Mortality Tables

Introduction:

It represents the large population in that particular areas in operation research which is beneficial for management and others.

Mortality Tables

The mortality theorem states that a large population is subjected to a given mortality law for a very long period of time. All deaths are immediately replaced by births and there are no other entries or exits. Here age distribution ultimately becomes stable and that the number of deaths per unit of time becomes constant, which is equal to the size of the total population divided by the mean age at death. If we consider the problem of human population, no group of people ever existed under the

Conditions that:

(a)That all deaths are immediately replaced by births.

(b)That there are no other entries or exists.

These two assumptions help to analyze the situation more easily, by keeping virtual human population in mind. When we consider an industrial problem, deaths refer to item failure of items or components and birth refers to replacement by a new component. Mortality table for any item can be used to derive the probability distribution of life span. If M (t) represents the number of survivors at any time ‘t’ and M (t – 1) is the number of survivors at the time (t – 1), then the probability that any item will fail in this time interval will be:

{M (t – 1) – M (t)} / N, ...(1)

where N is the number of items in the system. Conditional probability that any item survived up to age (t – 1) will die in next period, will be given by:

{M (t – 1) – M (t)} / M (t – 1)

Example:

Calculate the probability of failure of an item in good condition in each month from the following survival table:

Solution

Here ‘t’ is the number of month; M (t) is the number of items i.e. items in good condition at the end of tth month. The probability of failure in each month is calculated as under: