Types of Replacement Problem (2024)

Chapter: Mechanical : Engineering Economics & Cost Analysis : Replacement And Maintenance Analysis

Replacement study can be classified into two categories: (a) Replacement of assets that deteriorate with time (Replacement due to gradual failure, or wear and tear of the components of the machines). This can be further classified into the following types: (i) Determination of economic life of an asset. (ii) Replacement of an existing asset with a new asset. (b) Simple probabilistic model for assets which fail completely (replacement due to sudden failure).

Types of Replacement Problem

Replacement study can be classified into two categories:

(a) Replacement of assets that deteriorate with time (Replacement due to gradual failure, or wear and tear of the components of the machines).

This can be further classified into the following types:

(i)Determination of economic life of an asset.

(ii)Replacement of an existing asset with a new asset.

(b)Simple probabilistic model for assets which fail completely (replacement due to sudden failure).

Determination of Economic Life of an Asset

Any asset will have the following cost components:

üCapital recovery cost (average first cost), computed from the first cost (purchase price) of the machine.

üAverage operating and maintenance cost (O & M cost)

Total cost which is the sum of capital recovery cost (average first cost) and average maintenance cost.

Types of Replacement Problem (1)

EXAMPLE

A firm is considering replacement of an equipment, whose first cost is Rs. 4,000 and the scrap value is negligible at the end of any year. Based on experience, it was found that the maintenance cost is zero during the first year and it increases by Rs. 200 every year thereafter.

(a)When should the equipment be replaced ifi= 0%?

(b)When should the equipment be replaced ifi= 12%?

(a)Wheni= 0%. In this problem

(i)First cost = Rs. 4,000

(ii)Maintenance cost is Rs. 0 during the first year and it increases by Rs. 200 every year thereafter.

This is summarized in column B of Table

Types of Replacement Problem (2)

Column C summarizes the summation of maintenance costs for each replacement period. The value corresponding to any end of year in this column represents the total maintenance cost of using the equipment till the end of that particular year.

Average total cost = [ First cost (FC) + Summation of maintenance cost ] / Replacement period

Types of Replacement Problem (3)

Column F = Column E + Column D

The value corresponding to any end of year (n) in Column F represents the average total cost of using the equipment till the end of that particular year.

For this problem, the average total cost decreases till the end of year 6 and then it increases. Therefore, the optimal replacement period is six years, i.e. economic life of the equipment is six years.

(b) When interest rate,i= 12%. When the interest rate is more than 0%, the steps to be taken for getting the economic life are summarized with reference to Table

TableCalculations to Determine Economic Life (First cost = Rs. 4,000,Interest = 12%)

Types of Replacement Problem (4)

The steps are summarized now:

1. Discount the maintenance costs to the beginning of year 1.

Column D = Column B

1/ (1 + i)n

= Column B(P/F, i, n) = Column BColumn C.

2. Find the summation of present worth of maintenance costs through the year given (Column E = Column D).

3. Find Column F by adding the first cost of Rs. 4,000 to Column E.

4. Find the annual equivalent total cost through the years given.

Column H = Column Fi(1 + i)n/ (1 + i)n− 1

= Column F(A/P, 12%, n) = Column FColumn G

5. Identify the end of year for which the annual equivalent total cost is minimum.

For this problem, the annual equivalent total cost is minimum at the end of year 7. Therefore, the economic life of the equipment is seven years.

Replacement Of Exist Ing Asset With A New Asset

In this section, the c oncept of comparison of replacement of an existing asset with a new asset is presented. In this analysis, the annual equivalent cost of each alternative should be co mputed first.

Then the alternative which has the least cost should be selected as the best alternative. Before discu ssing details, some preliminary concepts whic h are essential for this type of replacem ent analysis are presented.

Capital Recovery with Return

Consider the follow ing data of a machine.

Let

P= purchase priice of the machine,

F= salvage valu e of the machine at the end of machine life,

n= life of the m achine in years, and

i= interest rate,, compounded annually

The corresponding cash flow diagram is shown in Fig

Types of Replacement Problem (5)

The equation for the annual equivalent amount for the above cash flow diagram is

AE(i) = (PF)(A/P,i,n) +Fi

This equation represents thecapital recovery with return.

