Replacement Models

Abu Bashar

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.

Replacement due

• 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.

• 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

Nature of failure

• 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.

• 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.

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.

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.

• 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.

• 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.

REPLACEMENT OF ITEMS WHOSE EFFICIENCY REDUCES ORMAINTENCNCE COST INCREASES WITH TIME OR DUE TO AGE AND MONEY

VALUE IS NOT CONSIDERED

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

Practical Problems

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

Maintainance Cost in Rs. 1000 2000 3500 5000 8000 11000 16000 24000

When the equipment should be replaced.