Age Replacement Research Articles

On stochastic ordering among extreme shock models

AbstractIn the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications. Communications in Statistics – Simulation and Computation49(1): 110–120] introduced two types of extreme shock models when the shocks arrive from one of $m\geq 1$ possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of $m$ sources, and shocks continue to arrive from the same source. In this paper, we prove that the lifetime of Model 1 is less than Model 2 in the usual stochastic ordering. We further show that if the inter-arrival times of shocks have increasing failure rate distributions, then the usual stochastic ordering can be generalized to the hazard rate ordering. We study the stochastic behavior of the lifetime of Model 2 with respect to the severity of shocks using the notion of majorization. We apply the new stochastic ordering results to show that the age replacement policy under Model 1 is more costly than Model 2.

Optimal age replacement policy for discrete time parallel systems

Optimal age replacement policy for discrete time parallel systems

The effects of cyber threats on maintenance outsourcing and age replacement policy

This research examines maintenance outsourcing in the presence of cyber-attacks. The research findings contribute to the literature on maintenance outsourcing by considering how cyber-attacks affect channel coordination and, specifically, cost subsidization. The Internet of Things assumes the risk that a “smart” or connected manufacturing system could become the target of a cyber-attack. Manufacturers have to face the difficult decision of adopting increasingly costly security technologies or having the manufacturing system remain vulnerable to cyber threats. This study develops a model addressing this dilemma by providing insight into the effects of cost subsidization and tools that manufacturers may use to evaluate the impact that installation of a security system has on a manufacturing system’s profit. The research also analyzes the effect of a cyber-attack on the system when using an age replacement policy. Under such a system, repairs may cost more than replacement which suggests that new components are required immediately after failure. For “smart” manufacturing systems that use either maintenance outsourcing or an age replacement policy, the study provides optimal solutions for firms to maximize the manufacturing system’s profit with consideration of the firms’ physical equipment failure and cyber-attack rates. The findings help determine the value of a security system by providing guidelines that address the effects of the cost, failure rate, and “successful” cyber-attack rate parameters.

A study on the number of failed components in a failed coherent system consisting of different types of components

In this paper, we consider a coherent system consisting of different types of components. It is of interest to study the number of failed components of each type when the system fails. The obtained results are next used in the classical age replacement policy when the corrective replacement of the system is applied if a system has failed, while the preventive replacement is done before failure. We formulate the optimization problem. We wish to find the optimal replacement time. We provide a numerical example to illustrate the theoretical results.

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.

An Optimal Random Hybrid Maintenance Policy of Systems under a Warranty with Rebate and Charge

Facilitated by advanced digital technologies, reliability managers can monitor system working cycles during the whole life cycle. Such a technological realization can help reliability managers ensure system reliability in real time by monitoring working cycles. In this paper, by incorporating a limited random working cycle, rebate and charge into warranty theory, a random free repair warranty with rebate and charge (RFRW-RC) is devised to ensure system reliability during the warranty stage. Under RFRW-RC, the rebate removes manufacturers’ responsibility for continuing to ensure system reliability, while the charge is a support where manufacturers continue to ensure system reliability. The warranty cost of RFRW-RC is derived, and a random discrete free repair warranty (RDFRW) is presented by simplifying RFRW-RC. By mixing random age replacement last (RARL) and classic age replacement (CAR), a random hybrid age replacement (RHAR) is designed in order to ensure system reliability during the post-warranty stage. In such an RHAR, RARL is applied to extend the replacement time during the post-warranty stage in order to maximize the remaining life of the system through warranty, and CAR is used to lower the maintenance cost of the system through warranty. The cost rate of RHAR is modeled, and the cost rate of RDFRW is offered as well by discussing parameter values. The decision variable is optimized by minimizing the cost rate model. The properties of the presented models are explored from numerical perspectives.

Optimal replacement scheduling for a multi-component system with failure interaction

In this study, we consider a system consisting of n different components with failure interaction. Each component suffers from either minor or major failure: the former is removed via minimal repair, while the latter induces complete failure of the system and requires corrective replacement of the system. This study investigates two scheduling problems of preventive replacement policies for a multi-component system that incorporates minimal repair, shortage, and excess costs. First, we consider the scheduling problem of an age replacement policy, in which the system is replaced at a planned time T or upon the occurrence of any major failure. Next, we consider that the system operates N successive random jobs without interruptions. In this scheduling problem, the system is replaced upon the accomplishment of N jobs or upon the occurrence of any major failure. For each scheduling problem, we derive the optimal scheduling parameter ( T * or N * ) analytically and numerically, according to their existence and uniqueness based on minimizing the mean cost rate function. Finally, a numerical example is designed to validate the theoretical results in this article.