Concept of Challenger and Defender

oIf an existing equipment is considered for replacement with a new equipment, then the existing equipment is known as thedefenderand the new equipment is known aschallenger.

oAssume that an equipment has been purchased about three years back for Rs. 5,00,000 and it is considered for replacement with a new equipment. The supplier of the new equipment will take the old one for some money, say, Rs. 3,00,000.

oThis should be treated as the present value of the existing equipment and it should be considered for all further economic analysis.

oThe purchase value of the existing equipment before three years is now known assunk cost, and it should not be considered for further analysis.

EXAMPLE

Two years ago, a machine was purchased at a cost of Rs. 2,00,000 to be useful for eight years. Its salvage value at the end of its life is Rs. 25,000. The annual maintenance cost is Rs. 25,000.

The market value of the present machine is Rs. 1,20,000. Now, a new machine to cater to the need of the present machine is available at Rs. 1,50,000 to be useful for six years. Its annual maintenance cost is Rs. 14,000. The salvage value of the new machine is Rs. 20,000.

Using an interest rate of 12%, find whether it is worth replacing the present machine with the new machine.

Solution

Alternative 1

Present machine

Purchase price = Rs. 2,00,000

Present value (P) = Rs. 1,20,000

Salvage value (F) = Rs. 25,000

Annual maintenance cost (A) = Rs. 25,000

Remaining life = 6 years

Interest rate = 12%

The cash flow diagram of the present machine is illustrated in Fig.

Types of Replacement Problem (6)

Fig.Cash flow diagram for alternative 1.

annual maintenance cost for the preceding periods are not shown in this figure. The annual equivalent cost is computed as

AE(12%) = (PF)(A/P, 12%, 6) +Fi+A

= (1,20,00025,000)(0.2432) + 25,0000.12 + 25,000

= Rs. 51,104

Alternative 2

New machine

Purchase price (P) = Rs. 1,50,000

Salvage value (F) = Rs. 20,000

Annual maintenance cost (A) = Rs. 14,000

Life = 6 years

Interest rate = 12%

The cash flow diagram of the new machine is depicted in Fig.

Types of Replacement Problem (7)

Fig.Cash flow diagram for alternative 2.

The formula for the annual equivalent cost is

AE(12%) = (PF)(A/P, 12%, 6) +Fi+A

= (1,50,00020,000)(0.2432) + 20,0000.12 + 14,000

= Rs. 48,016

Since the annual equivalent cost of the new machine is less than that of the present machine, it is suggested that the present machine be replaced with the new machine.

Simple Probabilistic Model For Items Which Fail Completely

Electronic items like transistors, resistors, tubelights, bulbs, etc. could fail all of a sudden, instead of gradual deterioration. The failure of the item may result in complete breakdown of the system. The system may contain a collection of such items or just one item, say a tubelight.

Therefore, we use some replacement policy for such items which would avoid the possibility of a complete breakdown.

The following are the replacement policies which are applicable for this situation.

(i)Individual replacement policy. Under this policy, an item is replaced immediately after its failure.

(ii)Group replacement policy.Under this policy, the following decision is

made:

At what equal intervals are all the items to be replaced simultaneously with a provision to replace the items individually which fail during a fixed group replacement period?

There is a trade-off between the individual replacement policy and the group replacement policy. Hence, for a given problem, each of the replacement policies is evaluated and the most economical policy is selected for implementation. This is explained with two numerical problems.

EXAMPLE

The failure rates of transistors in a computer are summarized in Table .

Types of Replacement Problem (8)

The cost of replacing an individual failed transistor is Rs. 9. If all the transistors are replaced simultaneously, it would cost Rs. 3.00 per transistor. Any one of the following two options can be followed to replace the transistors:

(a)Replace the transistors individually when they fail (individual replacement policy).

(b)Replace all the transistors simultaneously at fixed intervals and replace the individual transistors as they fail in service during the fixed interval (group replacement policy).

