Estimation and Application of Reliability Values for Strength of Material Following Gamma Distribution

감마분포를 따르는 재료강도의 신뢰도 예측과 응용

  • Park, Sung-Ho (Defence Systems Test Center, Agency for Defence Development) ;
  • Kim, Jae-Hoon (Dept. of Mechanical Design, Choongnam Nat'l Univ.)
  • 박성호 (국방과학연구소 종합시험단) ;
  • 김재훈 (충남대학교 기계설계공학과)
  • Received : 2011.06.07
  • Accepted : 2011.12.12
  • Published : 2012.02.01


The strength of brittle material has commonly been characterized by a normal distribution or Weibull distribution, but it may fit the gamma distribution for some material. The use of an extreme value distribution is proper when the largest values of a set of stresses dominate the failure of the material. This paper presents a formula for reliability estimation based on stress-strength interference theory that is applicable when the strength of material is distributed like a gamma distribution and the stress is distributed like an extreme value distribution. We verified the validity of the equation for the reliability estimation by examining the relationships among the factor of safety, the coefficient of variation, and the reliability. The required minimum factor of safety and the highest allowable coefficient of variation of stress can be estimated by choosing an objective reliability and estimating the reliabilities obtained for various factors of safety and coefficients of variation.


Reliability;Stress-Strength Interference Theory;Gamma Distribution;Extreme Value Distribution;Factor of Safety;Coefficient of Variation


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