The exact upper bound of the variance of properties from multiple sources is attained from sampling not more than two sources. This paper discusses important applications of this result referred to as variance upper bound theorem. A new conservative, non-parametric estimate has been proposed for the capability index of a process whose output combines contributions from multiple sources of variation. A new method for assessing and increasing the robustness of processes, operations and products where the mean value can be easily adjusted or is not critical has been presented, based on the variance upper bound theorem. We show that the worst-case variation of a property from multiple sources, obtained by using the variance upper bound theorem, can be used as a basis for developing robust engineering designs and products. If a design is capable of accommodating the worst-case variation of the reliability-critical parameters, it will also be capable of accommodating the variation of the reliability-critical parameters from any combination of sources of variation and mixing proportions. In this respect, a new algorithm for virtual testing based on the variance upper bound theorem has been proposed for determining the probability of a faulty assembly from multiple sources. For sources of variation that can be removed, the robustness can be improved further, by removing the source that yields the largest decrease in the variance upper bound. Consequently, the correspondent algorithm is also presented. A number of engineering applications have been discussed where the variance upper bound theorem can be used to assess and increase the robustness of mechanical and electrical components, manufacturing processes and operations.
Received on March 23, 2008, revised on November 11, 2008