Find out the optimal replacement policy, i.e. individual replacement policy or group replacement policy. If group replacement policy is optimal, then find at what equal intervals should all the transistors be replaced.

Solution

Assume that there are 100 transistors in use.

Let,

pibe the probability that a transistor which was new whenplaced in position for use, fails during theith week of its life. Hence,

Types of Replacement Problem (9)

Since the sum ofpisis equal to 1 at the end of the 7th week, the transistors are sure to fail during the seventh week.

Assume that

(a)transistors that fail during a week are replaced just before the end of the week, and

(b)the actual percentage of failures during a week for a sub-group of transistors with the same age is same as the expected percentage of failures during the week for that sub-group of transistors.

Let

Ni= the number of transistors replaced at the end of theith week

N0 = number of transistors replaced at the end of the week 0 (orat the beginning of the first week).

= 100

N1 = number of transistors replaced at the end of the 1st week

= N0p1 = 1000.07 = 7

N2 = number of transistors replaced at the end of the 2nd week

= N0p2 + N1p1

= 1000.11+ 70.07= 12

N3 = N0p3 + N1p2 + N2p1

= 1000.12+ 70.11+ 120.07

= 14

N4 = N0p4 + N1p3 + N2p2 + N3p1

= 1000.18+ 70.12+ 120.11 + 140.07

= 21

N5 = N0p5 + N1p4 + N2p3 + N3p2 + N4p1

= 1000.21+ 70.18+ 120.12 + 140.11 + 210.07

= 27

N6 = N0p6 + N1p5 + N2p4 + N3p3 + N4p2 + N5p1

= 1000.2 + 70.21 + 120.18 + 140.12 + 210.11 + 270.07

= 30

N7 = N0p7 + N1p6 + N2p5 + N3p4 + N4p3 + N5p2

+ N6p1

= 1000.11 + 70.2 + 120.21 + 140.18 + 210.12

+ 270.11 + 300.07

= 25

Calculation of individual replacement cost

Expected life of each transistor = Types of Replacement Problem (10)

= 10.07 + 20.11 + 30.12 + 40.18

+ 50.21 + 60.2 + 70.11

= 4.39 weeks

Average No. of failures/week = 100/4.39 = 23

(approx.) Therefore,

Cost of individual replacement

= (No. of failures/week Individual replacement cost/transistor) = 23 9 = Rs. 207.

Determination of group replacement cost

Cost of transistor when replacedsimultaneously = Rs. 3

Cost of transistor when replaced individually = Rs. 9

The costs of group replacement policy for several replacement periods are summarized in Table.

TableCalculations of Cost for Preventive Maintenance

Types of Replacement Problem (11)

From Table it is clear that the average cost/week is minimum for the fourth week. Hence, the group replacement period is four weeks.

Individual replacement cost/week = Rs. 207

Minimum group replacement cost/week = Rs. 196.50

Since the minimum group replacement cost/week is less than the individual replacement cost/week, the group replacement policy is the best, and hence all the transistors should be replaced once in four weeks and the transistors which fail during this four-week period are to be replaced individually.

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Mechanical : Engineering Economics & Cost Analysis : Replacement And Maintenance Analysis : Types of Replacement Problem |

Types of Replacement Problem (2024)

FAQs

Types of Replacement Problem? ›

Replacement of items that deteriorate with time. 2. Replacement of items that break down completely, and 3. Replacement of items that becomes out of date due to new developments.

What are the three types of replacement theory? ›

This can be further classified into the following types: (i) Determination of economic life of an asset. (ii) Replacement of an existing asset with a new asset. (b) Simple probabilistic model for assets which fail completely (replacement due to sudden failure).

What are the types of failure in replacement problem? ›

They are (i) Gradual failure and (ii) Sudden failure. Once again the sudden failure may be classified as: (a) Progressive failure, (b) Retrogressive failure and (c) Random failure.

What are the two types of replacement policy? ›

i) Replacement policy for items, efficiency of which declines gradually with time without change in money value. ii) Replacement policy for items, efficiency of which declines gradually with time but with change in money value.