Penentuan Interval Waktu Penggantian dan Perbaikan Komponen Kritis Mesin Bubut Type SS-850 di PT. Hamdan Jaya Makmur Dengan Metode Age Replacement

PT. Hamdan Jaya Makmur is a company that runs in the field of Machining, Engineering, Fabrication, Stamping, and Trading Company, which produces products for small, medium and modern industries. Less than optimal maintenance system with corrective maintenance causes PT. Hamdan Jaya Makmur often experiences machine failure. Based on historical data, it can be seen that the lathe machine type SS-850 experienced very high downtime. Therefore, it is necessary to plan optimal and preventive maintenance of the machine in order to produce according to the target and increase the reliability of the machine. The purpose of this research is to determine the time interval and cost of preventive replacement on components of the lathe machine type SS-850 at PT. Hamdan Jaya Makmur. The method used in this research is the Age Replacement method, namely by determining critical components, determining the distribution pattern of damage, determining distribution parameters, and calculating MTTF and MTTR, where the results obtained are preventive replacement time intervals, and calculating preventive replacement costs. The results obtained from this research are that there are four critical components on the lathe machine type SS-850, namely electric components with a preventive replacement time interval of 11 days and a preventive replacement cost of Rp.3,080,679,253, bearing components have a preventive replacement time interval of 14 days and a preventive replacement cost of Rp.4,931,989,307, the gearbox component has a preventive replacement time interval of 33 days and a preventive replacement cost of Rp.11,621,532,829, and bolt and nut components have a preventive replacement time interval of 11 days and a preventive replacement cost of Rp.1,615,296,412.

Preventive Maintenance Scheduling with Age Replacement Method at CNG Station

CNG Mother Station focused to distribute Compressed Natural Gas for various industries. In the period from December 2020 to November 2021, there were 40 breakdowns in the distribution process machine causing delays in distribution of CNG. Company has to pay attention to the maintenance scheduling for vulnerabl components. This study aims to determine Preventive Maintenance scheduling and calculating maintenance costs using Age Replacement method for the critical components. The results showed that the critical components are Air Supply’s Hose (ASH) and Double Nipple Stage 4 (DNS-4). The proposed optimal replacement time interval for the ASH is 20 days where 19 component replacements are scheduled in 1 year with a cost reduction up to 4.8% compared to existing. The optimal replacement time interval for DNS-4 components is 24 days, which is scheduled for 16 component replacements in 1 year with cost reduction up to 29.1% compared to existing.

Random maintenance policies for sustaining the reliability of the product through 2D-warranty

Rapid development and wide application of cyber-physical systems (CPS) have created the possibility of remotely monitoring product working cycles. This indicates that CPS can provide the technological support required for designing manufacturers’ warranties integrated with working cycle and for modelling users' (or consumers') random maintenance policies sustaining the reliability of the product through warranty. In this study, by designing limited working cycles as a warranty limit, we have proposed manufacturer's two-dimensional warranty first and last to ensure the product's reliability during the warranty coverage period. Subsequently, we have incorporated working cycle into the traditional maintenance policies and modelled users' random age replacement first and last to sustain the reliability of the product through its warranty. By analysing parameter values, we have offered some classic models, i.e., the expected long-run cost rates that represent certain special problems. Finally, sensitivities of both the proposed warranties and the modelled random age replacements have been analysed through numerical experiments. It has been demonstrated that whichever takes place first or last influences if the warranty cost of the proposed two-dimensional warranty is higher than that of the traditional one-dimensional warranty. Users can get a longer post-warranty period when the warranty limit m, i.e., the limited random working cycles, is lower.

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.

Assessment of Some Proposed Replacement Models Involving Moderate Fix-Up

Among all reasonable dynamic replacement strategies, the age replacement strategy is the best. Furthermore, when compared to optimal replacement time of the other alternative formations, the optimal replacement time of system with series formation is shorter. For such reason, this paper compared the optimal replacement times obtained under the standard age replacement policy (SARP) with optimal replacement times obtained under some proposed two replacement policies (policy A and policy B) for some four multicomponent systems. Two numerical examples are provided for simple illustrations of the replacement policies under SARP, policy A and policy B, so as to select and apply the best replacement policy with respect to a particular system in making a projected precautionary replacement maintenance action of the system.

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.

