Simple Probabilistic Model For Items Which Fail Completely

Simple Probabilistic Model For Items Which Fail Completely

Electronic items like transistors, resistors, tube lights, 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 tube light.

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.

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