Question

A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.8 mm and an upper specification limit of 23.2 mm. The standard deviation is 0.1 mm and the mean is 23 mm. Is the process capable of meeting requirements?

Answer 1

Upper specification limit (USL) = 23.2

Lower specification limit (LSL) = 22.8

Mean = 23

Standard deviation (SD) = 0.1

Cpl = (Mean - LSL) / (3 x SD) = (23-22.8)/(3x0.1) = 0.2/0.3 = 0.67

Cpu = (USL - Mean) / (3 x SD) = (23.2-23)/(3x0.1) = 0.2/0.3 = 0.67

Process capability index (Cpk) = Minimum of (Cpu, Cpl)

= Minimum of (0.67 , 0.67)

= 0.67

No, the process is not capable as the process capability index is less than 1.33