A Remaining Useful Life Model for Optimizing Maintenance cost and Spare-parts replacement of Production Systems in the Context of Sustainability

In reliability and maintenance engineering, predictive methods play a major role for estimating the remaining useful life (RUL) of equipment. However, in the most cases the RUL estimation is based on two types of approaches: model-based solution and data-driven solution. Data-driven solution is a very realistic solution, but requires the availability of large quantity of collected data using sensors networks, big storage capacity, supercomputers for processing, and high-level algorithms such as machines learning, convolutional Neural Networks, Hidden Markov Models. While model-based solution methods are less difficult to deploy, they use techniques based on the mean residual life (MRL) value. This paper proposes an integrated decision support model for minimizing the maintenance expected cost, and for reducing the excess of spare-parts usage of multi-component production systems. This decision support model includes three performance indicators that are: the renewal function (RF), the mean residual lifetime (MRL) and the renewal mean residual lifetime (RMLR). The contribution of this research consists of (1) introducing the MRL function for a class of useful probability distributions, (2) proposing the Renewal MRL (RMRL) as a predictive maintenance strategy, (3) applying the approach-MRL to maintenance scheduling problems, (4) dressing a comparative numerical study between the different proposed models using an industrial case study. Besides, the comparative study performing the RF, MRL, and RMRL is carried out using basic and modified replacement strategies consisting of an age replacement policy (ARP) and an opportunistic maintenance solution. In addition, a case study from an Electrical power system is proposed by providing numerical results that discuss and illustrate the outcome gains in terms of maintenance costs saving and spare parts replacements’ minimization. However, the proposed solution is demonstrated to have a positive effect to enhance sustainable development systems, and it is provided soon to cover other theoretical and application aspects of the MRL.

Estimation of Age Replacement Policy when Maintenance Cost is Linear and Nonlinear

Estimation of Age Replacement Policy when Maintenance Cost is Linear and Nonlinear

On Possibility of Extending the Optimal Replacement time of Series and Parallel Systems

Among all systems, the series system has the lowest optimal replacement time, while the parallel system has the highest optimal replacement time. This paper is comparing the standard age replacement strategy (SARS) with some proposed replacement strategies (strategy A and strategy B) for two multi-unit systems. Two numerical examples are provided for a simple illustration of the proposed replacement cost models under SARS, strategies A and B. The results obtained showed that strategy B can extend the optimal replacement time of a series system.

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.

A maintenance policy for a [formula omitted]-out-of-[formula omitted] system under enhancing the system’s operating time and safety constraints, and selling the second-hand components

In this paper, a new maintenance policy for k-out-of-n:F systems is proposed, which includes age replacement and minor repairs as preventive maintenance actions. After replacing a multi-component system, some components are still usable and can be sold as second-hand products. The price of these components depends on their original lifetime and the replacement time of the system. On the other hand, managers and engineers would like to reduce the imposed costs on the system while increasing system efficiency. With this in mind, long-run average cost is considered as the objective function. In addition, the optimal parameters of the proposed policy are obtained under two constraints: a safety constraint and a constraint for enhancing the relative mean operating time. By considering the first constraint, the system engineer is confident with a desired probability that no unplanned replacement will happen to the system in a pre-specified interval. The second constraint ensures the enhancement of the mean operating time of the system by applying the proposed policy. Moreover, the classical age replacement policy has been achieved as a special case of our results. To study the effect of the model’s parameters on the optimal solutions, extensive numerical computations are performed. Finally, a real data set of the tensile strength of cables is used to demonstrate the applicability of the proposed model.

Maintenance optimization for a single wind turbine component under time-varying costs

In this paper, we introduce a new, single-component model for maintenance optimization under time-varying costs, specifically oriented at offshore wind turbine maintenance. We extend the standard age replacement policy (ARP), block replacement policy (BRP) and modified block replacement policy (MBRP) to address time-varying costs. We prove that an optimal maintenance policy under time-varying costs is a time-dependent ARP policy. Via a discretization of time, the optimal time-dependent ARP can be found using a linear programming formulation. We also present mixed integer linear programming models for parameter optimization of BRP and MBRP. We present a business case and apply our policies for maintenance planning of a wind turbine gearbox and show that we can achieve savings up-to 23%.

Age replacement with Markovian opportunity process

This paper focuses on the age replacement problems under the assumption that the arrival of opportunities follows a stochastic point process. The opportunity is a chance to make the replacement, and one can replace a unit with a low cost at the opportunity. In this paper, the opportunity-based age replacement models by Dekker and Dijkstra (1992) and Zhao and Nakagawa (2012) are extended in the environment where the opportunity process is in accordance with a Markovian arrival process (MAP). The MAP is one of the general point processes, and involves a Poisson process and some renewal process classes. This work introduces the generalization of the arrival process of the preventive replacement problems with opportunities. Furthermore, a comprehensive evaluation of the opportunity-based age replacement policies by Dekker and Dijkstra (1992) and Zhao and Nakagawa (2012) in the generalized modeling framework is carried out.