Page 124 - Six Sigma Demystified

Chapter 5 m e a s u r e s tag e 105

DPmo and Sigma level estimates
When the process is in a state of statistical control, then the process is predict-
l
able, and short- and ong- term defect levels can be estimated. Unstable (i.e.,
out- of- control) processes, by definition, are the combination of multiple pro-
cesses. Their instability makes prediction of defect levels unreliable.
For controlled processes, the process capability index provides a comparison
between the calculated process location and its variation with the stated cus-
tomer requirements.
When the process is unstable (i.e., not in statistical control) or control cannot
be established because of lack of data, a process performance index may be used
as a rough estimate to compare observed variation with customer requirements.
Generally, many more samples are needed to reliably estimate process perfor-
mance when the process is unstable. Furthermore, as discussed earlier, there is
no reason to believe that the process will behave in this same fashion in the
future.
The calculated process capability or process performance metric can be con-
verted to corresponding defects per million opportunities (DPMO) and sigma
level using Appendix 8. Let’s see how these numbers are derived.
Assuming that the normal distribution is an adequate model for the process,
the normal probability tables (Appendix 1) are used to estimate the percentage
of the process distribution beyond a given value, such as a customer require-
ment (usually referred to as a specification). z values at x = USL and z at x =
L
LSL are calculated, where

z = (x – m)/s

USL refers to the upper specification limit, the largest process value allowed by
the customer. LSL refers to the lower specification limit, the smallest allowed
value.
The z value indicates how many s units the x value is from the mean (or
average, m). For example, if the USL for a process is 16, and the process average
and standard deviation are calculated as 10.0 and 2.0, respectively, then the z
value corresponding to the upper specification is z = (16 – 10)/2 = 3.0, imply-
ing that the upper specification is 3s units from the mean.
Using the normal tables of Appendix 1, a z value of 3 equals a probability of
0.99865, meaning that 99.865 percent of the process distribution is less than
the x value that is 3s sigma units above the mean. This implies that 1 – 0.99865
= 0.00135 (or 0.135 percent) of the process exceeds this x value (i.e., lies to its