He. Ascher et Ck. Hansen, Spurious exponentiality observed when incorrectly fitting a distribution to nonstationary data, IEEE RELIAB, 47(4), 1998, pp. 451-459
Failure data for a repairable system can be represented either by a set of
chronologically ordered arrival times at which the system failed, or by a s
et of interarrival times defined as the times observed between successive f
ailures (ignoring repair times in both cases). The two representations are
mathematically equivalent if the chronological order of the interarrival ti
mes is maintained. Methods aimed at describing the distribution of the obse
rved interarrival times are meaningful only if the interarrival times are i
dentically distributed. In all other cases, such analyses are meaningless a
nd often result in maximally misleading impressions about the system behavi
or, as demonstrated here by several examples. That is, when the information
in the chronological order of interarrival times is ignored, they often ap
pear spuriously exponential, leading to the impression that the system can
be modeled using a homogeneous Poisson process. Misunderstandings of this n
ature can be avoided by applying an appropriate test for trend before attem
pting to fit a distribution to the interarrival times. If evidence of trend
is determined, then a. nonstationary model such as the nonhomogeneous Pois
son process should be fitted using the chronologically ordered data.