Abstract
As a particular structure in reliability, a sequential k-out-of-n system fails if more than n - k of its n components fail, where the failure of some component may affect the residual lifetimes of the remaining components of the system. Sequential order statistics serve as a model for the (ordered) lifetimes of the components and the system, respectively. When dealing with the conditional proportional hazard rate model with pre-fixed baseline distribution, the model parameters α1, α2, … are usually unknown and have to be estimated from data. Confidence intervals for single model parameters as well as multidimensional confidence regions for respective vectors are proposed, and desirable properties including optimality in the sense of minimum coverage probabilities of false parameters and minimum (expected) volume are also obtained. The confidence sets are illustrated and compared in terms of a simulation study indicating further properties.
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Bedbur, S., Lennartz, J.M. & Kamps, U. Confidence Regions in Models of Ordered Data. J Stat Theory Pract 7, 59–72 (2013). https://doi.org/10.1080/15598608.2013.756340
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DOI: https://doi.org/10.1080/15598608.2013.756340