Analysis of the strength data of wood structures on limit states design II. Proposal of the method of calculating one-side tolerance limit for weibull distribution

Kazumi Horie, Noboru Nakamura, Yasuo Iijima

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 (Xβ) of Weibull distribution is calculated. 2) At the point the mean (μβ) and standard deviation (σβ) of equivalent normal distribution to Weibull distribution are calculated. σβ=φ[Φ-1[β]]/f(Χ β) μβ= Χββ·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 ΤLαβ= μβ-Κ·σβ 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 ΤL5,75 was calculated. This trial was repeated 10,000 times. Finely, the number of ΤL5,75 which was under X5 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 languageEnglish
Pages (from-to)455-460
Number of pages6
JournalMokuzai Gakkaishi/Journal of the Japan Wood Research Society
Volume45
Issue number6
Publication statusPublished - 1999
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Chemical Engineering(all)

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