### Abstract

Two problems are considered: 1) testing the hypothesis that the shape parameters of k 2-parameter Weibull populations are equal, given a sample of n observations censored (Type II) at r failures, from each population; and 2) Under the assumption of equal shape parameters, the problem of testing the equality of the p-th percentiles. Test statistics (for these hypotheses), which are simple functions of the maximum likelihood estimates, follow distributions that depend only upon r, n, k, p and not upon the Weibull parameters. Critical values of the test statistics found by Monte Carlo sampling are given for selected values of r, n, k, p. An expression is found and evaluated numerically for the exact distribution of the ratio of the largest to smallest maximum likelihood estimates of the Weibull shape parameter in k samples of size n, Type II censored at r = 2. The asymptotic behavior of this distribution for large n is also found.

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

Pages (from-to) | 186-192 |

Number of pages | 7 |

Journal | IEEE Transactions on Reliability |

Volume | R-24 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1975 |

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### All Science Journal Classification (ASJC) codes

- Safety, Risk, Reliability and Quality
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Reliability*,

*R-24*(3), 186-192. https://doi.org/10.1109/TR.1975.5215145

}

*IEEE Transactions on Reliability*, vol. R-24, no. 3, pp. 186-192. https://doi.org/10.1109/TR.1975.5215145

**Multiple Comparison for Weibull Parameters.** / McCool, John I.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Multiple Comparison for Weibull Parameters

AU - McCool, John I.

PY - 1975/1/1

Y1 - 1975/1/1

N2 - Two problems are considered: 1) testing the hypothesis that the shape parameters of k 2-parameter Weibull populations are equal, given a sample of n observations censored (Type II) at r failures, from each population; and 2) Under the assumption of equal shape parameters, the problem of testing the equality of the p-th percentiles. Test statistics (for these hypotheses), which are simple functions of the maximum likelihood estimates, follow distributions that depend only upon r, n, k, p and not upon the Weibull parameters. Critical values of the test statistics found by Monte Carlo sampling are given for selected values of r, n, k, p. An expression is found and evaluated numerically for the exact distribution of the ratio of the largest to smallest maximum likelihood estimates of the Weibull shape parameter in k samples of size n, Type II censored at r = 2. The asymptotic behavior of this distribution for large n is also found.

AB - Two problems are considered: 1) testing the hypothesis that the shape parameters of k 2-parameter Weibull populations are equal, given a sample of n observations censored (Type II) at r failures, from each population; and 2) Under the assumption of equal shape parameters, the problem of testing the equality of the p-th percentiles. Test statistics (for these hypotheses), which are simple functions of the maximum likelihood estimates, follow distributions that depend only upon r, n, k, p and not upon the Weibull parameters. Critical values of the test statistics found by Monte Carlo sampling are given for selected values of r, n, k, p. An expression is found and evaluated numerically for the exact distribution of the ratio of the largest to smallest maximum likelihood estimates of the Weibull shape parameter in k samples of size n, Type II censored at r = 2. The asymptotic behavior of this distribution for large n is also found.

UR - http://www.scopus.com/inward/record.url?scp=0016537155&partnerID=8YFLogxK

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U2 - 10.1109/TR.1975.5215145

DO - 10.1109/TR.1975.5215145

M3 - Article

AN - SCOPUS:0016537155

VL - R-24

SP - 186

EP - 192

JO - IEEE Transactions on Reliability

JF - IEEE Transactions on Reliability

SN - 0018-9529

IS - 3

ER -