by Stanley N. Deming AL
Statistics in the Laboratory: The Apparent Capability of an Industrial Process
It’s important to realize that information gets filtered and distorted by the inherent behavior of a measurement process. In this column, we’ll ignore biases and look closely at the relationship between industrial process variation and measurement process variation.
Figure 1 shows an ideal process. At the far left we see starting materials entering the industrial process. A sample of the industrial process output becomes the input to the measurement process. The output of the mea- surement process becomes a description of how the industrial process appears to be behaving.
Let’s assume that the industrial process is lined out, rock solid, no varia- tion. This is depicted in the two small graphs above the industrial process. The upper graph shows the true values of the process output P plotted on the vertical axis as a function of time on the horizontal axis—the output P is absolutely constant. The lower graph shows the same thing in a differ- ent way: the true values of the process output P are now plotted on the horizontal axis with something related to their probability density on the
vertical axis—again, there is no variation. Clearly, the inherent standard deviation of the industrial process σP
is zero.
Now let’s look at the two graphs below the measurement process. The lower graph depicts the values obtained from repetitive measurements of a reference material M plotted on the vertical axis as a function of time on the horizontal axis. The upper graph shows the same thing in a different way—the measured values are now plotted on the horizontal axis. Clearly, the inherent standard deviation of the measurement process σM
is zero.
Here’s an equation that will be important to us. It illustrates how variations from more than one source combine to give the total variation. Note that the standard deviations aren’t additive—the variances (standard devia- tions squared) are additive:
(1.1)
If the industrial process has zero variation (σP process has zero variation (σM industrial process will be zero (σT
= 0), and if the measurement
= 0), then the total variation of the measured = 0). This is shown in the two graphs at
the upper right of Figure 1, where the variation of the industrial process (P) and the variation of the measurement process (M) are combined (P+M). The upper graph shows the measured values as a function of time (rock solid), and the lower graph shows the same thing in a different way. Either way you look at it, there is no variation in the measured values.
But look closely at this lower graph. It also shows a lower specification L and an upper specification U separated by five units. In the last column in this series, L and U were specifications for the measurement process, but here they are specifications for the output of the industrial process. If the output is centered midway between the specifications, and if σT Cpk
is infinite! If this process behaves in the future as it has behaved in the
past, then we will never encounter any measurements that indicate the industrial process is producing product that is out of specification. This is clearly what management wants to see.
But Figure 1 is unrealistic. Industrial processes don’t have zero variation. Measurement processes don’t have zero variation. So what does the real world look like? Let’s have some fun.
Figure 1 – The relationship between an industrial process and a measure- ment process.
AMERICAN LABORATORY 23
Figure 2 is the analytical chemist’s egotistical view of the world. In this universe, the measurement process has zero variation (we analytical
JANUARY/FEBRUARY 2017
= 0, then
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