Dear Allstatters,
Thank you to those people who kindly responded to my urgent query. Your
responses did help me to resolve the issue with my client so thanks again
for that.
The consensus of the responses I received was that using the between-run
variance to set control limits is permissible even when it is significantly
higher than the within run variance provided the resulting control limits
does not allow products to be out of specification whilst the process is
deemed to be within control. In my case, the client is using a 1-way
specification where (nearly) all products had to exceed a minimum value.
The target value comes from a model I built for them and the control limits
were set using the within run variance around this target. Had I used the
between-run variance, there would be a significant risk of products below
specification. I have therefore encouraged my client to use the control
limits primarily as a tool to continually validate the model I built and to
use an alternative sampling plan based on specified alpha and beta risks to
determine if the process is making products that meet specification even
though the process may be out of control. Until they make improvements to
their process by reducing the between-run variance, it would not be safe to
allow them to use control limits based on between-run variance.
I would like to share one response that I received from Robin Henderson who
mentioned a method I wasn't aware of. This is something that is known as
triple charts and is available in Minitab. The Minitab help facility
apparently states the following:
"I-MR-R/S (Between/Within) Chart produces a three-way control chart using
both between-subgroup and within-subgroup variations. An I-MR-R/S chart
consists of:
. An individuals chart
. A moving range chart
. A R chart or S chart
When collecting data in subgroups, random error may not be the only source
of variation. For example, if you sample five parts in close succession
every hour, the only differences should be due to random error. Over time,
the process could shift or drift, so the next sample of five parts may be
different from the previous sample. Under these conditions, the overall
process variation is due to both between-sample variation and random error.
Variation within each sample also contributes to overall process variation.
Suppose you sample one part every hour, and measure five locations across
the part. While the parts can vary hour to hour, the measurements taken at
the five locations can also be consistently different in all parts. Perhaps
one location almost always produces the largest measurement, or is
consistently smaller. This variation due to location is not accounted for,
and the within-sample standard deviation no longer estimates random error,
but actually estimates both random error and the location effect. This
results in a standard deviation that is too large, causing control limits
that are too wide, with most points on the control chart placed very close
to the centerline. This process appears to be too good, and it probably is.
You can solve this problem by using I-MR-R/S (Between/Within) to create
three separate evaluations of process variation:
Individuals chart: charts the means from each sample on an individuals
control chart, rather than on an Xbar chart. This chart uses a moving range
between consecutive means to determine the control limits. Since the
distribution of the sample means is related to the random error, using a
moving range to estimate the standard deviation of the distribution of
sample means is similar to estimating just the random error component. This
eliminates the within-sample component of variation in the control limits.
Moving range chart: charts the subgroup means using a moving range to remove
the within-sample variation. Use this chart, along with the Individuals
chart, to track both process location and process variation, using the
between-sample component of variation.
R chart or S chart: charts process variation using the within-sample
component of variation.
Thus, the combination of the three charts provides a method of assessing the
stability of process location, the between-sample component of variation,
and the within-sample component of variation."
Regards
Nigel Marriott
Chartered Statistician
<http://www.marriott-stats.com/> www.marriott-stats.com
Ground Floor, 21 Marlborough Buildings, Bath BA1 2LY, United Kingdom
Tel (mobile) +44 (0)773 4069997
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Fax +44 (0)870 6221969
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883304029
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Tilehurst, Reading, RG31 5AL
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