## Abstract

The methods proposed for calculating one-side tolerance limit of Weibull distribution until now are very complicated. We proposed a relatively easy method for calculating one-side tolerance limit of lower β% with α% confidence level. The algorithm is as follows : 1) The lowerβ% point (X_{β}) of Weibull distribution is calculated. 2) At the point the mean (μ_{β}) and standard deviation (σ_{β}) of equivalent normal distribution to Weibull distribution are calculated. σ_{β}=φ[Φ^{-1}[β]]/f(Χ _{β}) μ_{β}= Χ_{β}-σ_{β}·Φ ^{-1}[β] f ( · ) : probability density function φ ( · ) : probability density function of normal distribution Φ ( · ) : cumulative distribution function of normal distribution 3) The value with α% confidence level is calculated by the following formula ΤL_{αβ}= μ_{β}-Κ·σ_{β} Κ : factor for one-side tolerance limit in normal distribution A numerical simulation was done to ascertain validity of this method. Namely, random numbers were generated according to the original Weibull distribution. The parameters of the Weibull distribution for generated random numbers were estimated by the moment method. The ΤL_{5,75} was calculated. This trial was repeated 10,000 times. Finely, the number of ΤL_{5,75} which was under X_{5} of the original Weibull distribution was counted. Ratios of the number to the theoretical number are 1.022 and 1.036 in case of 2P Weibull and 3P Weibull distribution, respectively. Therefore, this method was proved to be valid.

Original language | English |
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Pages (from-to) | 455-460 |

Number of pages | 6 |

Journal | Mokuzai Gakkaishi/Journal of the Japan Wood Research Society |

Volume | 45 |

Issue number | 6 |

Publication status | Published - 1999 |

Externally published | Yes |

## Keywords

- Confidence level
- One-side tolerance limit
- Weibull distribution

## ASJC Scopus subject areas

- Chemical Engineering(all)