Cpk Vs. ppm Table

The performance of a process may be characterized in terms of how close it gets to hitting its target or meeting its specifications and how consistent it is in doing so.  For a process whose output data comprise a normal distribution, its performance can be conveniently quantified in terms of its process capability index, Cpk.

The Cpk of a process measures how centered the output of the process is between its lower and upper specification limits and how variable (and therefore how stable or non-stable) the output is.  In fact, the Cpk is expressed as the ratio of how far the mean of the output data is from the closer spec limit (the centering of the process) to three times their standard deviation (the process variability).

If the mean of the process data is closer to the lower spec limit LSL and the standard deviation of the process data is Stdev, then Cpk = (Mean-LSL) / (3 Stdev). If the mean of the process data is closer to the upper spec limit USL, then

Cpk = (USL-Mean) / (3 Stdev).

An ideal process is one whose output is always dead center between the spec limits, such that the mean of its output data equals this dead center and the standard deviation is zero.  The Cpk of this ideal process is infinite.

As a process becomes less centered between the spec limits or as it becomes more variable, its Cpk decreases.  As its Cpk decreases, the probability of it exhibiting an output that is outside its specification limits increases. Thus, every Cpk value corresponds to a percent defective rate, which may be expressed in parts per million, or ppm.

Table 1 shows some Cpk values and their equivalent ppm rates.  In the semiconductor industry, the Cpk goal for a process is normally set at 1.67, although a Cpk of 1.33 is still considered acceptable.

Table 1. Cpk Vs. ppm
 Cpk Sigma ppm 0.43 - 193,600 0.47 - 161,510 0.50 1.50 133,610 0.53 - 109,600 0.57 - 89,130 0.60 - 71,960 0.63 - 57,430 0.67 - 45,500 0.70 - 35,730 0.73 - 27,810 0.77 - 21,450 0.80 - 16,400 0.83 - 12,420 0.87 - 9,322 0.90 - 6,934 0.93 - 5,110 0.97 - 3,732 1.00 3.00 2,700 1.03 - 1,935 1.07 - 1,374 1.10 - 967 1.13 - 674 1.16 ~3.50 465 1.20 - 318 1.23 - 216 1.27 - 145 1.30 - 98 1.33 4.00 64 1.37 - 41 1.40 - 27 1.43 - 17 1.47 - 11 1.50 4.50 7 1.53 - 4 1.57 - 3 1.60 ~5.00 0.5 2.00 6.00 0.00198