An Equipment Replacement Problem

This paper describes a study undertaken to develop a model for the replacement of a particular type of machine. The dominant operating costs are identified, and existing replacement models reviewed. One of the most important factors is the cost of production stoppages which can sometimes result from the breakdown of these machines. In order to predict the effects of this in terms of the machines' age, a simulation model is developed.The results from the replacement model are investigated in terms of their sensitivity to the variability in the estimates of the parameters required by the model. In particular some interesting results relating the method used for calculating the resale values and the optimal replacement interval are presented.     

A Study in Equipment Replacement

A Study in optimum replacement of fork lift trucks is described, using two models. The first is related to minimum average costs per truck per year, the second uses the approach of discounted cash flow. The parameters used in these models include the purchase price, the resale value and the maintenance costs of the equipment. The effect of capital allowances for tax purposes is included.     

Equipment Replacement in an Unsteady Economy

The decision problem concerning the replacement of members of a fleet of fork lift trucks during a period of inflation and economic uncertainty is considered. Based upon the analysis of data collected over a 2 year period of considerable inflation, a model of the expected operating costs for a truck is developed. The usual replacement criteria are not applicable here and an alternative criterion function based upon relatively short term estimates of costs and discount rate is presented. Using this function, the replacement decision is determined for both constant and variable discount rate situations.     

A Robust Replacement Model with Applications to Medical Equipment

Perceived shortcomings in the applicability of capital equipment replacement modelling, identified in a 1987 survey within the UK are addressed and a robust replacement model formulated. First, however, a comparison between the 1987 survey and a similar 1988 survey undertaken within the USA is made and explanations for apparent differences in conclusions are presented. A replacement model is then developed in the context of medical equipment where factors such as service and risk play a role in replacement decision-making. A mechanism for quantitatively allowing for qualitative and for political type factors within a short time horizon replacement model is introduced by means of a penalty factor. A case example is presented for medical ventilator equipment.     

Utilizing Weibull Failure Rates in Repair Limit Analysis for Equipment Replacement/Preventive Maintenance Decisions

Repair limit analysis was originally proposed as a methodology for determining whether to repair or to replace an operating unit. The approach structures the problem as a Markov or semi-Markov decision process in which state-dependent repair limits trigger the replacement decision. Such a basic framework can easily be applied to more general equipment repair/overhaul environments in which typical maintenance condition monitoring information can serve as the overhaul trigger. One unnecessary limitation of repair limit analysis found in the literature is the use of a constant force of mortality within each state of the model. The purpose of this paper is to extend the repair limit analysis by incorporating a changing force of mortality as the unit ages. In this way, the analysis is more flexible in the parameter estimation phase and it is argued here more appealing since a changing (and usually increasing) force of mortality is utilized in equipment maintenance environments.     

Replacement Strategies

Components of a system function for a time and then fail. A central problem is to decide whether a strategy of scheduled replacement is preferable to the running of all components until failure. This is considered by comparing some simple strategies for component replacement. Considerations from probability theory and renewal theory are used to obtain expressions for the average cost of replacements per unit time for each strategy. After obtaining some general conditions for one strategy to be preferable to another, a detailed comparison is made when the interfailure times are independent samples from a gamma distribution.     

Tax-Adjusted Replacement Models

The 1984 UK Finance Act introduced changes in tax legislation with consequences for both capital and revenue expenditure on plant. The one- and two-cycle rent models for capital equipment replacement and the infinite-cycle discounted-cost model are extended here to incorporate the new tax features. A specific replacement problem is used as the basis of an analyis of the sensitivity of the optimal replacement period to parameters. Whilst all these models are consistently insensitive to the new tax legislation, there is no consistency across models with respect to which parameters dominate choice of optimal replacement period.     

Two-Stage Replacement Strategies

The following replacement problem is considered. N items, which are subject to failure, can be divided into two groups distinguished by the fact that the individual replacement cost in one group is higher than in the other. A strategy is required to minimize replacement costs. In some cases the cheapest policy is to replace each item, when it fails, by a new item. However, the paper shows that this policy can usually be improved upon by what is called a two-stage policy. In a two-stage policy the failures in one group are replaced by new items; those in the other group are replaced by items already operating in the first group. Under some circumstances it is shown to be worth while to create a second group. Formulae are given for calculating the optimum two-stage strategies for any life distribution, but the emphasis is on the formulation of general conditions under which two-stage schemes are preferable to simple replacement. Some extensions and generalizations are briefly indicated.     

An Economic Replacement Model

The report is based on a study of the replacement of Army vehicles. These vehicles are currently phased out of service by a system of decision rules called repair limits. Existing repair limit systems, although superior to group replacement policies, appear to be sub-optimum.A theory of repair limits is proposed. This leads to the determination of optimum repair limits by a simulation method. A second optimization method is introduced based on the use of certain frequency distributions which are found to represent the repair cost data.The results show that the methods proposed can be expected to lead to financial savings.     

WDM Fiber Replacement Scheduling

We consider the migration of a WDM telecommunication network to a new technology. In the course of the migration process, shared network resources must be temporarily shut down, affecting the network connections that use them. In this paper we describe an ILP-based approach to find a migration schedule that minimizes the total service disruption occurring in the network.     

On String Replacement Exponentiation

The string replacement (SR) method was recently proposed as a methodfor exponentiation a ^e in a group G. The canonicalk-SR method operates by replacing a run of i onesin a binary exponent,0k, with i-1 zeroes followedby the single digit b=2 ⁱ -1. After recoding, it was shown in[5] that the expected weight of e tends to n/4 forn-bit exponents. In this paper we show that the canonicalk-SR recoding process can be described as a regular language andthen use generating functions to derive the exact probability distribution ofrecoded exponent weights. We also show that the canonical 2-SR recodingproduces weight distributions very similar to (optimal) signed-digitrecodings, but no group inversions are required.     

Replacement Policies under Minimal Repair

In many situations where system failures occur the concept of ‘minimal repair’ is important. A minimal repair occurs when the failed system is not treated so as to return it to ‘as new’ condition but is instead returned to the average condition for a working system of its age. Examples include complex systems where the repair or replacement of one component does not materially affect the condition of the whole system.For a system with decreasing reliability it will become increasingly expensive to maintain operation by minimal repairs, and the question then arises as to when the entire system should be replaced. We consider cases where the failure distribution can be modelled by the Weibull distribution. Two policies have been suggested for this case. One is to replace at a fixed time and the other is to replace at a fixed number of failures. We consider a third policy, to replace at the next failure after a fixed time, and show that it is optimal.Expressions to decide the replacement point and the cost of this policy are derived. Unfortunately these do not give rise to explicit representations, and so they are used to provide extensive numerical comparisons of the policies in a search for effective explicit approximations. Conclusions are drawn from these comparisons regarding the relative effectiveness of the policies and approximations.