Question

Explain the difference between process capability and statistical control.

Suppose that a process with a normally distributed output has a mean of 50.0 cm. and a variance of 3.61 cm. If the specifications are 51.0 +/- 3.75 cm.,

a. Compute Cp and Cpk

b. What are your conclusions about this process?

Answer 1

Process capability is checking the process using appropriate measures about whether the process is producing the product within the specified range. The upper range is called Upper specification limit and the lower one is called Lower specification limit. It is measured using Process capability index or process performance index.

Statistical control employs statistical methods to monitor and control the process and perform the quality control. It can be used in any process where the output is measurable.

Given that,

USL = 51 + 3.75 = 54.75 cm

LSL = 51-3.75 = 47.25cm

Mean = 50cm, Variance = V = 3.61cm,

Hence, Standard deviation = s = sq. root (V) = 1.90cm

A.)

Cp = (USL-LSL)/6s = (54.75 - 47.25) / (6 x 1.9) = 0.6578

CpU = (USL - m)/3s = (54.75 - 50) / (3 x 1.9) = 0.8333

CpL = (m-LSL)/3s = (50 - 47.25) / (3 x 1.9) = 0.4825

CpK = minimum (CpU, CpL) = minimum (0.8333, 0.4825) = 0.4825

Conclusion: There is a gap between Cp (0.6578) and CpK (0.4825). The gap shows that the average differs from the target value. The gap will close when the average reached the target value.