If a process variable is normally distributed, in the long run virtually all observed va...

If a process variable is normally distributed, in the long run virtually all observed values should be between μ – 3σ and μ ₊ 3σ , giving a process spread of 6σ.

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

_b. The C_p 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 C_pk 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 C_p and C_pk compare, and when are they equal?