The document discusses replacement models and the factors involved in replacement decisions. It covers: 1) Types of replacement problems including items that deteriorate over time, sudden failures, and replacement due to new technology. 2) Nature of failures including gradual, sudden, progressive, retrogressive, and random failures. 3) Costs associated with replacement and maintenance including capital, salvage, and running costs. 4) Terminology used in replacement models including capital cost, salvage value, maintenance cost, and average cost. 5) An example problem calculating the optimal time to replace equipment based on costs.

1. Replacement Models
Abu Bashar

2. INTRODUCTION
• The problem of replacement arises when any one of
the components of productive resources, such as
• machinery, building and men deteriorates due to time
or usage. The examples are:
• (a) A machine, which is purchased and installed in a
production system, due to usage some of its
components wear out and its efficiency is reduced.
• (b) A building in which production activities are carried
out, may leave cracks in walls, roof etc, and needs
repair.
• (c) A worker, when he is young, will work efficiently, as
the time passes becomes old and his work efficiency
falls down and after some time he will become unable
to work.

3. Replacement due

4. • Thus the problem of replacement is experienced
in systems where machines, individuals or
capital assets are the main production or job
performing units.
• The characteristics of these units is that their
level of performance or efficiency decreases
with time or usage and one has to formulate
some suitable replacement policy regarding
these units to keep the system up to some
desired level of performance.

5. • We may have to take different type of decision
such as:
• (a) We may decide whether to wait for complete
failure of the item (which may result in some
losses due to deterioration or to replace earlier at
the expense of higher cost of the item,
• (b) The expensive item may be considered
individually to decide whether we should replace
now or, if not, when it should be reconsidered for
replacement,
• (c) Whether the item is to be replaced by similar
type of item or by different type for example item
with latest technology

6. Nature of failure

7. • Gradual failure:
• In this class as the life of the machine increases or due continuous
usage, due to wear and tear of components of the facility, its efficiency
deteriorates due to which the management can experience:
• (a) Progressive Increase in maintenance expenditure or operating costs,
• (b) Decreased productivity of the equipment and
• (c) decrease in the value of the equipment i.e. resale value of the
equipment/facility decreases.
• Examples of this category are: Automobiles, Machine tools, etc.
• Sudden failure:
• In this case, the items ultimately fail after a period of time. The life of
the equipment cannot be predicted and is some sort of random variable.
The period between installation and failure is not constant for any
particular type of equipment but will follow some frequency
distribution, which may be:
• Progressive failure:
• In this case probability of failure increases with the increase in life of an
item. The best example is electrical bulbs and computer components.

8. • Retrogressive failure:
• Some items will have higher probability of failure in the
beginning of their life, and as the time passes chances of
failure becomes less.
• That is the ability of the item to survive in the initial period
of life increases its expected life. The examples are newly
installed machines in production systems, new vehicles,
and infant baby (The probability of survival is very less in
infant age, but once the baby get accustomed to nature,
the probability of failure decreases).
• (c) Random failure:
• In this class, constant probability of failure is associated
with items that fail from random causes such as physical
shocks, not related to age. Example is vacuum tubes.

9. Costs Associated with Maintenance
• (a) Purchase cost or Capital cost: ( C )
• This cost is independent of the age of the machine or usage of the
machine. This is incurred at the beginning of the life of the machine, i.e.
at the time of purchasing the machine or equipment. But the interest on
the invested money is an important factor to be considered.
• (b) Salvage value / Scrap value / Resale value / Depreciation: (S)
• As the age of the machine increases, the resale value decreases as its
operating efficiency decreases and the maintenance costs increases. It
depends on the operating conditions of the machine and life of the
machine.
• (c) Running costs including maintenance, Repair and Operating costs:
• These costs are the functions of age of the machine and usage of the
machine. As the usage increases or the age increases, due to wear and
tear, many components fail to work and they are to be replaced. As the
age increases, failures also increase and the maintenance costs goes on
increasing. At some period the maintenance costs are so high, which will
indicate that the replacement of the machine or equipment is essential.

10. TYPES OF REPLACEMET PROBLEMS
• Replacement of Capital equipment, which looses
its operating efficiency due to aging (passage of
time), or due to continuous usage (due to wear
and tear of components).
• Examples are: Machine tools, Transport and other
vehicles, etc., Here the system can maintain the
level of performance by installing a new unit at
the beginning of some unit of time (year, month
or week) and decide to keep it up to some
suitable period so as to minimize the operating
and maintenance costs.

11. • Replacement of items that fail completely all
in a sudden in a random nature. We use
Group replacement or Preventive
maintenance technique for these items and
these are expensive to replace individually.
• Examples are: Electric
bulbs, Transistors, Electronic components
etc., Here replacement of items are done in
anticipation of failure, which is known as
preventive maintenance.

12. • Replacement of human beings in
organizations, known as Staffing problem, or
known as Human resource planning or Staffing
problem.
• This problem requires the knowledge of life
distribution for service of staff in a system.
• Miscellaneous problems such as replacement
of existing units due to availability of more
effective and new and advanced technology.
In these problems replacement will become
necessary due to research of new and
advanced and more effective technology and
old technology becomes out of date.

13. REPLACEMENT OF ITEMS WHOSE
EFFICIENCY REDUCES OR
MAINTENCNCE COST INCREASES
WITH TIME OR DUE TO AGE AND
MONEY
VALUE IS NOT CONSIDERED

14. Terminologies
• Let C = Purchase cost or Capital cost of the item,
• S = Scrap value or resale value of the item, it is assumed
that this cost will remain constant over time.
• Let u (t) be the maintenance or running cost at the time ‘t’.
• M(y) is the cumulative maintenance cost during year y’’.
• The total cost incurred on the item during period Y”
• ‘y’ = Capital cost + total maintenance cost in the period ‘y’ -
Scrap value. = C + M(y) – S
• Hence average cost per unit of time incurred during the
period ‘y’ on the item is given by:
• G (y) = {C + M (y) – S}/y, to find the value of ‘y’ for which G
(y) is minimum

15. Practical Problems

17. The cost of an equipment is Rs.62,000 and its
scrap value is Rs. 2,000. The life of the
equipment is 8 years. The maintenance costs for
each year are given below.
Year 1 2 3 4 5 6 7 8
Maintainanc
e Cost in Rs. 1000 2000 3500 5000 8000 11000 16000 24000
When the equipment should be replaced.