Ralf Bohle GmbH, a German manufacturing company, produces bicycle and wheelchair tires under the Schwalbe Tire brand name. Road and racing cyclists require specific tires that meet demanding specifications, and Ralf Bohle is concerned about monitoring the width of its road tires for these picky consumers. The company has a lower specification limit of 23 mm and an upper specification limit of 24 mm for the width of their flagship Schwlbe Pro One TT racing tire. After monitoring their process for some time, the company determines that the widths of tires produced is normally distributed with a standard deviation in width of 0.33 mm and a mean of 23.5 mm wide. a) What is the process capability index for the process? ) Assume the standard formulation for process capability where ?? = 1 refers to a threesigma process (i.e. ?? = 1 means that the upper and lower specification limits span ± 3?). b) What is the probability that a tire will either be too wide or too narrow? Stated differently, what is the combined total probability of being outside of the specification limits? c) The company now wants to reduce its defect probability to 1%. To what value would it have to reduce the standard deviation in the process to meet this target?

Ralf Bohle GmbH, a German manufacturing company, produces bicycle and wheelchair tires under the Schwalbe Tire brand name. Road and racing cyclists require specific tires that meet demanding specifications, and Ralf Bohle is concerned about monitoring the width of its road tires for these picky consumers. The company has a lower specification limit of 23 mm and an upper specification limit of 24 mm for the width of their flagship Schwlbe Pro One TT racing tire. After monitoring their process for some time, the company determines that the widths of tires produced is normally distributed with a standard deviation in width of 0.33 mm and a mean of 23.5 mm wide. a) What is the process capability index for the process? ) Assume the standard formulation for process capability where ?? = 1 refers to a threesigma process (i.e. ?? = 1 means that the upper and lower specification limits span ± 3?). b) What is the probability that a tire will either be too wide or too narrow? Stated differently, what is the combined total probability of being outside of the specification limits? c) The company now wants to reduce its defect probability to 1%. To what value would it have to reduce the standard deviation in the process to meet this target?