### Abstract

It is an important problem in reliability analysis to decide whether for a given k-out-of-n system the static or the sequential k-out-of-n model is appropriate. Often components are redundantly added to a system to protect against failure of the system. If the failure of any component of the system induces a higher rate of failure of the remaining components due to increased load, the sequential k-out-of-n model is appropriate. The increase of the failure rate of the remaining components after a failure of some component implies that the effects of the component redundancy are diminished. On the other hand, if all the components have the same failure distribution and whenever a failure occurs, the remaining components are not affected, the static k-out-of-n model is adequate. In this paper. we consider nonparametric hypothesis tests to make a decision between these two models. We analyze test statistics based on the profile score process as well as test statistics based on a multivariate intensity ratio and derive their asymptotic distribution. Finally, we compare the different test statistics.

Original language | English |
---|---|

Pages (from-to) | 626-639 |

Number of pages | 14 |

Journal | Journal of Statistical Planning and Inference |

Volume | 140 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2010 |

### Keywords

- Hypothesis testing
- Multivariate intensity ratio
- k-out-of-n model
- Profile score process
- Sequential k-out-of-n model
- Static k-out-of-n model
- GENERALIZED ORDER-STATISTICS
- INFERENCE
- RATES

## Cite this

*Journal of Statistical Planning and Inference*,

*140*(3), 626-639. https://doi.org/10.1016/j.jspi.2009.08.005