Optimal Age Replacement Research Articles

Optimal Age and Block Replacement for a General Maintenance Model

We continue the study of our general cost structure for a maintained system. Here we focus on the optimization questions for an age or block policy. The notion of a marginal cost function is rigorously formulated and its utility investigated. Various applications are considered, including a new model in which minimal repairs are performed as long as the total accumulated repair costs do not exceed a fixed amount.

A sequential scheme to estimate the optimal age replacement policy

Consider a system which is subject to failure and must be replaced when this occurs. If it costs less to replace the system in advance before failure, it may be advantageous to use an age replacement policy. However, the optimal age to replace the system is unknown if the underlying failure distribution is unknown. This paper develops a scheme to update the current estimate of the optimal age replacement policy in an on-line fashion and simultaneously controlling costs by reducing system failures.

Public sector projects in a mathematical modeling course

Student teams in a mathematical modeling course have carried out several projects for the City of Bloomington. IL, a small municipality with a population of 50,000. The first project was a water meter replacement model. Since water meters lose accuracy with age, older meters are a source of lost revenues. The team attempted to determine the optimal meter replacement age. The second project was a police patrol car workload model. This multi-dimensional queueing model involves police call arrival rates, service times, and overall patrol car workloads. The third and fourth projects were carried out for the Bloomington Fire Department. The third project applied various queueing models to the behavior of their three fire stations. The city planned to add a fourth station, and the final project applied a parametric allocation model to the question of where the additional station should be located. Experiences relevant to these projects, as well as the philosophy of student projects in general are discussed.

A new graphic presentation of cost optimal age replacement policies

Cost optimal age replacement policy has a special importance in the development and application of a preventive maintenance programme. The well known mathematical model for this policy has been solved by a computer package for a wide range of situations. In the paper, two sets of graphs have been presented; one for determination of optimal replacement age and the other for determination of associated replacement cost. In the former set of graphs, the so-called z-curves are plotted, where z indicates the closeness of optimal age to the characteristic life. Weibull failure distribution has been used to express failure statistics because of the generality of this distribution.

Optimal Replacement Policies for Irreparable Warrantied Items

This article investigates age replacement policies for irreparable items sold under warranty. Since the costs of replacement depends on terms of warranty, the analysis of age replacement policies is more complex. Optimal age replacement policies that minimize the long run average cost rate are constructed. For warrantied items with increasing failure rates, the optimal policy is to replace functioning items after a finite period of time. A few examples are presented to illustrate the theory.

Optimal age-replacement policy for equipment monitored by a stochastically failing indicator : B. K. Yoo and C. S. Sung. IEEE Trans. Reliab.R-34 (2) 162 (1985)

Optimal age-replacement policy for equipment monitored by a stochastically failing indicator : B. K. Yoo and C. S. Sung. IEEE Trans. Reliab.R-34 (2) 162 (1985)

Indivisibility, irreversibility, and the demand for consumer durables

A deeper understanding of the volatility of expenditures on consumer durables is sought in the properties of those goods and the transactions by which they are acquired: durability, indivisibility, and irreversibility. When these properties constrain optimization we find: 1) variation in the lengths of endogenously determined replacement cycles rather than stock-level adjustments may account for much of the volatility, 2) the qualitative nature of an individual consumer's response to a shock depends on the age of his existing unit relative to its optimal replacement age when the shock occurs, 3) the aggregate distribution of unit ages relative to their optimal replacement ages conditions the aggregate response to shocks, and 4) shocks actually change that distribution. A simple aggregation methodology is demonstrated which depicts exaggerated aggregate reactions to shocks.

Optimal Age-Replacement Policy for Equipment Monitored by a Stochastically Failing Indicator

An optimal age-replacement policy is presented for the system composed of a single piece of equipment and an indicator. The state of the equipment (good or failed) is monitored by the indicator, and both the equipment and the indicator can fail. Our model generalizes one of Barlow & Hunter, in that it duplicates their model when the indicator is perfect.

