Page 128 - Six Sigma Demystified

Chapter 5 m e a s u r e s tag e 109

unit, still may have bias because it may be consistently wrong! Bias is a simple,
consistent offset in the estimate, and it can be corrected through calibration of
the measurement system, much like watches are synchronized for accuracy.
Measurement systems need to be analyzed for stability to ensure that their
accuracy does not degrade over time. While this is often not a concern during
the short time period of a Six Sigma project, it may become a concern for
future control of the process improvements.
Another concern is that of linearity: Does the measurement system provide
the same level of accuracy across its full range of use? If the error is higher for
larger measurements, then the estimates of variation in these cases are inflated,
which will have an unfavorable effect on improvement and control efforts.
Unfortunately, even a regularly calibrated measurement system may be sub-
ject to additional sources of error.
When measurements are taken of a process or population, the variation esti-
mated between the samples includes both the actual variation between the
sample units and measurement error. Mathematically, the total variance is com-
posed of the actual variance between the items and the variance, or error, of the
measurement:

s 2 total = s 2 item + s 2 measurement

The measurement error appears as variation between repeat samples of a given
sample unit. Bias does not affect this measurement error because bias alone will
cause the measurement system to measure each sample unit consistently.
When the variance of the measurements is known, a gauge discrimination
ratio can be calculated to provide a practical estimate of the measurement
system resolution. The discrimination ratio is the number of distinct categories

discernible by the measurement equipment. A value of 2, for instance, indicates
that the gauge is useful only for attribute analysis because it can only effectively
classify the parts as being in one group or the other (e.g., good or bad). A dis-
crimination ratio of 8 or more is suitable for statistical analysis of the data.
A primary tool to estimate the variance of the measurements is R&R analy-
sis, which categorizes the error as either a repeatability or a reproducibility error.
Repeatability error is associated with the equipment and procedures, whereas
reproducibility error is associated with the differences between personnel use
of the measurement equipment. Repeatability is estimated by comparing mul-
tiple measurements of the same sample unit. Reproducibility is estimated by
obtaining measurements of the same sample units by multiple personnel. Cat-
egorizing the error in this manner allows one to address and reduce the error.