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Individual replacement policy

Individual replacement policy

In this policy a particular time ‘t’ is fixed to replace the item whether it has failed or not. It can be done when one knows that an item has been in service for a particular period of time and has been used for that time period. In case of moving parts like bearings this policy is very useful to know when the bearing should be replaced whether it fails or not. Failure of a bearing can cause a lot of damage to the equipment in which it is fitted and the cost of repairing the equipment is much more than the cost of bearing If it had been replaced well in time. If it is possible to find out the optimum service life ‘t’ the sudden failure and hence loss to the equipment and production loss etc can be avoided. However, when we replace items on a fixed interval of preventive maintenance period certain items may be .left with residual useful life which goes waste. Such items could still perform for another period of time (not known) and so the utility of items has been reduced. Consider the case of a city corporation wanting to replace its street lights. If individual replacement policy is, adopted then replacement can be done simultaneously at every point of failure. If
replacement policy is adopted then many lights with residual life will be replaced incurring unnecessary costs.

Analysis of the cost of replacement in case of items/equipments that fail without warning is similar to finding out the probability of human deaths or finding out the liability of claims of life-insurance company the death of a policy holder.

The probability of failure or survival at different times can be found out by using mortality tables or life tables.

The problem of human births and deaths as also individual problems where death is equivalent to failure and birth is equivalent t replacement can also be studied as part of the replacement policy. For showing such problems, we make the following assumptions.

  1. All deaths or past failures are immediately replaced by births or part replacements and
  2. There are no other, except the ones under consideration, entries or exits.

Let us find out the rate of deaths that occur during a particular time period assuming that each item in a system fails just before a particular time period. The aim is to find out the optimum period of time during which an item can be replaced so that the costs incurred are minimum. Mortality or life tables are used to find out the probability destination of life span of items in the system.

Let f (t) – number of items surviving at time (t – 1) n = Total number of item; with system under consideration. The probability of failure of items between ‘t’ and (t- 1) can be found out by