Probability of overlap
- Quality Engineering
- April 2020
- Volume 32 Issue 2
- pp. 260-261
- Jensen, Willis A., Si, Wujun
The copyright of this article is not held by ASQ.
Consider a situation where we measure the strength of two different components that go into a finished product. In order for the product to work well, it is crucial that the strength of component A, not be greater than the strength of component B with a certain safety margin. The strength of both components is obtained using tensile testing and thus are measured in the same units (kgf).
If we assume that the strength of component A is a random variable denoted as X with some distribution f(x) and the strength of component B is a random variable denoted as Y with some distribution f(y), then we need to determine the distribution of the difference Y-X, or the distribution of the ratio Y/X. For the strength data, we need to determine the probability Pr(Y-X>c1) or Pr(Y/X