ABSTRACT
Typically failure-time data are right censored. This means that failure time T is known if it does not exceed a value C, called censoring time. Otherwise it is only known that failure time T is greater than C. Left censoring means that failure time T is known if it is greater or equal
to C, also called censoring time. Otherwise it is only known that failure time T is smaller than C. Left censoring is fairly rare in analysis of reliability data with explanatory
variables and is not considered here. Right censoring mechanisms can be various: 1) If n units are tested a prespecified time t then censoring is called Type I
censoring. For all units censoring time C = t. 2) If a life test is terminated after a specified number r, r < n, of failures
occurs then censoring is called Type II censoring. For all units censoring time C is the moment of the rth failure. 3) If units are put on test at different time points t1, · · · , tn, and the data
are to be analyzed at a fixed time point t, t > max ti, then censoring time for the ith unit Ci = t − ti is non-random. Such censoring is called progressive right censoring. 4) If the failure times T1, · · · , Tn and the censoring times C1, · · · , Cn are mu-
tually independent random variables then censoring will be called independent right censoring. For example, if several failure modes are possible and interest is focused on one particular failure mode then failure of any other mode can be considered as random censoring time. Type I censoring is a particular case of progressive right censoring. Both
are particular cases of independent right censoring. Suppose that data are right censored, Ti and Ci are failure and censoring
times. Set Xi = Ti ∧ Ci, δi = 1{Ti≤Ci} (i = 1, · · · , n),
where a ∧ b = min(a, b), 1A is the indicator of the event A. Usually right censored data are presented in the following form:
(X1, δ1), · · · , (Xn, δn). (4.1) i = X
i the moment Xi, i.e. unit is censored at the moment Ci = Xi. There is another way to describe right censored data. Denote by
the number of failures of the ith unit in the interval [0, t]. It is equal to 1 if failure is observed in this interval. Otherwise it is equal to 0. Set
Yi(t) = 1{Xi≥t}.
