If any equipment or machine is used for a long period of time, due to wear and tear, the item tends to worsen. A Replacement Model or remedial action to bring the item or equipment to the original level is desired. Then the need for replacement becomes necessary. This need may be caused by a loss of efficiency in a situation leading to economic decline. By efflux of time the parts of an item are being worn out and the cost of maintenance and operation is bound to increase year after year.
The resale value of the item goes on diminishing with the passage of time. The depreciation of the original equipment is a factor, which is responsible not to favour replacement because the capital is being spread over a long time leading to a lower average cost. Thus there exists an economic trade-off between increasing and decreasing cost functions.
We strike a balance between the two opposing costs with the aim of obtaining a minimum cost. The problem of replacement is to determine the appropriate time at which a remedial action should be taken which minimizes some measure of effectiveness. Another factor namely technical and / or economic obsolescence may force us for replacement.
DEFINITION OF REPLACEMENT MODEL
The Replacement Model Theory in Operations Research is used in the decision making process of replacing a used equipment with a substitute; mostly a new equipment of better usage. The replacement might be necessary due to the deteriorating property or failure or breakdown of particular equipment
In fact, in any system the efficacy (efficiency) of an item deteriorates with time. In such cases, either the old item should be replaced by a new item, or some kind of restorative action (maintenance) is necessary to restore the efficiency of the whole system.
The cost of maintenance depends upon a number of factors, and a stage comes at which the maintenance cost is so large that it is more profitable to replace the old item. Thus, there is a need to formulate the most effective replacement policy. Replacement models are concerned with the problem of replacement of machines, individuals, capital assets, etc. due to their deteriorating efficiency, failure, or breakdown. It is evident that the study of replacement is a field of application rather than a method of analysis. Actually, it is concerned with methods of comparing alternative replacement policies.
EQUIPMENT MAINTENANCE/ REPLACEMENT/ REENGINEERING
To decide the effective mode of maintenance it is essential to carry out reliability analysis of critical parts of the equipment in all modern automated and semiautomated plants. These critical parts may be individual pieces of equipment or a combination of parts that from systems.
Before considering the purchase of any capital equipment, the evaluation of its reliability is essential, which directly depends upon the probability of failures. It is desirable to obtain a reliability index (numerical value) for each machine which is based on such factors as visual inspection tests and measurements, age, environment duty cycle of the equipment. These numbers, so calculated, represent the reliability of particular equipment. It is also possible to combine these indices and express an aggregate reliability index number for the complete system.
From the evaluation of the above index numbers, schedules can be set for equipment maintenance. Wherever needed, the maintenance efforts can be expanded. From the reliability reports it is possible to determine the actions that are required to maintain the operational availability at the desired level. Cost estimates for such maintenance for much maintenance functions can also be prepared based on the reliability information.
Similarly, the decision to replace existing equipment will require the consideration of the following questions, economic factors and reliability index numbers calculated for the existing equipment.
i. Will the maintenance cost come down with the replacement of the old equipment?
ii. Will the cost per unit of production/service come down due to automated test features of the mew equipment?
iii. Is the existing equipment not sufficient to meet the future production/service targets?
iv. Will the new equipment be environment friendly and provide better safety to operators?
v. Is there any possibility of adding additional accessories to existing equipment in order to make it more versatile for future use, or is the rebuilding of existing equipment possible through minor modifications?
Optimal replacement policy of the equipment can be determined if reliable estimates of revenue (return from equipment), up keep (maintenance cost) cost and replacement costs are available. The equipment in use in industries can be mainly divided into (1) equipment with diminishing efficiency and (2) equipment with constant efficiency. The first category deteriorates with time resulting in increase in operating cost including maintenance cost, and second category operates at constant efficiency for a certain time period and then deteriorates suddenly.
Several models have been developed using repair vs. time and cost, in order to solve the replacement problem of equipment with diminishing efficiency. Replacement is considered to be the regeneration point of whole life where the operating cost function initially starts. In practice such methods really work well and the life of the equipment/system is enhanced.
On the other hand the concept of reengineering in lieu of replacement is one viable model as the operating cost increases with time. This model maximizes the gain between the operating costs before and after the overhauls. Reengineering can be perceived as the adjustment, alteration, or partial replacement of a process or product in order to make it to meet a new need. Successful implementation of reengineering will improve the equipment or process performance and this reduces the maintenance and operating costs.
CONVENTIONAL REPLACEMENT PROBLEM
The replacement problems are concerned with the issue that arises when the performance of an item decreases, failure or breakdown occurs. The decrease in performance or breakdown may be gradual or sometimes sudden. The need for replacement of items is felt when,
i. The existing item or system has become inefficient or require more maintenance.
ii. The existing equipment has failed due to accident or otherwise and does not work at all.
iii. The existing equipment is expected to fail shortly.
iv. The existing equipment has become obsolete due to the availability of equipment with latest technology and better design.
