A vibration-isolation bushing as shown below is assembled in a manufacturing system. The assembly consists of two steel plates with a rubber plate between them. The steel plates have a nominal thickness of 3mm, and the rubber plate has 0.5min. The overall dimension has a specification of 6.5 ? 0.35 mm. It is necessary that the standard deviation of the rubber-plate thickness ? _R should be half of the standard deviation of the steel- plate thickness as ? _S . Calculate the required ? _R and ? _S according to the following assumptions.

(a) Assume C _p = 1

(b) Assume C _p = 1.33

(c) Assume that the overall dimensional specification has a tolerance of ? 0.5mm with C _p = 1.33.

3 mm 3 mm 0.5 mm