寿命分布类的偏序及其应用

Partial Orderings of Certain Classes with Applications

讨论寿命分布类ＩＦＲ和ＩＦＲＡ中元件之间的偏序关系，证明了在ＩＦＲＡ中，具有星序的两个元件的色散序和随机序是等价的．作为应用，进而研究了凸序和星序在更新计数过程中的行为特征：当系统时间充分大时，具有两种序关系的元件的更新次数也具有相应的随机序关系；即ＩＦＲ性和ＩＦＲＡ性较弱的元件的失效次数随机地小于相应性质较强的元件的失效次数．

The convex ordering and the star shaped ordering of {IFR} and {IFRA}, are dealt with respectively. It is proved that, with respect to two elements with star shaped ordering in {IFRA}, dispersive ordering is equivalent to the stochastic ordering. Also, the behaviors of the two elements with above orderings in renewal counting process are discussed, with the results that, under some mild conditions, the less one of the two elements with either convex ordering or star shaped ordering will have a stochastically smaller number of replacements, as t→∞.