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Chapter 19: B. Statistical Process Control 295
Once the production starts, the manufacturer conducts capability studies to
compare the measures of the quality characteristic of the manufactured product
with the specification limits. This is the point where process capability indices
are used.
The first generation PCIs were established by the Japanese in the 1970s. They
used the following indices:
C p
Inherent capability of a process
k Position of the process in relation to the target value
C pk Position of the 6s process in relation to the target value
C pl Position of the 6s process in relation to the lower
specification limit
C pu Position of the 6s process in relation to the upper
specification limit
In this section we study these and other capability indices that are frequently
used in process capability analysis. Here we are not going to address every aspect
of these indices. However, an excellent reference for a more detailed study of these
indices is Kotz and Lovelace (1998).
Throughout the study of these indices we are going to assume that the process
producing the desired quality characteristic is under control, and thus
predictable.
Process Capability Index: C p
Let X be the process quality characteristic that we want to monitor. Let USL and
LSL be the upper specification limit and lower specification limit, respectively. The
performance of the process with respect to these limits is defined as follows:
Percentage of nonconforming produced by the process at the upper end
= P(X > USL).
Percentage of nonconforming produced by the process at the lower end
= P(X < LSL).
Thus, the total percentage of nonconforming produced by the process is defined
as
P(X < LSL or X > USL) = 1 – P(LSL < X < USL).
In the above paragraph we saw the performance of the process with respect to the
specification limits. Now we look into the performance of the process with respect
to the natural tolerance limits, that is, the upper natural tolerance limit (UNTL) and
the lower natural tolerance limit (LNTL).
The performance of the process with respect to the natural tolerance limits is
the percentage of the product produced by the process with its quality characteristic
falling within the interval (m – 3s, m + 3s), where m and s are respectively
the mean and the standard deviation of the process quality characteristic. Assuming
that the process quality characteristic is normally distributed and the process
Part IV.B.5