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Type-I hybrid censoring of multiple samples. (English) Zbl 1432.62329
Summary: We consider inference based on multiple samples subject to type-I hybrid censoring. The original data is supposed to be obtained as failure times from $$k \geq 2$$ independent type-I censored sequential $$r$$-out-of-$$n$$ systems. For the mean $$\vartheta$$ of exponentially distributed lifetimes, we derive the distribution of the maximum likelihood estimator $$\hat{\vartheta}$$ given the condition that at least one failure has been observed in the $$k$$ samples. As special cases, we get results for particular multi-sample hybrid censoring models, that is, for multi-sample type-I hybrid censoring and multi-sample type-I progressive hybrid censoring, respectively. As a tool, we need expressions for the convolutions of B-splines in terms of iterative divided differences. The resulting expressions are used to determine the exact density functions efficiently as well as to construct exact confidence intervals for $$\vartheta$$. Furthermore, we propose two approximated two-sided confidence intervals as an alternative for larger sample sizes. The results are illustrated by data as well as by simulations.

##### MSC:
 62N01 Censored data models 90C90 Applications of mathematical programming
StInt
Full Text:
##### References:
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