Question

A Quality analyst is checking the process capability associated with the production of struts, specifically the amount of torque used to tighten the fastener. Twenty five samples of size 4 have been taken. These were used to create X bar and R charts. The values for these charts are as follows: The upper and lower control limits for the X-bar chart are 75 Nm and 72.16 Nm respectively. X double bar is 73.58 Nm, R bar is 1.66. The specification limits are 81.5Nm ± 10. Calculate Cp and Cpk. Interpret the values.

Answer 1

Given values:

X-double bar= 73.58 Nm

R-bar = 1.66

Upper specification limit (USL) = 81.5 + 10 = 91.5 Nm

Lower specification limit (LSL) = 81.5 - 10 = 71.5 Nm

Solution:

Cp is calculated as;

Cp = (USL - LSL) / 6

Standard deviation, = R-bar / d2

From 3 control limits chart, For n = 4 (sample size = 4), d2 = 2.059

= 1.66 / 2.059

= 0.8062

Cp = (USL - LSL) / 6

Cp = (91.5 - 71.5) / (6 x 0.8062)

Cp = 4.13

Cpk is calculated as;

Cpk = Minimum of [(USL - X-double bar)/ 3] and [(X-double bar - LSL)/ 3]

Cpk = Minimum of [(91.5 - 73.58)/ (3 x 0.8062)] and [(73.58 - 71.5)/ (3 x 0.8062)]

Cpk = Minimum of (7.41) and (0.86)

Cpk = 0.86

Cp = 4.13 > 1.00, means that the variation is small.

Cpk = 0.86 < 1.00, means that the process is not capable of meeting the specifications.