Suppose a process generates 15 batches of a product. For each
batch, 2 samples are taken and the thickness of each sample is
measured 2 times.
Using the standard SQC charting techniques described in the
previous sections, we can analyze the process using X-Bar and S
Charts:
Analyzing the above data yields the following X Bar and S charts:
Question: is your process out of control? With the above
technique, you can not be certain.
Considering the above charts, the X-Bar chart is severely
out-of-control. In interpreting these charts, one should realize
that the control limits in the X-Bar chart were calculated on the
basis of the standard deviations within the subgroup on the basis of
the within-sample variability. The subsequent subgroups, however,
are not only subject to within-sample variability, but also to
between sample to sample and batch to batch variability.
What are the sources of variation in a product response? There
are three major sources of variation in a process:
1. Measurement variability
2. Sampling variability (within batch)
3. Batch to batch variability
Each of the three sources of variability adds variation or error
to the results. The sample pulled from the batch and tested yields
to:
E = X - Xbar
(Average)
Where:
E is the error,
X is the measurement and
Xbar (Average) is the population
average.
The overall error has three components corresponding to three
sources of variations:
E = E Batch +
E Sample + E
Measurement
Where:
E Batch is the error caused by
batch to batch variability,
E Sample is the error caused by
batch to sampling variability and
E Measurement is the error caused
by batch to measurement variability.
By definition, these errors have zero averages and can be assumed
to be represented as normal distributions with fixed variances.
The standard deviation,
This is lots of statistics, however, the Advanced SQC for
Excel™ version makes this very easy to handle.
However, you need to run Advanced SQC for Excel™ version
and you get the following chart:
Now you can say you are in control. If you have multiple sources
of data you should consider Advanced SQC for Excel™.
