Optimal Age Replacement Research Articles

Optimal maintenance policies for a k-out-of-n system with replacement bias costs

In this paper, the issue of determining an optimal age replacement is explored by incorporating minimal repair, preventive replacement, and corrective replacement into a k-out-of-n system subject to shocks. The k-out-of-n system in question consists of n identical components, and functions if at least k components function. Each shock causes the failure of a random number of components; if at least n-k + 1 components fail, the system fails and implements corrective replacement, otherwise the system is minimally repaired. The system is scheduled to implement preventive replacement before failure at age T or at the complement of a random working cycle, whichever occurs first or last. In order to balance the bias time between preventive replacement and corrective replacement, a replacement bias cost is also taken into account for planning replacement policies. The present paper develops a two-phase maintenance methodology and determines the optimal number of components and preventive replacement age that minimize the expected cost rate functions. For each model, the expected cost rate function is formulated analytically and optimized theoretically, and a numerical example is given to illustrate the applicability of the proposed methodology.

Optimal age replacement in parallel systems with random components

Optimal age replacement in parallel systems with random components

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 age replacement time for coherent systems under Geometric Point Process

In spatial context, the understanding of event dynamics and point distributions is a fundamental requirement. This study addresses a critical need by introducing the Geometric Point Process (GPP) and explaining its potential impact on optimizing the determination of optimal replacement ages for coherent systems. Our paper has three overarching aims: firstly, to bridge the gap by presenting the novel GPP model that effectively captures the geometric distribution of points, filling a void in point process theory. Secondly, we calculate the optimal replacement age for the coherent system based on the principles of GPP. This involves employing the Infinitesimal-Look Ahead stopping rule within the framework of Smooth Semi-Martingale (SSM) decomposition. A comprehensive comparative analysis is conducted to assess the distinct features and advantages of the GPP in relation to other point processes, offering valuable insights into its applicability and performance. Lastly, we extend the practical application of GPP by examining optimal replacement strategies for components in coherent systems, offering a bridge between theory and real-world practices, especially in the context of aircraft and wind turbine component deterioration. Additionally, we conduct reliability and sensitivity analyses, providing management suggestions, and present Monte Carlo simulations as an alternative method for validating optimal solutions. This research invites the industrial community to utilize the proposed replacement policy, paving the way for exploring geometric characteristics in stochastic processes. The timeliness and significance of this work are underscored by the relatively unexplored field of smooth semi-martingales, with the most recent publication dating back to 2015 by Bueno.

Optimal opportunity-based age replacement policies in discrete time

Optimal opportunity-based age replacement policies in discrete time

On the point process with finite memory and its application to optimal age replacement

There has been extensive study of various repair models in the literature, mostly under the assumption that these repairs are minimal or imperfect/better than minimal. Although this is often a realistic assumption, it may not be sufficient to model instances where the repair is worse than minimal. The generalized Polya process (GPP) that has been used to describe this type of repair takes into account all previous events/repairs, which is not often the case in practice. Therefore, in this paper, we define a new process with finite memory that starts as the GPP but, after a certain number of events or elapsed time, becomes the non-homogeneous Poisson process of repairs (minimal repairs). The corresponding age replacement policy is defined and the optimal solutions that minimize the long-run expected cost rate are analyzed. The detailed numerical examples illustrate our findings.

Maintenance optimization of a two‐component series system considering masked causes of failure

AbstractMaintenance planning of two‐component systems has been extensively studied in recent decades. In the literature, most studies assume that the failure cause of a two‐component system is self‐announcing. In some real applications, the failure cause is masked, and a diagnosis with professional equipment is needed to reveal the failed component. This study investigates a preventive replacement policy of a two‐component series system considering masked causes of failure. When an unexpected failure occurs, we can carry out a diagnosis to reveal the failed component and replace it subsequently, or we can directly replace the whole system without diagnosis. Meanwhile, when we carry out a preventive replacement on a component, the other component can be replaced opportunistically. We formulate the problem as a semi‐Markov decision process, and prove the existence of the stationary optimal policy. The optimal preventive replacement age thresholds for each component and the corresponding optimal maintenance actions upon each failure are jointly obtained to minimize the long‐term average maintenance cost per time unit. A comprehensive numerical study is provided to illustrate the effectiveness of our proposed model.

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.

Preventive replacement policy of a system considering multiple maintenance actions upon a failure

AbstractAge‐based preventive replacement policy has been extensively studied in the literature. Upon an unexpected failure, most studies assume that only one type of maintenance actions can be executed to restore the system back to work. For example, minimal repair or corrective replacement that bring the system to respective as‐bad‐as‐old and as‐good‐as‐new states. Few studies consider both two types of maintenance actions, while predetermine the structure of the maintenance policy. Modern systems are becoming increasingly complex. Besides minimal repair and corrective replacement, imperfect repair can also be carried out to restore a failed system back to work, which brings it to a state between as‐bad‐as‐old and as‐good‐as‐new. This study investigates an optimal age‐based replacement policy, where minimal repair, corrective replacement, and imperfect repair can be carried out upon an unexpected failure with different maintenance effects. We formulate the problem as a semi‐Markov decision process (SMDP), and prove the existence of the stationary optimal policy. The optimal preventive replacement age threshold and the corresponding optimal maintenance action upon each failure are jointly obtained to minimize the long‐term average maintenance cost per time unit. A numerical study is provided to illustrate the effectiveness of our proposed model.