What are some important replacement situations? ›

Reasons for Replacement of Equipment's:
  • (i) Deterioration: It is the decline in performance due to wear and tear or misalignment indicated by; ...
  • (ii) Obsolescence: ADVERTIsem*nTS: ...
  • (iii) Inadequacy: ...
  • (iv) Working Conditions: ...
  • (v) Economy: ...
  • (i) Technical Factors: ...
  • (ii) Financial/Cost Factors: ...
  • (iii) Tangible Factors:

What are replacement methods? ›

Definition. 1. The replacement cost method involves arriving at an asset's value by reference to the present-day cost, in an arms-length transaction, of replacing that asset with a similar asset in a similar condition 1 (plus, if appropriate, payment of any taxes due).

What are the replacement models? ›

Replacement models deal with the problem of finding the optimal random time for a preventive replacement of a technical system. A large class of such models has been considered in the literature recently. In this paper a unifying approach to the replacement problem is given regarding it as an optimal stopping problem.

What are the 4 modes of failure? ›

For mechanical devices, there are four Failure Mechanisms: corrosion, erosion, fatigue and overload. While those Failure mechanisms exists many places in nature, they may or may not be present in the specific working environment of an asset.

What are the 4 modes of material failure? ›

A number of material failure modes were introduced in this article, including impact, spalling, wear, brinelling, thermal shock, and radiation damage. These mechanisms can affect metals, polymers, ceramics, and composites in various applications and in many different environments.

What are the three failure modes? ›

Examples of failure modes are: Ductile fracture. Brittle fracture. Fatigue fracture.

What are the list of replacement rules? ›

Common rules of replacement include de Morgan's laws, commutation, association, distribution, double negation, transposition, material implication, logical equivalence, exportation, and tautology.

What is an example of policy replacement? ›

Policy replacement is "...an action which eliminates the original policy or diminishes its benefits or values." Examples of this are policy loans, taking reduced paid-up insurance, or withdrawing dividends.

What is considered a replacement policy? ›

A replacement occurs when a new policy or contract is purchased and, in connection with the sale, you discontinue making premium payments on the existing policy or contract, or an existing policy or contract is surrendered, forfeited, assigned to the replacing insurer, or otherwise terminated or used in a financed ...

What is an example of replacement? ›

We need a replacement for our old vacuum cleaner. Where can we get replacement parts for the tractor?

What are the four reasons for replacement? ›

Equipment are generally considered for replacement for the following reasons:
  • (i) Deterioration: ...
  • (ii) Obsolescence: ...
  • (iii) Inadequacy: ...
  • (iv) Working Conditions: ...
  • (v) Economy: ...
  • (i) Technical Factors: ...
  • (ii) Financial/Cost Factors: ...
  • (iii) Tangible Factors:
Jun 8, 2019

What are replacement events? ›

Replacement Event means, with respect to any Lender, (a) the commencement of or the taking of possession by, a receiver, custodian, conservator, trustee or liquidator of such Lender, or the declaration by the appropriate regulatory authority that such Lender is insolvent or (b) the making of any claim by any Lender ...

What are the two approaches to replacement analysis? ›

Two basic approaches to analyzing replacement problems are the cash-flow approach and the opportunity-cost approach. The cash flow approach explicitly considers the actual cash-flow consequences for each replacement alternative as it occurs.

What is an example of a group replacement? ›

Example: A system consists of 10000 electric bulbs. When any bulb fails, it is replaced immediately and the cost of replacing a bulb individually is Re. 1/- only.

What is the replacement theory in management? ›

The replacement theory is concerned with the situations that arise when some items such as machines, electric light bulbs, computer, etc. need replacement due to their decreased efficiency, failure or break-down. Such decreased efficiency or complete breakdown may either be gradual or all of a sudden.

What is individual replacement? ›

The individual replacement policy is concerned with replacing an item as at when it fails and Equation (1) is the average individual replacement cost per period.

What is the use of study of replacement problems? ›

Introduction:- The. replacement problems are concerned with the situations that arise when some items such as men, machines and usable things etc need replacement due to their decreased efficiency, failure or breakdown. Such decreased efficiency or complete breakdown may either be gradual or all of a sudden.

