Optimal Age Replacement Policy Research Articles

BOOTSTRAP CONFIDENCE INTERVAL OF OPTIMAL AGE REPLACEMENT POLICY

In this paper, we consider an interval estimation of the age replacement problem, where the underlying failure time probability is given by the two-parameter Weibull distribution. The parametric bootstrap is used to obtain the probability distribution of an estimator for the optimal age replacement time minimizing the expected cost per unit time in the steady state. We focus on both cases with complete and incomplete samples of failure time data, and calculate not only the higher moments of an estimator for the optimal age replacement time but also the confidence interval.

Some New Results on Uncertain Age Replacement Policy

Age replacement policy is a commonly policy in maintenance management of spare part. It means that a spare part is always replaced at failure or fixed time after its installation, whichever occurs first. An optimal age replacement policy of spare parts concerns with finding the optimal replacement time determined by minimizing the expected cost per unit time. The age of the part was generally assumed to be a random variable in the past literatures, but in many situations, there are few or even no observed data to estimate the probability distribution of part's lifetime. In order to solve this phenomenon, a new uncertain age replacement policy has been proposed recently, in which the age of the part was assumed to be an uncertain variable. This paper discusses the optimal age replacement policies by dealing with the parts' lifetimes as different distributed uncertain variables. Several results on the optimal age replacement time are provided when the lifetimes are described by the uncertain linear, zigzag and lognormal distributions.

The Effects of a Renewing Free-Replacement Warranty on the Discrete Age Replacement Policy

This paper presents the effects of a renewing free-replacement warranty (RFRW) on the age-replacement policy in a discrete time process. Consider a product that should be operating over an indefinitely long operation cycle n (n=1,2,...); under the discrete age-replacement policy, a product is replaced at cycle N (N=1,2,...) after its installation, or at failure, whichever occurs first. The cost models from the customer's perspective are developed for both warranted, and non-warranted products. The corresponding optimal replacement age N* (i.e., the optimal number of operation cycles for a preventive replacement) is derived such that the long-run expected cost rate is minimized. Under the assumption of the discrete time increasing failure rate, the existence and uniqueness of the optimal N* are shown, and the impacts of a RFRW on the optimal replacement policies are investigated analytically. The optimal N* for a warranted product is closer to the end of the warranty period than for a non-warranted product. Finally, a numerical example is demonstrated for the optimal policy illustration and verification. The observations from the technical analysis and numerical results provide valuable information for a buyer (user) to adjust the optimal age-replacement policy if a product is operating in discrete time under a RFRW.

Optimisation of gearbox replacement policy using vibration measurement data

Gearbox system reliability is a critical factor in the success of any industrial project. Poor reliability directly affects both the project’s revenue stream through increased operation and maintenance (OM increased risk, or at least the perception of increased risk, is generally accompanied by increased financing fees or interest rates. However, this paper explores a reliability based on a developed an analytical mathematical method for predicting remaining lifetime of cracked gear tooth. The development is focused specifically on the investigation of a generalised statistical method for characterising and predicting system Weibull density function degradation (hazard rate). Using this method, optimal preventive age replacement policy is determined to maximise gearbox system reliability, and consequently an optimal cost analysis can be estimated. A simple geared system is used as a medium for real data collection, where the torsional vibration acceleration was measured and analysed. The results indicate that the knowledge of the remaining lifetime and the optimised replacement cost of the faulty gear can enhance the process of scheduling maintenance, ordering spare parts and using resources; consequently a reduction of maintenance cost.

Technical Uncertainty and Value of Information with Application to Optimal Network Component Replacement

Optimal age replacement policies for network components such as cables, overhead lines or transformers are usually identified based on gathered knowledge about the state of a component and its stochastic deterioration process. In this context, uncertainty is an important challenge because current information about the aging process may be false. Especially in the context of innovative use of newly developed network equipment some experience knowledge from similar equipment might exist or pre-testing under laboratory conditions could allow setting up hypothesis about the characteristics of aging. Nonetheless, substantial uncertainty is still common in replacement. An example in this context is the lifetime of PE tubes in gas networks, which is not very well explored due to the fact that no tubes older than 40 years exist. The length of the aging process as well as the expected starting date can be inferred only to some confidence probability. Apart from newly developed equipment, production imperfections like the Water treeing Effect in cable insulations led to very early replacement of complete lots of cables because the insulation deteriorated much earlier than initially expected. Hence, the question arises how these different sources of uncertainty will impact the network operator's replacement decision. Further it is of interest how much value can be attributed to the reduction of the uncertainty. In this paper, an optimal replacement strategy in an analytical stationary state model is derived explicitly with local and global optima. Based on a discrete mixture model of failure rates under perfect replacement, we show how different assumptions about the underlying type of uncertainty will affect the replacement decision. In a further step, the value of information representing the cost difference between a state of parameter certainty and the state of parameter uncertainty is derived. Trough the course of some applications, it is shown that the value of information increases with the level of uncertainty. Some exemplary calculations are presented to show that the magnitude of the value of information is significant.