AGE-BASED REPLACEMENT WITH IMPERFECT REPAIR AND RISK AS LOW AS REASONABLY PRACTICABLE

Maintenance policies must consider system reliability and the risk of accidents in systems where equipment failures represent a risk. In this context, this work proposes an age replacement policy with Bayesian imperfect repair and considers the “as low as reasonably practicable” (ALARP) principle. The policy determines the age of replacement that minimizes the long-run cost per unit time when the failure rate is ALARP. The model also supposes that failures are either minimally or perfectly repaired, depending on the skill of the maintainer. Numerical applications are performed with and without the disproportion factor in ALARP, both for infinite and one-replacement-cycle horizons. The results show that considering imperfect repair leads to an increase in replacement costs and a decrease in the optimal replacement age when considering the ALARP principle. The model applies to situations where there are conflicts of interest between maintenance management and risk; that is, cases where the aim is to reduce the cost of replacing equipment and minimize the risks. Maintenance policies must consider system reliability and the risk of accidents in systems where equipment failures represent a risk. In this context, this work proposes an age replacement policy with Bayesian imperfect repair and considers the “as low as reasonably practicable” (ALARP) principle. The policy determines the age of replacement that minimizes the long-run cost per unit time when the failure rate is ALARP. The model also supposes that failures are either minimally or perfectly repaired, depending on the skill of the maintainer. Numerical applications are performed with and without the disproportion factor in ALARP, both for infinite and one-replacement-cycle horizons. The results show that considering imperfect repair leads to an increase in replacement costs and a decrease in the optimal replacement age when considering the ALARP principle. The model applies to situations where there are conflicts of interest between maintenance management and risk; that is, cases where the aim is to reduce the cost of replacing equipment and minimize the risks.

Optimal renewing free-maintenance warranty period and preventive replacement age for repairable products

This paper proposes a decision model for determining the optimal renewing free-maintenance warranty (RFMW) period and preventive replacement age of a general repairable product with a random workload. To model a maintenance action, if a failure occurs, either a corrective replacement or a minimal repair is performed, in case of catastrophic failure or minor failure, respectively. To avoid catastrophic failures occurring for a degraded product, a preventive replacement is predetermined for implementation at age T or at the completion of a working time, whichever comes last. During RFMW, any maintenance action (either repair or replacement) is free of charge to the customer. However, each catastrophic failure still results in a downtime cost to the customer, while a planned maintenance action increases the initial purchasing cost. The aim of this paper is to determine the optimal warranty period and preventive replacement age, from the collection viewpoint of the manufacturer as well as the customers, while minimising the corresponding expected cost rate functions. The effects of RFMW on the optimal preventive replacement model are further investigated by some comparative studies and demonstrated via a numerical example. It is shown that the proposed model provides a generalised application in maintenance theory and warranty strategy.

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.

PENENTUAN UMUR DUMP TRUCK DENGAN METODE OPTIMAL REPLACEMENT INTERVAL DI CV. X

Every asset in the operation of certain services, transportation or services will experience a change in each period of time. Replacement is made on an asset that is damaged, operating costs are too high, or a change in technology makes an equipment unusable. CV. X is a company engaged in providing services for transportation fleets, one of which is dump trucks. Today, companies are often faced with complex replacement problems and only apply the depreciation method to determine the life of their equipment. This study aims to propose determining the age of dump trucks with optimal replacement intervals and to find out the hourly usage costs incurred by the company at the optimal replacement age. This method uses the hourly cost as the basis for determining the optimal replacement life. The research data is in the form of secondary company data consisting of maintenance data such as vehicle purchase price data, fuel consumption, lubricant consumption, labor wages, annual operating hours, productivity, rental rate, interest rate value, and income tax rate. The parameters are in 1000 hour intervals. The optimal replacement life for dump trucks is in the interval of 30,000 hours – 40,000 hours or 12-16 years. The hourly usage cost at the optimal replacement life interval with the productivity approach is $159.74 and the hourly usage cost with the rental rate approach is $104.64.

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.

Reliability modeling and optimal random preventive maintenance policy for parallel systems with damage self-healing

Materials with intrinsic self-healing phenomenon possess the ability to heal in response to external random shocks. Introducing a recovery factor to quantitatively measure the damage self-recovery efficiency, this paper designs a self-healing mechanism corresponding to both damage load and shock arrival numbers for a parallel redundant system consisting of multiple non-identical components. From the actual engineering perspective, each shock arriving on the system selectively affects one component or more but not necessarily all units in parallel, and consequently, random shocks are categorized according to their sizes, attributes and affected components. This study investigates novel reliability models and schedules optimal preventive maintenance policies, in which the closed-form reliability quantities are derived analytically and the optimum preventive replacement interval is demonstrated theoretically. In addition, a Nelder-Mead downhill simplex method is introduced to seek the optimal replacement age in minimizing the long-run average maintenance cost rate for the condition system failure distribution is rather complex. A micro-electro-mechanical system (MEMS) whose constitutional materials are integrated by microcrystalline silicon, where polymer binders with self-healing capability are always synthesized, is designed to verify the results we obtained numerically, illustrating the significance of considering damage self-healing phenomena.