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The Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. There are several alternative formulations of this distribution in the literature. It is named after Z. W. Birnbaum and S. C. Saunders. ==Theory== This distribution was developed to model failures due to cracks. A material is placed under repeated cycles of stress. The ''j''th cycle leads to an increase in the crack by ''X''j amount. The sum of the ''X''j is assumed to be normally distributed with mean ''nμ'' and variance ''nσ''2. The probability that the crack does not exceed a critical length ''ω'' is : where ''Φ''() is the cdf of normal distribution. If ''T'' is the number of cycles to failure then the cumulative distribution function (cdf) of ''T'' is : The more usual form of this distribution is: : Here ''α'' is the shape parameter and ''β'' is the location parameter. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Birnbaum–Saunders distribution」の詳細全文を読む スポンサード リンク
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