Abstract
Although fatigue itself is considered to be a phenomenon in which the failure rate increases with time, it might be possible to have a case that the failure rate of a mixed population decreases monotonously with time even if failure is caused by fatigue. In order to make clear whether this is truely possible and thus to help proper understanding of field data, the time dependence of the failure rate of a mixed population has been investigated theoretically. This mixed population is composed of members each of which has been extracted from each own original (native) population, and each original population has the failure rate of h(t)*=w·h(t), where the function h(t) is common to all the populations and the coefficient w takes different values in different populations. From the study of time dependence of the failure rate of this mixed population, the following conclusions were obtained. (1) When the failure rate of each original population h*(t) has the property of dh*/dt≤0 for all t, the failure rate of the mixed population decreases monotonously with time. (2) When each original population has the Weibull-type failure rate h*(t)∝tα-1 with α>1, the failure rate of the mixed population does not decrease monotonously with time. This implies that, if fatigue is characterized by the Weibull-type failure rate with α>1, the failure rate of the mixed population subjected to fatigue does not decrease monotonously with time. (3) However, if each original population has the failure rate of the form h*(t)∝(tα-1+constant) with α>1, the failure rate of the mixed population λ(t) can decrease monotonously with time. This implies that there is a case in which λ(t) can decrease monotonously with time even if dh*/dt≤0 for all t (the condition mentioned in (1) above) is not satisfied.