Experience with a Stochastic Replacement Model

This paper reports on a study initiated to check the validity of an existing six-monthly block replacement policy for a set of filling valves in a canning line. After dealing with inadequacies in the data and changing to a production-based time measure, the paper shows how a renewal function measure of the expected number of valve replacements was obtained and led to the conclusion that the current block replacement policy could not be justified. The possibility of an age-based replacement policy being of value remained. In order to model such a policy, it was necessary to reverse the usual analysis of renewal-type processes in that an estimate was required of the distribution function of time between renewals, given the renewal function. A finite optimal replacement age was found which depended upon the objective being to minimize a measure of downtime due to replacements, or operating costs attributable to replacements. Calculations were further complicated by part of the plant having a finite remaining life before being upgraded.

Optimal Age Replacement versus Condition Based Replacement: Some Theoretical and Practical Considerations

When times to failure of a unit follow the Weibull distribution, achievement of optimal costs under age replacement is shown to be quite insensitive to the value of the shape parameter. Moreover, it is shown that under condition based replacement consid..

On Optimal Replacement of Farm Tractors

Two important parameters influencing replacement of farm tractors are (a) the tractor's remaining (terminal) market value and (b) income tax incentives. Peacock and Brake were among the first to estimate remaining value (RV) equations for tractors and other large farm machines. Remaining value equations are also presented in the Agricultural Engineers Yearbook and other recent publications. Chisholm modeled the effects of special income tax investment incentives on optimal replacement ages. Kay and Rister further examined and clarified the tax impacts of the United States. Bates, Rayner, and Custance extended previous studies by investigating the tax effects of inflation on optimal replacement ages. Each of these optimal replacement studies estimated replacement ages for tractors to be seven to fourteen years. This seems to be longer than ages actually used by many U.S. farm tractor owners. Kay and Rister (p. 358) list four possible reasons for the longer estimates: (a) misestimation of the repair-cost time pattern, (b) possible incorrect estimation of opportunity costs of tractor breakdowns, (c) owners' desires to replace with larger tractors, and (d) no consideration for replacing with technically improved machines. Kay and Rister assessed the potential impact of alternative repair and breakdown costs by generating alternative data. However, none of the studies examined the impact of using alternative RVs. Both the Kay-Rister study and the Bates-Rayner-Custance study relied upon the Peacock-Brake RV equation; Chisholm's study relied upon a single series of RV observations developed for Australian wheat farms in the 1960s. Also, each study reflected tax regulations existing in 1976 or earlier. With the passage of the Economic Recovery Tax Act of 1981 (ERTA-81), many changes were made to stimulate capital investment. Thus, the new tax law may cause more frequent replacement. The research reported in this paper examines the importance of RV forecasts in optimal replacement decisions. An original aspect of the research is the specification and estimation of a more generalized RV equation which includes more situation-specific explanatory variables than previous RV equations. Optimal tractor replacement decisions using forecasts from this generalized equation are compared to decisions based on three other RV equations. In addition, effects of the Economic Recovery Tax Act of 1981 on optimal replacement decisions are examined.

Optimal Age Replacement Policies for Items from a Mixture

An optimal age-replacement policy with items drawn from a mixture of two types is discussed. Conditions under which it is worth testing (at a cost) to obtain the extra information of item type are derived and a numerical example presented.

Reliability evaluation of a flow network : S. H. Lee. IEEE Trans. Reliab.R-29 (1) 24 (April 1980)

A general age-replacement model in which incorporates minimal repair, planned and unplanned replacement, is considered in this paper for products under a renewing free-replacement warranty policy. For both warranted and non-warranted products, cost models from the user’s perspective are developed, and the corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. The impacts of a product warranty on the optimal replacement model are investigated analytically. Furthermore, we show that the optimal replacement age for a warranted product is closer to the end of the warranty period than for a non-warranted product. Finally, numerical examples are given for illustration.