The solution to replacement problem is nothing but arriving at thebest policy that determines the time at which the replacement is most economical instead of continuing at an increased maintenance cost. The Main objective of replacement policy is to direct the organization in many situations so that it can take right decision. For Example, few situations are:
i. Waiting for complete failure of item or to replace earlier at the expense of higher cost of the item.
ii. Whether to replace the underperforming equipment with the similar kind of item or by different kind (latest model) of item.
The problem of replacement occurs in the case of both men and machines. Using probability it is possible to estimate the chance of death (failure) at various ages.
TYPES OF FAILURES
As the term ‘failure’ encompasses wider concept, failures can be discussed under the following two categories.
Gradual Failure: In this, the failure mechanism is progressive. As the age of an item increases, its performance deteriorates. This results in:
• Decreased productivity of the item
• Decrease in resale value of item
(Ex: Mechanical items like pistons, bearing rings, tyres, etc.,)
Sudden Failure: This type of failure can be observed in the itemsthat do not deteriorate gradually with age but which fail suddenly after some period of service. The time period between installation and failure will not be constant for any particular equipment. However the failure pattern will follow certain frequency distribution that may be progressive, retrogressive or random in nature.
Progressive failure: It is said to be progressive failure, when probability of failure increases with the age of an item. Ex: light bulbs, tyres etc.
Retrogressive failure: Certain items will have more probability of failure in the initial years of their life and with the increase in the life of an item the chances of failure become less. That is, the ability of the item to survive in the initial years of life increases its expected life. Aircraft engines exemplify industrial equipments with this type of distribution of life span.
Random failure: It is said to be random failure, when constant probability of failure is associated with equipment that fails because random causes such as physical shocks that are independent of age. In the case of random failure, virtually all items fail before aging has any effect. For example, vacuum tubes, items made of glass or mirror, fruits, vegetables etc may fail independent of their age.
The replacement situations generally are divided into the following four types:
i. Replacement of capital equipment whose performance decreases with time, e.g., machine tools, vehicles in a transport organization, airplanes, etc.
ii. Group replacement items that fail completely, e.g., electrical bulbs, etc.
iii. Problem of mortality and staffing.
REPLACEMENT OF ITEMS WITH GRADUAL DETERIORATION
As mentioned earlier the equipment, machineries and vehicles undergo wear and tear with the passage of time. The cost of operation and the maintenance are bound to increase year by year. A stage may be reached that the maintenance cost amounts prohibitively large that it is better and economical to replace the equipment with a new one. We also take into account the salvage value of the items in assessing the appropriate or opportune time to replace the item. We assume that the details regarding the costs of operation, maintenance and the salvage value of the item are already known. The problem can be analysed first without change in the value of the money and later with the value included.
If the interest rate for the money is zero the comparison can be made on an average cost basis. The total cost of the capital in owning the item and operating is accumulated for n years and this total is divided by n.
Since we have discrete values for the costs for various years, an analysis is done using the tabular method, which is simple one to use discontinuous data. There are also the classical optimization techniques using finite difference methods for discrete parameters and using the differential calculus for continuous data.
Now we take an example in which an automobile fleet owner has the following direct operation cost(Petrol and oil) and increased maintenance cost (repairs, replacement of parts etc). The initial cost of the vehicle is #70,000. The operation cost, the maintenance cost and the resale price are all given in table 1 for five years.
Table 1
| Year of Service | Annual Operating Cost (#) | Annual Maintenance Cost (#) | Resale Value (#) |
| 1 | 10000 | 6000 | 40000 |
| 2 | 15000 | 8000 | 20000 |
| 3 | 20000 | 12000 | 15000 |
| 4 | 26000 | 16000 | 10000 |
| 5 | 32000 | 20000 | 10000 |
Table 2
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| At the end of the yr (n) | Annual Operating Cost (#) | Annual Maintena nce Cost (#) | Total RunningCost (#) (2+3) | Cummulative Running Cost (#) | Capital Cost (#) | TotalAverage Cost (#) (5+6) | Annual Cost (#) (7/n) |
| 1 | 10 | 6 | 16 | 16 | 30 | 46 | 46.00 |
| 2 | 15 | 8 | 23 | 39 | 50 | 89 | 44.50 |
| 3 | 20 | 12 | 32 | 71 | 55 | 126 | 42.00 |
| 4 | 26 | 16 | 42 | 113 | 60 | 173 | 43.52 |
| 5 | 32 | 20 | 52 | 165 | 60 | 225 | 45.00 |
Table 2 gives the details of the analysis to find the appropriate time to replace the vehicle. The cumulative running cost and capital (Value - Resale value) required for various years are tabulated and the average annual cost is calculated. The corresponding year at which this average annual cost is minimum is chosen to be the opportune time of replacement.
It is evident from the last column of table 2 that the average annual cost is least at the end of three years. (equal to 42,000). Hence this is the best time to purchase a new vehicle.
Example: A mill owner finds from his past records the costs of running a machine whose purchase price is #6000 are as given below.
