On properties of progressively Type-II censored conditionally N-ordered statistics arising from a non-identical and dependent random vector

Abstract

In some systems, we observe the lifetimes of its components but the classical model based on progressively Type-II censored order statistics (PCOS-II) do not use this information to analysis the lifetime of the system. For example, when we use PCOS-II to consider the lifetime of a parallel system we do not use the lifetime of each component. In fact, we just use the lifetime of the system which equals the maximum lifetimes of its component. Some other example of these systems in which we do not use all the information that we observed during the lifetime testing procedure based on PCOS-II are repairable system and a system with n stand-by components. Instead of it, if we use progressively Type-II censored conditionally N-ordered statistics (PCCOS-N) to analysis the lifetime of these systems we can use all the information that we observed and obtained a more accurate analysis for lifetime of the system. PCCOS-N is introduced by Bairamov.[Progressive Type II censored order statistics for multivariate observations. J Mult Anal. 2006;97:797–809] In this paper, we investigate PCCOS-N arising from a system with identical as well as non-identical but dependent components, jointly distributed according to an Archimedean copula with completely monotone generator (PCCOSDNARCM-N). Our results generalized the results in Bairamov (2006) and is more flexible than those in practice, because of considering the dependency between components that is a common fact for real data. A simulation study with a method of parameter estimation is also finally provided.

Keywords:

• Archimedean copula
• order statistics
• progressive censoring
• progressively Type-IIcensored order statistics
• reliability systems

AMS Subject Classification:

• 60E15
• 62E15

Acknowledgments

The authors also express their sincere thanks to the associated editor and anonymous referee for several helpful and insightful comments on this manuscript which led to this improved version.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The authors received no funding for this work.