1. f (x) - PDF Expectation Operator x (fracture stress) Nomenclature/Preliminaries

2. Various Types of Probability Density Functions Available 1.Gauss (Normal) 2.Lognormal 3.Beta 4.Poisson 5.Log Pearson 6.Extreme Value Distributions 7.Type I Maximum Minimum 8.Type II Maximum - Frechet Minimum 9.Type III Maximum Minimum - Weibull PDF Must Satisfy 2 Conditions

3. Nomenclature/Preliminaries The Normal Distribution The normal probability density function (PDF) is given by the expression for. Here s (a scatter parameter) is the standard deviation and m (a central location parameter) is the mean.

4. Nomenclature/Preliminaries TWO PARAMETER WEIBULL DISTRIBUTION The Weibull probability density function (PDF) is given by the expression for, and for. Here m (a scatter parameter) and sq (a central location parameter) are distribution parameters that define the Weibull distribution in much the same way as the mean (a central location parameter) and standard deviation (a scatter parameter) are parameters that define the Gaussian (normal) distribution.

5. The cumulative distribution function for the two-parameter Weibull distribution is given by the expression for, and for. Note that a three-parameter formulation exists for the Weibull distribution. However, the two-parameter formulation yields conservative results. In addition, the three-parameter formulation is not used unless there is overwhelming evidence of threshold behavior. Nomenclature/Preliminaries

6. The Lognormal Distribution The normal probability density function (PDF) is given by the expression for. Here and are found from the following two expressions: Where s X (a scatter parameter) is the standard deviation and m X (a central location parameter) is the mean. These parameters are estimated from data, and the distribution parameter and are found from the expressions above.

7. Nomenclature/Preliminaries The Reliability Index b

8. Nomenclature/Preliminaries