Question

C&A is making steel rods with an average diameter of 1 mm. The process has a standard deviation of 0.2 mm. The upper and lower specification limits are 1.2 mm and 0.8 mm respectively. What is C&A’s process capability index?

Answer 1

Calculation of process capability index(cpk) :

Mean = 1 mm.

standard deviation = 0.2 mm.

Upper Specification Limit(USL) = 1.2 mm.

Lower Specification Limit(LSL) = 0.8 mm.

Cpl = (Mean - LSL) / 3 sigma where sigma is the standard deviation

= (1 - 0.8) / (3 X 0.2) =(0.2 / 0.6) = 0.33

Cpu = (USL - Mean) / 3 sigma where sigma is the standard deviation

= (1.2 - 1) / (3 X 0.2) = (0.2 / 0.6) = 0.33

Therefore,process capability index is 0.33

(Note : Process capability index is taken as the smaller of either Cpl or Cpu.But in this case Cpl is equal to Cpu.So the process capability index is 0.33 and also the process capability is 0.33.This indicates that the process is centered at the exact midpoint of the specification limits)