This is the second paper in a series relating to stochastic methods in mechanical design. The first is entitled, “Some Property Data and Corresponding Weibull Parameters for Stochastic Mechanical Design,” and the third, “Some Stochastic Mechanical Design Applications.” When data are sparse, many investigators prefer employing coordinate transformations to rectify the data string, and a least-square regression to seek the best fit. Such an approach introduces some bias, which the method presented here is intended to reduce. With mass-produced products, extensive testing can be carried out and prototypes built and evaluated. When production is small, material testing may be limited to simple tension tests or perhaps none at all. How should a designer proceed in order to achieve a reliability goal or to assess a design to see if the goal has been realized? The purpose of this paper is to show how sparse strength data can be reduced to distributional parameters with less bias and how such information can be used when designing to a reliability goal.
Transient chaos under coordinate transformations in relativistic systems
