ABSTRACT
Finite mixture distributions1 have been widely used in nearly all fields of applied statis-
tical science to model heterogeneous populations. Such a population is a composition of
m (m ≥ 2) different subpopulations. When dealing with lifetime distributions the reason for the existence of several subpopulations is that a unit can have more than one failure
mode. For example, if some units in a batch are freaks (e.g., have gross defects due to the
material processed or to improper manufacturing), then such units will have short lifetimes
or will fail at lower stress levels. The remaining units will have longer lifetimes and will
endure higher stress. In this case, the DF of the time to failure can have a bimodal or mul-
timodal shape.2 Consequently, the finite mixed WEIBULL distribution is a good candidate
to represent these times to failure.