OPTIMAL AGE REPLACEMENT AND INSPECTION POLICIES WITH RANDOM FAILURE AND REPLACEMENT TIMES

It is well-known in the standard age replacement policy that a finite preventive replacement time does not exist when the failure time is exponential and the optimal preventive replacement time is nonrandom. It is shown that when the failure time is exponential, a finite time exists by introducing the shortage and excess costs. In addition, the random age replacement is proposed and similar discussions are made. Furthermore, the periodic and random inspection policies are taken up, and their optimal policies are shown to correspond theoretically to those of the age replacement ones. It is shown finally that when the random inspection cost is the half of the periodic one, two expected costs are almost the same.

A multi-objective approach to simultaneous determination of spare part numbers and preventive replacement times

Different models have been proposed in the field of preventive maintenance planning for finding optimal age replacement policies. While previous studies have focused mainly on classical cost objectives, this paper presents a novel multi-objective model for preventive replacement of a part over a planning horizon. The proposed model considers different objectives and practical issues, such as corrective replacement and its consequences, residual lifetime objective, and kind of productivity index. Also, the model determines number of spare parts, required for replacement with the defected part, to be provided at the beginning of the planning horizon. The multi-objective model is applicable for machines or equipments which are repaired through replacing their defected part with new spare part. For solving the multi-objective model, regarding to ability of ε-constraint method to generate different pareto-optimal solutions, a procedure is developed based on this method. The procedure shows how the ε-constraint method can be used for finding preferred solution in situations where there is no access to decision maker. The model and solution procedure are illustrated by a numerical example.

The Effect of a Pro-Rata Rebate Warranty on the Age Replacement Policy With Salvage Value Consideration

This paper presents the effects of salvage value on the optimal age-replacement policy for non-repairable products sold with a pro rata rebate warranty (PRRW). Cost models from the customer's perspective are developed for both warranted, and non-warranted products. The corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. Under the increasing failure rate assumption, the existence and uniqueness of the optimal age for preventive replacement are shown, and the impacts of a PRRW on the optimal age-replacement policy are investigated analytically. Finally, a numerical example is provided for the optimal policy illustration and verification.

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 age-replacement policy for renewing warranted products

Preventive replacement is a well-known topic in the literature of operational research and reliability. The effects of a renewing free-replacement warranty (RFRW) on the age replacement policy for a repairable product with a general failure model are discussed. There are two types of failure when the product fails. One is type I failure, which can be removed by a minimal repair, and the other is type II failure, which can be removed only by a replacement. After a minimal repair, the product is operational but the failure rate of the product remains unchanged. For both warranted and non-warranted products, cost models are developed and the corresponding optimal replacement ages are derived based on the minimized long run expected cost rate. The impacts of the RFRW on the optimal replacement age are investigated analytically. Finally, numerical examples are given for the purposes of illustration.

Optimal age-replacement policy for repairable products under renewing free-replacement warranty

This paper investigates the effects of a renewing free-replacement warranty (RFRW) on the age replacement policy for a repairable product with a general failure model. In the general model, there are two types of failure when the product fails. One is type I failure (minor failure), which can be removed by a minimal repair; and the other is type II failure (catastrophic failure), which can be removed only by a replacement. After a minimal repair, the product is operational but the failure rate of the product remains unchanged. For both warranted and nonwarranted products, cost models are developed, and the corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. The impacts of the RFRW on the optimal replacement age are investigated analytically. Finally, numerical examples are given for illustration.

Extended optimal age-replacement policy with minimal repair of a system subject to shocks

An operating system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur the system has two types of failure: type I failure (minor) or type II failure (catastrophic). A generalization of the age replacement policy for such a system is proposed and analyzed in this study. Under such a policy, if an operating system suffers a shock and fails at age y (⩽ t), it is either replaced by a new system (type II failure) or it undergoes minimal repair (type I failure). Otherwise, the system is replaced when the first shock after t arrives, or the total operating time reaches age T (0 ⩽ t ⩽ T), whichever occurs first. The occurrence of those two possible actions occurring during the period [0, t] is based on some random mechanism which depends on the number of shocks suffered since the last replacement. The aim of this paper is to find the optimal pair ( t ∗, T ∗) that minimizes the long-run expected cost per unit time of this policy. Various special cases are included, and a numerical example is given.