Optimal Scheduled-Maintenance Policy Based on Multiple-Criteria Decision-Making

Usually, more than one independent (conflicting) criterion is important in determining the replacement age of a critical item for a maintained system. In this study, mathematical models have been developed for three such criteria: 1) minimum replacement cost-rate, 2) maximum availability, and 3) lower-bound on mission reliability. The solutions are obtained using four methods for multiple criteria decision making: 1) strictest-selection, 2) lexicographic, 3) Waltz lexicographic, and 4) sequential multiple-objective problem-solving technique (SEMOPS). Using an aircraft engine as an example, the optimal replacement age has been found by the four different methods. The results and the implications of the methods are discussed.

Optimal replacement policy and approximate replacement rules

An iterative procedure for calculating the optimal replacement age of capital equipment under certain assumptions about future costs is presented and shown to be a practicable method of determining replacement policy. This procedure is compared empirically with three approximate replacement rules, the Terborgh rule and two payoff period rules. The increase in production cost that results from following these approximate rules is calculated and it is shown that a combination of these rules improves on any one of them individually. However, the iterative procedure for calculating the optimal policy is computationally simple enough to make the use of approximate rules unnecessary.

Inflation and Farm Tractor Replacement in the U.S.: A Simulation Model

Two recent contributions to this Journal (Chisholm; Kay and Rister) have been concerned to extend the literature on the replacement problem to encompass the real world decision milieu of the farmer via taxation considerations. These extensions, while welcome and useful, seem to us to be incomplete in the inflationary world of the 1970s: specifically, they make no explicit allowance for the link between optimal replacement age and the nature of the allowances permitted by the taxation authorities in an economy with rising prices. We would suggest that inflation has not been so negligible in most developed economies that it can be disregarded in this aspect of farm decision making. The principal purpose of this note, then, is an attempt to extend further the tax-adjusted replacement model to embrace relevant considerations of inflation. We shall extend the results of Kay and Rister, but whereas previous contributions have utilized discrete time models, we shall use a continuous time model. It may be noted that Perrin developed a continuous time depreciation model, but without consideration of taxation and inflation. His examples, however, utilized discrete, annual models only. It finds the optimal replacement age exactly, an advantage of some importance in its own right, but more important, one which enables the sensitivity of replacement to changes in other conditions to be assessed with greater precision.

Determining Optimal Replacement Age of Beef Cows in the Presence of Stochastic Elements

Feeder calf producers face a problem common to all owners of productive assets: how long should the asset (brood cow) be used before it is replaced? Expected productivity of a brood cow can be measured by two parameters: (1) the likelihood that she will wean a calf, and (2) its anticipated weight when weaned. Both are independent functions of the cow's age which decline annually after reaching peaks in the early years of her productive life. The calf producer who expects to maximize profits in the long run must choose an optimal rate of replacement for his brood cows.

Age Replacement with Discounting for a Continuous Maintenance Cost Model

The optimal age replacement policy according to the criterion of Fox [5] is obtained for the model, introduced by Scheaffer [7], containing a continuously increasing maintenance cost factor. The new results beyond the generalisation to a new model are mainly in sensitivity analysis. Examples are given where the optimal replacement age increases with the interest rate, as well as examples of the opposite.

The regulation of the trucking industry—deterministic replacement model application

An attempt has been made to analyze the impact of a country's regulatory policy of its trucking industry on the correlation between the preferable usage of trucks according to national interests and its counterpart according to private interests, by using a deterministic replacement model. Operational data has been obtained from time series derived from a cross‐sectional survey of the country's truck fleet. Trucks were grouped into 15 strata according to characteristics of load capacity, technological specification, and type of fuel. For each stratum the optimal replacement age was determined according to the criteria of minimal average cost of hauling ton × km, maximal average profit, and minimal average annual cost, and the corresponding costs or profits were calculated for both interests. By comparing the optimal conditions in the various strata, the preferable fuel types and load capacities were determined for the national interest and recommendations for regulation have been provided coinciding the n...

Effects of Tax Depreciation Policy and Investment Incentives on Optimal Equipment Replacement Decisions

AbstractA model is developed to analyze the effects of income tax policy on the optimal timing of replacement for farm machinery. The impact of some forms of tax investment incentives on optimal replacement age was found to be substantial, while the influence of different tax depreciation methods is minimal.