What are the elements of replacement theory? ›

the two categories of costs required to determine the optimum period for replacement of an equipment which has a gradual failure mechanism are: (i) Depreciation cost (ii) Operating cost.

What are the six common mechanisms of failure? ›

There are six basic mechanisms of failure for steel structures: ductile yielding, brittle fracture, buckling, fatigue, stress corrosion cracking, and creep.

What are the two main types of failure? ›

Think of it this way: There are two kinds of failure. The first comes from never trying out your ideas because you are afraid, or because you are waiting for the perfect time. This kind of failure you can never learn from, and such timidity will destroy you. The second kind comes from a bold and venturesome spirit.

What is the most common failure mode? ›

Fatigue failure

In materials science, fatigue – the weakening of a material caused by cyclic loading resulting in progressive, brittle, localized structural damage – is the most common failure mode and the one that generally produces other types of failure.

What are the five theories of failure? ›

  • THEORIES OF FAILURE.
  • Maximum principal strain theory.
  • Maximum shear stress theory.
  • Maximum strain energy theory.
  • Design conditions for various failure theory.

What are three 3 causes of material failure? ›

The usual causes of material failure are incorrect materials selection, incorrect processing, incorrect manufacturing procedures, inadequate design or incorrect use.

What are the four stages of failure mode effect analysis? ›

FMEA is widely used in manufacturing industries at various stages of the product life cycle. There are four main types of FMEA analysis: System FMEA, Design FMEA, Process FMEA, and Equipment FMEA.

How many types of failure are there? ›

These are preventable, unavoidable/complexity-related, and innovative or intelligent failures. All organisations can benefit from understanding what kinds of failures they can face.

What are the types of material failure? ›

Material Failure
  • Corrosion.
  • Erosion.
  • Fatigue.
  • Stress corrosion cracking.
  • Cavitation.
  • Galling.
  • Fretting.
  • Foreign object damage.
Jul 10, 2018

What are common cause failure modes? ›

Common cause failures are either common event failures, where the cause is a single external event, or common mode failures, where two systems fail in the same way for the same reason. Common mode failures can occur at different times because of a design defect or a repeated external event.

How many rules of replacement are there? ›

We have ten such rules, which are called the rules of replacement. The difference between these two sets of rules is that the rules of inference are themselves inferences whereas rules of replacement are not. However, the rules of replacement are restricted to change or change in the form of statements.

What does replacement mean in law? ›

replacement n

1 a : the act of replacing. : the state of being replaced. b : an insurer's option under a policy to replace or repair damaged property rather than pay the insured for the loss. 2 : something that replaces. ;specif.

What are the types of replacement policies in economics? ›

This can be further classified into the following types: (i) Determination of economic life of an asset. (ii) Replacement of an existing asset with a new asset. (b)Simple probabilistic model for assets which fail completely (replacement due to sudden failure).

What does replacement mean in life insurance? ›

A replacement occurs: Where the purchase of an individual life insurance contract is likely to result in termination, cancellation or reduction in benefits of another insurance contract.

What would cause a replacement of an insurance policy? ›

Resumption of the payment period. Loss of permanent protection. Loss of the right to pay up the policy. Reduction of the benefit period.

What is a replacement transaction in life insurance? ›

Definition: Replacement is any transaction where, in connection with the purchase of New Insurance or a New Annuity, you lapse, surrender, convert to Paid-up Insurance, Place on Extended Term, or borrow all or part of the policy loan values on an existing insurance policy or an annuity.

What does replacement mean in healthcare? ›

a medical operation in which a part of the body, especially a hip or knee, is replaced with an artificial one: A lot of ex-athletes need knee or hip replacements. After ankle replacement surgery, the pain was gone.

What is an example of replacement cost coverage? ›

For example, if you paid $5,000 for a new couch 10 years ago, and it got destroyed in a fire, the RCV option would typically pay what it costs to replace your couch, which could be more or less than $5,000, minus your deductible. Learn more about homeowners insurance coverages.

