A partitioned polynomial integration algorithm for failure probability evaluation

Devices and components are subjected to stresses of certain types which the device must withstand to maintain proper operation. The applied stress and the withstand capability of a device are typically random quantities with associated probability distributions which can have arbitrary shapes. Previous workers approximated these distributions by standard shapes, for example, normal or Weibull, to calculate the failure probability analytically. This letter avoids the approximation of distributions and presents an efficient algorithm which can handle any distribution shape with complete control of the computation accuracy.