### Abstract

Inference for R = P(Y < X) is considered when X and Y are independently distributed as scaled Burr type X random variables. Under this model, exact inference procedures for R cannot be found. Hence, based on the expected Fisher information matrix which is derived here, asymptotic inference procedures for R and other general functions of the parameters are developed. A bootstrap method to estimate variance for the maximum likelihood estimators is also discussed. To illustrate these techniques, an example using carbon fiber strength data is given. Simulations to assess the effectiveness of these techniques, as well as other concerns, are presented.

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

Pages (from-to) | 187-200 |

Number of pages | 14 |

Journal | Lifetime Data Analysis |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - 2001 |

### Keywords

- Burr distributions
- Carbon composite materials
- Fisher information
- Maximum likelihood
- Stress-strength model

## Fingerprint Dive into the research topics of 'Inference for Reliability and Stress-Strength for a Scaled Burr Type X Distribution'. Together they form a unique fingerprint.

## Cite this

Surles, J. G., & Padgett, W. J. (2001). Inference for Reliability and Stress-Strength for a Scaled Burr Type X Distribution.

*Lifetime Data Analysis*,*7*(2), 187-200. https://doi.org/10.1023/A:1011352923990