Optimal maintenance policies for serial, multi‐machine systems with non‐instantaneous repairs

AbstractWe study optimal age‐replacement policies for machines in series with non‐instantaneous repair times by formulating two nonlinear programs: one that minimizes total cost‐rate subject to a steady‐state throughput requirement and another that maximizes steady‐state throughput subject to a cost‐rate budget constraint. Under reasonable assumptions, the single‐machine cost‐optimal and throughput‐optimal solutions are unique and orderable, and the multi‐machine optimal solutions have appealing structure. Furthermore, we establish equivalence between the two formulations and provide an illustrative numerical example. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Optimal Age-Replacement Policy for Nonrepairable Products Under Renewing Free-Replacement Warranty

This paper investigates the effects of a renewing free-replacement warranty on the age replacement policy for a nonrepairable product. For both warranted, and nonwarranted products, cost models are developed, and the corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. Furthermore, we show that the optimal replacement age for a warranted product is closer to the end of the warranty period than for a nonwarranted product. Finally, numerical examples are given to evaluate the impact of a product warranty on the optimal replacement age.

Optimal age-replacement policy of a system subject to shocks with random lead-time

This paper considers a generalized age-replacement policy of a system subject to shocks with random lead-time. A system is subject to shocks that arrive according to a non-homogeneous Poisson process. A model is developed for the average cost per unit time and is based on the stochastic behavior of the assumed system and reflects the cost of storing a spare as well as the cost of system downtime. The minimum-cost policy time is described and discussed. Various special cases are considered. Because the model and its analysis are general, several existing results are shown to be subsumed by this model.

A note on the upper bound for the optimal work size

Mi (2002) recently considered a two-dimensional optimization problem for the optimal age-replacement policy and the optimal work size. In order to find (y∗,T∗), Mi (2002) found the optimal age-replacement policy T∗(y) for each fixed work size y, and then searched for the optimal work size y∗. When applying this approach, for each fixed work size y, Mi (2002) obtained the bounds for T∗(y). However, no bound for the optimal work size y∗ was derived. In this note, the results on the upper bound for the optimal work size y∗ are given.

A note on the upper bound for the optimal work size

Mi (2002) recently considered a two-dimensional optimization problem for the optimal age-replacement policy and the optimal work size. In order to find (y ∗,T ∗), Mi (2002) found the optimal age-replacement policy T ∗(y) for each fixed work size y, and then searched for the optimal work size y ∗. When applying this approach, for each fixed work size y, Mi (2002) obtained the bounds for T ∗(y). However, no bound for the optimal work size y ∗ was derived. In this note, the results on the upper bound for the optimal work size y ∗ are given.

Age replacement policies in two time scales

AbstractWe develop and estimate optimal age replacement policies for devices whose age is measured in two time scales. For example, the age of a jet engine can be measured in the number of flight hours and the number of landings. Under a single‐scale age replacement policy, a device is replaced at age τ or upon failure, whichever occurs first. We show that a natural generalization to two scales is to replace nonfailed devices when their usage path crosses the boundary of a two‐dimensional region M, where M is a lower set with respect to the matrix partial order. For lifetimes measured in two scales, we consider devices that age along linear usage paths. We generalize the single‐scale long‐run average cost, estimate optimal two‐scale policies, and give an example. We note that these policies are strongly consistent estimators of the true optimal policies under mild conditions, and study small‐sample behavior using simulation. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 592–613, 2003.

Age-replacement policy and optimal work size

Suppose that there is a sequence of programs or jobs that are scheduled to be executed one after another on a computer. A program may terminate its execution because of the failure of the computer, which will obliterate all work the computer has accomplished, and the program has to be run all over again. Hence, it is common to save the work just completed after the computer has been working for a certain amount of time, say y units. It is assumed that it takes a certain time to perform a save. During the saving process, the computer is still subject to random failure. No matter when the computer failure occurs, it is assumed that the computer will be repaired completely and the repair time will be negligible. If saving is successful, then the computer will continue working from the end of the last saved work; if the computer fails during the saving process, then only unsaved work needs to be repeated. This paper discusses the optimal work size y under which the long-run average amount of work saved is maximized. In particular, the case of an exponential failure time distribution is studied in detail. The properties of the optimal age-replacement policy are also derived when the work size y is fixed.

Age-replacement policy and optimal work size

Suppose that there is a sequence of programs or jobs that are scheduled to be executed one after another on a computer. A program may terminate its execution because of the failure of the computer, which will obliterate all work the computer has accomplished, and the program has to be run all over again. Hence, it is common to save the work just completed after the computer has been working for a certain amount of time, say y units. It is assumed that it takes a certain time to perform a save. During the saving process, the computer is still subject to random failure. No matter when the computer failure occurs, it is assumed that the computer will be repaired completely and the repair time will be negligible. If saving is successful, then the computer will continue working from the end of the last saved work; if the computer fails during the saving process, then only unsaved work needs to be repeated. This paper discusses the optimal work size y under which the long-run average amount of work saved is maximized. In particular, the case of an exponential failure time distribution is studied in detail. The properties of the optimal age-replacement policy are also derived when the work size y is fixed.