If a process variable is normally distributed, in the long run virtually all observed values should be between and

, giving a process spread of 6s.

a. With LSL and USL denoting the lower and upper specification limits, one commonly used process capability index is . Cp 5 (USL 2 LSL)/6s The value Cp 5 1 indicates a process that is only marginally capable of meeting specifications. Ideally, Cp should exceed 1.33 (a “very good” process). Calculate the value of Cp for each of the cork production processes described in the previous exercise, and comment.

b. The Cp index described in

(a) does not take into account process location. A capability measure that does involve the process mean is Calculate the value of Cpk for each of the cork-production processes described in the previous exercise, and comment. [Note: In practice, m and s have to be estimated from process data; we show how to do this in Section 16.2]

c. How do Cp and Cpk compare, and when are they equal?
Cpk 5 min 5(USL 2 m)/3s, (m 2 LSL)/3s6