期刊
JOURNAL OF APPLIED PROBABILITY
卷 40, 期 2, 页码 485-504出版社
APPLIED PROBABILITY TRUST
DOI: 10.1239/jap/1053003558
关键词
mixture; increasing linear failure rate; increasing failure rate; bathtub failure rate; modified bathtub shape
Populations of specific components are often heterogeneous and consist of a small number of different subpopulations. For example, there are often two groups: defective components with shorter lifetimes and standard components with longer lifetimes. Another heterogeneous population results when components produced by two different manufacturing lines are combined. In either case a mixture results. The resulting population can be described using the statistical concept of a mixture. It is a well-known result that a mixture of distributions with decreasing failure rates has a decreasing failure rate. However, little is known about the monotonicity of a mixture when the various subpopulations have failure rates which are not necessarily decreasing. In this paper we study and attempt to determine the shape as well as the overall behavior of the failure rate of a mixture from two subpopulations each of which has an increasing linear failure rate.
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