126.96.36.199 Treatment of Failure
Failure data are usually obtained from a) test results or b)
field failure reports. Experience has shown that a good way to present these
data is to compute and plot either the failure density function, f(t), or the
hazard rate, h(t), as a function of time.
Remember from Section
5 that f(t) is given by the ratio of the number of failures occurring in
the time interval to the size of the original population, divided by the
length of the time interval. The hazard rate, h(t), on the other hand, is
given by the ratio of the number of failures occurring in the time interval to
the number of survivors at the beginning of the time interval, divided by the
length of the time interval.
Although f(t) and h(t) are defined as continuous functions,
piecewise continuous functions of f(t) and h(t) are computed, graphed results
are examined, and a continuous model is chosen which best fits the data.
Once having found f(t) from the data, F(t) (the cumulative
distribution of time to failure) and R(t) = 1 - F(t), the reliability function
or survival probability, can be readily determined from the relationships.