Table 3
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Running Cost (#) | 1000 | 1200 | 1400 | 1800 | 2300 | 2800 | 3400 |
| Resale Value (#) | 3000 | 1500 | 750 | 375 | 200 | 200 | 200 |
Determine at what age is a replacement due?
Solution: We prepare the following table 3 to find the solution.
| 1 | 2 | 3 | 4 | 5 |
| At the end of year n | Cummulative Running Cost(#) | Capital Cost (K) | Total Cost (#) (2+3) | Average Annual Cost (K) |
| 1 | 1000 | 3000 | 4700 | 4000 |
| 2 | 2200 | 4500 | 6700 | 3350 |
| 3 | 3600 | 5250 | 8850 | 2950 |
| 4 | 5400 | 5625 | 11025 | 2756 |
| 5 | 7700 | 5800 | 13500 | 2700 |
| 6 | 10500 | 5800 | 16300 | 2717 |
| 7 | 13900 | 5800 | 19700 | 2814 |
From the table 3 above we conclude that the machine should be replaced at the end of the fifth year, indicated by the least average annual cost (#2700) in the last column.
The mill owner in the previous problem has now three machines, two of which are two years old and the third one year old. He is considering a new type of machine with 50% more capacity than one of the old ones at a unit price of #8000. He estimates the running costs and resale price for the new machine will be as follows;
Table 4
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Running Cost (#) | 1200 | 1500 | 1800 | 2400 | 3100 | 4000 | 5000 |
| Resale Price (#) | 4000 | 2000 | 1000 | 500 | 300 | 300 | 300 |
Assuming that the loss of flexibility due to fewer machines is of no importance, and that he will continue to have sufficient work for three of the old machines, what should his policy be?
Solution: As in the previous problem we prepare a table 4 to find the average annual cost of the new type of machine
| At the end of year n | CummulativeRunning Cost(K) | Capital Cost(K) | Total Cost (#) (2+3) | Average Annual Cost(K) |
| 1 | 1200 | 4000 | 5200 | 5200 |
| 2 | 2700 | 6000 | 8700 | 4350 |
| 3 | 4500 | 7000 | 11500 | 3833 |
| 4 | 6900 | 7500 | 14400 | 3600 |
| 5 | 10000 | 7700 | 17700 | 3540 |
| 6 | 14000 | 7700 | 21700 | 3617 |
| 7 | 19000 | 7700 | 26700 | 3814 |
From the above table 4 we observe that the average annual cost is least at the end of five years and it would be #3540 per machine. But the new machine can handle 50% more capacity than the old one. So in terms of the old, the new machine's annual cost is only # (3540) (2/3) = #2360. This amount is less than the average annual cost for the old machine, which is #2700. If we replace the old machine with the new one, it is enough to have two new machines in place of with the new one; it is enough to have two new machines in place of three old machines. On comparing the cost of 2 new machines (# 7080) with that for 3 old machines (#8100), it is clear that the policy should be that the old machines have to be replaced with the new one. Still we have to decide about the time when to purchase the new machines.
The new machines will be purchased when the cost for the next year of running the three old machines exceeds the average annual cost for two new types of machines. Examining the table 3 pertaining to the previous problem, we find, the total yearly cost of one small machine from the column 4. The successive difference will give the cost of running a machine for a particular year. For example, the total cost for 1 year is #4000. The total cost for 2 years is #6700. The difference of #2700 will be accounted as the cost of running a small machine during the second year. Similarly we have #2150, #2175, #2475 and #2800 as the cost of running the old machine in the third, fourth, fifth and sixth year respectively.
Now, with this information we calculate the total costs next year for the two smaller machines, which are two years old (entering the third year of service) and one smaller machine aged one year (and hence entering second year of service), which will be 2 x 2150 + 2700 = #7000
This is less than the average annual cost of two new machines, which is #7080. So the policy is not to replace right now. If we wait for the subsequent years, the total cost of running the old machines will be #6500, #7125 and #8025 etc., for years 2, 3 and 4 etc. This indicates that the cost of running the old machine exceeds the average annual cost (#7000) of the two new machines after 2 years from now. Hence the best time to purchase the new type machine will be after 2 years from now.
CONCLUSION
We cannot ignore the contribution of machines and machine based engineering in global developing world as well as developing country like Zambia. Therefore, it is impossible to avoid the importance of machine and its components. The concepts of machine /machinery /components have been fully supported by reliability of the system. Here reliability refers the probability of the system or component which can be worked under given environment and specified time limit without any failure.
The possibilities viz. re-engineering the equipment, replacement of the equipment etc. to ensure the equipment delivers its n
ASSIGNMENT QUESTIONS
•
Discuss types of failures you in replacement model
•
What are the conventional replacement model
Eiselt,
H.A., & Sandblom, C.L. (2012). Operations Research: A Model Based Approach,
2nd ed., New York: Springer Heidelberg
Gupta,
P.K., & Hira, D.S. (2012). Operations Research, New - Delhi: S. Chand &
Company.
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