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Chapter 13: G. Measurement System Analysis 123
variation. As mentioned earlier, the total process variation can be divided into two
major categories, that is, variation due to parts and variation due to gages or the
measurement system. Part-to-part variation may be due to environment, methods,
materials, machines, or some combination thereof, and other factors. The variation
due to the measurement system mainly consists of two major components:
one due to the instrument being used for taking measurements, and the other
due to the operators who use the instrument. In the industrial world, these components
are usually referred to as repeatability and reproducibility, respectively.
Thus, repeatability and reproducibility may be considered as the major indicators
of measurement system performance. A little later we will discuss repeatability
and reproducibility in more detail.
Since repeatability refers to the variation generated by the instrument
(that is, measurement equipment or gage) it is referred to as equipment variation
(EV). Reproducibility refers to variation generated by operators using measurement
instruments and is referred to as appraiser (or operator) variation (AV). The
study of gage repeatability and reproducibility is usually referred to as a gage
R&R study.
In the Automotive Industry Action Group (AIAG) reference manual on MSA
several methods for conducting GR&R are given. In this book we will study two
methods: the range-based method and the analysis of variance (ANOVA) method.
Since analysis of variance is an advanced statistical technique that is not covered
in this book, we will not go into much detail. We will focus our attention on
explaining and interpreting the results of an example that we will work out using
computer software.
Part II.G
THE RANGE-BASED METHOD
The method discussed in this section has been presented by various authors
including IBM (1986) and Barrantine (2003). Before we discuss the details of this
method, we will define certain terms, namely, measurement capability index, K 1
factor, and K 2 factor. In addition, we will define some other terms that are very useful
in understanding the measurement system analysis.
A measurement system analysis is a technique for collecting data and
analyzing it to evaluate the effectiveness of the gage. In order to collect data we
randomly select some parts and select a certain number of operators (three or
more, but as a general rule, the more the better). Then each operator takes multiple
measurements (at least two) on each part. All the parts are measured in random
order. These measurements are also known as trials. Using the terminology of
control charts, the measurements on each part or the number of trials constitutes
a rational subgroup and the number of parts times the number of operators constitutes
the number of subgroups or samples. Then R – is defined as the average of
the ranges of trials within the same operator and R – is defined as the average of the
R – ’s among the operators.
Measurement capability index (MCI) is a measurement that quantifies our belief
that the gage is reliable enough to support the decisions that we make under the
existing circumstances. The MCI relates to four characteristics of a measurement
system that are the key to any measurement system. These characteristics are: