### Abstract

Existing results are reviewed for the maximum likelihood (ML) estimation of the parameters of a 2-parameter Weibull life distribution for the case where the data are censored by failures due to an arbitrary number of independent 2-parameter Weibull failure modes. For the case where all distributions have a common but unknown shape parameter the joint ML estimators are derived for i) a general percentile of the j-th distribution, ii) the common shape parameter, and iii) the proportion of failures due to failure mode j. Exact interval estimates of the common shape parameter are constructable in terms of the ML estimates obtained by using i) the data without regard to failure mode, and ii) existing tables of the percentage points of a certain pivotal function. Exact interval estimates for a general percentile of failure-mode-y distribution are calculable when the failure proportion due to failure-mode-j is known; otherwise a joint s-confidence region for the percentile and failure proportion is calculable. It is shown that sudden death endurance test results can be analyzed as a special case of competing-mode censoring. Tabular values for the construction of interval estimates for the 10-th percentile of the failure-mode-j distribution are given for 17 combinations of sample size (from 5 to 30) and number of failures.

Original language | English (US) |
---|---|

Pages (from-to) | 25-31 |

Number of pages | 7 |

Journal | IEEE Transactions on Reliability |

Volume | R-25 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1976 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering
- Safety, Risk, Reliability and Quality
- Computer Graphics and Computer-Aided Design
- Hardware and Architecture
- Software

### Cite this

*IEEE Transactions on Reliability*,

*R-25*(1), 25-31. https://doi.org/10.1109/TR.1976.5214946

}

*IEEE Transactions on Reliability*, vol. R-25, no. 1, pp. 25-31. https://doi.org/10.1109/TR.1976.5214946

**Estimation of Weibull Parameters With Competing-Mode Censoring.** / McCool, John I.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Estimation of Weibull Parameters With Competing-Mode Censoring

AU - McCool, John I.

PY - 1976/1/1

Y1 - 1976/1/1

N2 - Existing results are reviewed for the maximum likelihood (ML) estimation of the parameters of a 2-parameter Weibull life distribution for the case where the data are censored by failures due to an arbitrary number of independent 2-parameter Weibull failure modes. For the case where all distributions have a common but unknown shape parameter the joint ML estimators are derived for i) a general percentile of the j-th distribution, ii) the common shape parameter, and iii) the proportion of failures due to failure mode j. Exact interval estimates of the common shape parameter are constructable in terms of the ML estimates obtained by using i) the data without regard to failure mode, and ii) existing tables of the percentage points of a certain pivotal function. Exact interval estimates for a general percentile of failure-mode-y distribution are calculable when the failure proportion due to failure-mode-j is known; otherwise a joint s-confidence region for the percentile and failure proportion is calculable. It is shown that sudden death endurance test results can be analyzed as a special case of competing-mode censoring. Tabular values for the construction of interval estimates for the 10-th percentile of the failure-mode-j distribution are given for 17 combinations of sample size (from 5 to 30) and number of failures.

AB - Existing results are reviewed for the maximum likelihood (ML) estimation of the parameters of a 2-parameter Weibull life distribution for the case where the data are censored by failures due to an arbitrary number of independent 2-parameter Weibull failure modes. For the case where all distributions have a common but unknown shape parameter the joint ML estimators are derived for i) a general percentile of the j-th distribution, ii) the common shape parameter, and iii) the proportion of failures due to failure mode j. Exact interval estimates of the common shape parameter are constructable in terms of the ML estimates obtained by using i) the data without regard to failure mode, and ii) existing tables of the percentage points of a certain pivotal function. Exact interval estimates for a general percentile of failure-mode-y distribution are calculable when the failure proportion due to failure-mode-j is known; otherwise a joint s-confidence region for the percentile and failure proportion is calculable. It is shown that sudden death endurance test results can be analyzed as a special case of competing-mode censoring. Tabular values for the construction of interval estimates for the 10-th percentile of the failure-mode-j distribution are given for 17 combinations of sample size (from 5 to 30) and number of failures.

UR - http://www.scopus.com/inward/record.url?scp=0016944301&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016944301&partnerID=8YFLogxK

U2 - 10.1109/TR.1976.5214946

DO - 10.1109/TR.1976.5214946

M3 - Article

VL - R-25

SP - 25

EP - 31

JO - IEEE Transactions on Reliability

JF - IEEE Transactions on Reliability

SN - 0018-9529

IS - 1

ER -