the failure rate of the system at the random time of its occurrence, thus forming a corresponding shot-noise process. The real deterioration of the system is partially observed via observation of the shock process at time ${T}_S$. The corresponding optimization problem is solved and a detailed numerical example demonstrates that the long-run cost rate for the proposed optimal hybrid strategy is smaller than that for the standard optimal age replacement policy.

Optimal age replacement policy for parallel and series systems with dependent components

Maintenance plays a very vital role throughout the lifetime of a system and also in reality, the lifetime of components of a system may be dependent on each other that should be considered in a maintenance policy. This paper deals with age replacement policy for repairable series and parallel systems with n dependent components. We present two optimal age replacement policies based on the minimum expected cost function and maximum availability function. In this work, the copula framework is used to model the dependence structure for components and formulate the optimal decision problems. Therefore managers can use the results to decrease the cost imposed or increase the availability of their series or parallel systems with dependent components. The effects of the parameters of the model on the optimal solutions are studied and also the comparison of copulas is presented. An application on offshore wind turbine systems as a case study is discussed.

Complementary optimal age maintenance (COAM) policy for repairable systems

A Complementary Optimal Age Maintenance (COAM) policy is proposed in this work for repairable systems which require high level of availability and safety standard by exploiting the comparative advantage of minimum expected cost-based optimal age replacement policy and maximum limiting availability-based optimal age replacement policy. The failure distribution, cost of preventive and failure maintenance and downtime of preventive and failure maintenance, which affect the age at which an operating system is replaced, were used to formulate the expected cost and limiting availability functions for repairable systems.

The failure probability of components in three-state networks with applications to age replacement policy

Abstract In this paper we investigate the stochastic properties of the number of failed components of a three-state network. We consider a network made up of n components which is designed for a specific purpose according to the performance of its components. The network starts operating at time t = 0 and it is assumed that, at any time t > 0, it can be in one of states up, partial performance, or down. We further suppose that the state of the network is inspected at two time instants t1 and t2 (t1 < t2). Using the notion of the two-dimensional signature, the probability of the number of failed components of the network is calculated, at t1 and t2, under several scenarios about the states of the network. Stochastic and ageing properties of the proposed failure probabilities are studied under different conditions. We present some optimal age replacement policies to show applications of the proposed criteria. Several illustrative examples are also provided.

Optimal age-replacement policy for non-repairable technical objects with warranty

optimal age-replacement policy for non-repairable technical objects with warranty

Adaptive Age Replacement Using On-Line Monitoring

Age replacement is one of the most used maintenance policies based on preventive action in order to prevent the failure of a system. Age replacement means that a system is replaced at failure or at a specified replacement age, whichever occurs first. In current age replacement policies, the replacement age is identified without consideration of the effects from operating conditions. However, the lifetime of a system may be affected by various operating conditions, such as the surrounding environment and the operators. In such cases, the replacement age of the system should differ for different situations. Thanks to the improvement of information communication technology, various information about the systems operating conditions can be obtained via the on-line monitoring. This research proposed an adaptive age replacement policy for systems under variable operating conditions using a cumulative exposure model. Based on the on-line information, we proposed a new time-scale instead of the age with consideration of operating conditions. Next, the new time-scale is used to determine the optimal replacement interval which will minimize the average maintenance cost per unit time (also known as cost rate). Some numerical examples are carried out in order to illustrate the proposed adaptive age replacement policy. The optimal age replacement policy considering the operating conditions reduces the total maintenance costs and enhances the effective maintenance plan for systems operating under various conditions.

Preventive maintenance optimization for a stochastically degrading system with a random initial age

This paper investigates the optimal age replacement policy for used systems, such as second-hand products, which start their second life-cycle in a more severe environment with an initial age that is uncertain. This uncertain age is modelled as a random variable following continuous probability distributions. A mathematical model is developed to minimize the total expected cost per unit of time for these systems on an infinite time horizon. Optimality and existence conditions for a unique optimal solution are derived and used in a numerical procedure to solve the problem. Numerical experiments are provided to demonstrate the added value and the impacts of the random initial age on the optimal replacement policy.

An optimal age-replacement policy for a cold standby repairable system with priority in use and repair

ABSTRACTIn this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. Assume that Component 2 after repair is ‘as good as new’ while Component 1 after repair is not, but Component 1 has priority in use and repair. Under these assumptions, using a geometric process, we consider a replacement policy based on Component 1 age T as the system age under which the cold standby system is replaced when the system age reaches T. Our problem is to determine an optimal replacement policy T* such that the average cost rate of the system is minimised. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy T* can be determined analytically or numerically. Finally, a numerical example is given to illustrate the model developed, and some sensitivity analysis on the optimal solution is also conducted.

An optimal age-replacement policy for a simple repairable system with delayed repair

ABSTRACTIn this article, a simple repairable system (i.e., a repairable system consisting of one component and one repairman) with delayed repair is studied. Assume that the system after repair is not “as good as new”, and the degeneration of the system is stochastic. Under these assumptions, using the geometric process repair model, we consider a replacement policy T based on system age under which the system is replaced when the system age reaches T. Our problem is to determine an optimal replacement policy T*, such that the average cost rate (i.e., the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy T* can be determined by minimizing the average cost rate of the system. Finally, a numerical example is given to illustrate some theoretical results and the model's applicability.

Optimal age replacement policy with replacement occurrence while the warranty is in effect

This study considers an age replacement policy (ARP) for a repairable product with an increasing failure rate with and without a product warranty. As for the warranty policy to consider in association with such an age replacement policy, we adapt a renewable minimal repair-replacement warrant (MRRW) policy with 2D factors of failure time of the product and its corresponding repair time. The expected cost rate during the life cycle of the product is utilized as a criterion to find the optimal policies for both with and without the product warranty. We determine the optimal replacement age that minimizes the objective function which evaluates the expected cost rate during the product cycle and investigate the impact of several factors on the optimal replacement age. The main objective of this study lies on the generalization of the classical age replacement policy to the situation where a renewable warranty depending on 2D factors is in effect. We present some interesting observations regarding the effect of relevant factors based on numerical analysis.