2.1 Process Accuracy and the C _a Index

While the precision index C _p discussed in Chapter 1 measures the magnitude of the process variation, the index k, to be defined below, describes the process capability in terms of departure of the process mean ? from the center (mid) point m and provides a quantified measure of the extent that a process is off-center. The index k is one of the original Japanese indices and is defined as:

where ? is the process mean, d = ( USL LSL) / 2 is the half specification width, USL and LSL are, as above, the upper and the lower specification limits, and m is the midpoint between the upper and lower specification limits ( m = ( USL + LSL)/2). This index measures the departure of process mean from the mid-point of specifications. For example, k = 0 indicates that the process is centered at the target ( ? = m), k = 1 means that the process mean is located at one of the specification limits. When 0 < k < 1, the process mean is located between the target and one of the specification limits. Obviously, k > 1 indicates that ? fall outside the specification limits (i.e. ? > USL or ? < LSL), the process is severely off-center and it needs...