SS2 Third Term Further Mathematics Lesson Note – Replacement Model

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WEEK SIX

REPLACEMENT MODEL:

CONTENT

(a) Concept of replacement

(b) Individual Replacement of sudden failure item

(c) Replacement of items that wear out gradually.

SUB TOPIC: CONCEPT OF REPLACEMENT

In replacement model, we consider situations that occur when certain items such as equipment, machines and even men need replacement as a result of decreased efficiency or total breakdown which may be sudden or gradual. Conditions that necessitate replacement of certain items:

1. When an old item is no longer efficient or has become expensive to maintain;
2. When an old item has failed or is expected to fail shortly;
3. When there is innovation and better equipment is developed and the old item becomes obsolete.

In this model, our major concern is to determine the best time at which replacement of an item is most economical.

Our major objective generally is to enable an organization to minimize its cost or to maximize its profit.

Types of Replacement

We have two major types of replacement problems namely;

1. Replacement due to gradual failure – the cause may be wearing and tearing of machine components.
2. Replacement due to sudden failure – a simple probabilistic model is constructed for assets which fail completely or suddenly in this case.

Examples of replacement due to gradual failure are motor vehicle in a transport organization, machine tools etc. which are more capital equipment.

Examples of items that require replacement due to complete or sudden failure are light bulbs, electronic valves and radio tubes etc

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