## Abstract

The k-out-of-n model is commonly used in reliability theory. In this model the failure of any component of the system does not influence the components still at work. Sequential k-out-of-n systems have been introduced as an extension of k-out-of-n systems where the failure of some component of the system may influence the remaining ones. We consider nonparametric estimation of the cumulative hazard function, the reliability function and the quantile function of sequential k-out-of-n systems. Furthermore, nonparametric hypothesis testing for sequential k-out-of-n-systems is examined. We make use of counting processes to show strong consistency and weak convergence of the estimators and to derive the asymptotic distribution of the test statistics.

Original language | English |
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Pages (from-to) | 605-626 |

Number of pages | 22 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 60 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Sep 2008 |

Externally published | Yes |

## Keywords

- Martingale methods
- Nelson-Aalen estimator
- Nonparametric estimation
- Nonparametric hypothesis testing
- Sequential k-out-of-n systems