What is an example of an unfair claims practice? ›

Underpayment: Trying to settle a claim at a lower amount than is advertised and expected. Delay of payment: Using various tactics to pressure claimant to accept less money. Lack of explanation: Failing to give a consumer complete or valid justification when denying a claim.

What is the rule of the replacement decision? ›

Replacement Decision is one of the most important classifications of capital budgeting. It is a decision concerning whether an existing asset should be replaced by a newer version of the same machine or even a different type of machine that has the same functionality as the existing machine.

What is replacement decisions? ›

Replacement decisions happen when an organization already has a particular asset and they are considering replacing it with something else, such as deciding between keeping a legacy software system and redeveloping it from the ground up.

What are the five major types of events? ›

Types of events
  • Mega events.
  • Major events.
  • Regional events.
  • Local and community events.

What is an example of without replacement? ›

Probability without replacement means once we draw an item, then we do not replace it back to the sample space before drawing a second item. In other words, an item cannot be drawn more than once. For example, if we draw a candy from a box of 9 candies, and then we draw a second candy without replacing the first candy.

What is the difference between replacement and without replacement? ›

With replacement means the same item can be chosen more than once. Without replacement means the same item cannot be selected more than once.

What are the types of replacement theory in operation research? ›

The replacement situations may be placed into the following two main categories : (1) Replacement of capital equipment that deteriorates with time, e.g., machine tools, buses in transport organization, planes, etc. (2) Individual or group replacement of items that fail completely, e.g., light bulbs, tubes, etc.

What is the replacement model theory? ›

The replacement theory of modern human origins stipulates that populations outside of Africa were replaced by a new African species of modern humans.

What is the difference between group and individual replacement theory? ›

Individualreplacement policy, demands immediate replacement of the item on its failure.In Group replacement, we replace all items at a particular time whether it has failed or not. Meanwhile if any item fail we can replace it individually.

What is the replacement theory of human development? ›

The Replacement model asserts that there was a single origin of hom*o sapiens in Africa and that these anatomically modern humans migrated out from Africa and replaced all other less evolved humans throughout Europe and Asia - hence the name, Replacement model.

What is a replacement problem? ›

Replacement problems involve items that degenerate with use or with the passage of time and those that fail after a certain amount of use or time. Items that deteriorate are likely to be large and costly (e.g., machine tools, trucks, ships, and home appliances).

What are the types of replacement problem in economics? ›

Replacement of items that deteriorate with time. 2. Replacement of items that break down completely, and 3. Replacement of items that becomes out of date due to new developments.

What are three methods used to solve an operations research problem? ›

The three phases of the process are formulation, analysis, and interpretation. During the formulation phase of the process, the analyst defines the problem, determines assessment criteria, and develops alternatives. These elements are followed by an analysis phase using modeling and optimization.

What are the assumptions of replacement theory? ›

Following assumptions are essentially required for replacement decisions: i) The quality of the output remains constant. ii) Replacement and maintenance costs remain constant. iii) The operational efficiency of the equipment remains constant.

What is the objective of replacement theory? ›

 The key objective of replacement theory is to determine the optimal time to replace an item, such as a machine or a vehicle, based on factors such as its maintenance costs, repair costs, and residual value.

What is the use of study of replacement problem? ›

Replacement problems involve items that degenerate with use or with the passage of time and those that fail after a certain amount of use or time. Items that deteriorate are likely to be large and costly (e.g., machine tools, trucks, ships, and home appliances).

What is replacement in operations research? ›

The Replacement 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.

What is the replacement model modern humans? ›

The replacement model of Christopher Stringer and Peter Andrews proposes that modern humans evolved from archaic humans 200,000-150,000 years ago only in Africa and then some of them migrated into the rest of the Old World replacing all of the Neandertals and other late archaic humans beginning around 60,000-40,000 ...

What are the 4 major theories of human development? ›

Major theories of development include the cognitive-development, learning, systems, and psychoanalytic. These systems of thought give rise to various theories on development.

What are the four types of changes in human development? ›

Human development is a lifelong process of physical, behavioral, cognitive, and emotional growth and change.

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