Joint distribution of a random sample and an order statistic: A new approach with an application in reliability analysis (original) (raw)
2019, Reliability Engineering & System Safety
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Journal of Multivariate Analysis, 1976
Let ðX 1 ; X 2 ; y; X n Þ and ðY 1 ; Y 2 ; y; Y n Þ be gamma random vectors with common shape parameter a ð0oap1Þ and scale parameters ðl 1 ; l 2 ; y; l n Þ; ðm 1 ; m 2 ; y; m n Þ; respectively. Let X ðÞ ¼ ðX ð1Þ ; X ð2Þ ; y; X ðnÞ Þ; Y ðÞ ¼ ðY ð1Þ ; Y ð2Þ ; y; Y ðnÞ Þ be the order statistics of ðX 1 ; X 2 ; y; X n Þ and ðY 1 ; Y 2 ; y; Y n Þ: Then ðl 1 ; l 2 ; y; l n Þ majorizes ðm 1 ; m 2 ; y; m n Þ implies that X ðÞ is stochastically larger than Y ðÞ : However if the common shape parameter a41; we can only compare the the first-and last-order statistics. Some earlier results on stochastically comparing proportional hazard functions are shown to be special cases of our results.
A Non-Parametric Order Statistics Software Reliability Model
Software Testing, Verification & Reliability, 1998
This paper addresses a family of probability models for the failure time process known as order statistic models. Conventional order statistics models make rather strong distributional assumptions about the detection times: typically they assume that these come from some parametric family of distributions. In this paper a new model is presented that relaxes these distributional assumptions, and -in the tradition of non-parametric statistics generally -'allows the data to speak for themselves'. The accuracy of the new model is compared on some real data sets with the predictions that come from several of the better parametric reliability growth models.
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