8.3.2.4 __Censored Data__

If a sample contains both complete and incomplete lifetimes, the
incomplete lifetimes are referred to as
“censored” observations. These consist primarily of lifetimes which are too
long to be observed completely (“terminated” observations) and lifetimes in
which the item being observed is lost before completion of observation (“lost”
observation). In the case of terminated observations, the length of
observation time is controlled; in the case of lost observations, the length
of observation time is not controlled. In either case, the investigator knows
that the lifetime of the item exceeds the period of time during which the item
was being observed. Terminated
observations do not present a problem to the investigator other than to
increase the complexity of the calculations, but lost observations may
constitute a real problem because they maybe associated with only a portion of
the population.

For example, for the case of the
exponential distribution in which n items are put on test, r of them fail at
time t_{1},
t_{2} . . . t_{r}, with the test discontinued at
t_{r} when the r^{th} failure
occurs, the MTBF is given by

where t_{i} is the time
of each failure and (n - r) represents the number of surviving items at time
t_{r}. In this nonreplacement
case, the failed items are not repaired or replaced upon failure.

The mathematics become somewhat
more difficult when analyzing censored data where distributions other than the
exponential are involved, or when using nonparametric methods. These cases are
treated in detail in References [1], [3], [4]
and [5].