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Many applications in reliability theory and biostatistics involve the modeling of lifetime data. In these applications the outcome of interest is the time T, until some event occurs. This event may be death, the appearance of a tumor, the development of some disease, recurrence of a disease, conception, cessation of smoking, and so forth. The basic quantity employed to describe time-to-event phenomena is the survival function. This function, also known as the survivor function or survivorship function, is the probability an individual survives beyond time t.
A second life distribution class is the class of new better than used (NBU) distributions. The NBU class of life distributions has been widely studied in the theory of reliability and life-testing. The class, which emphasizes that a new item has a stochastically larger life length than does a used one with any age t>0, arises in many situations in which a better maintenance policy is believed to exist. Because it is easy to make a valuable judgment when such a model really exists, and because incorporating this model into an inferential procedure increases its statistical efficiency, it is desirable to recognize the existence of the model and to select a corresponding maintenance policy.
In the context of reliability theory, testing H0:F is exp(μ) against an alternative that F belongs to any one of the above three classes, or other, and not exponential was taken up by many authors for quite some time. When H0 is rejected, and thus F is IFR [NBU, NBUC], estimating F as well as other related functions, such as the hazard rate or the mean residual life time, is an interesting and open problem. |
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- U-Statistics. Marcel Dekker, New York, NY. By Lee, A. J., (1989).
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