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Statistical Process Control | R-Chart (Control Chart for Ranges) - YouTube
Channel: Joshua Emmanuel
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Welcome to this series on Statistical Process Control.
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In this video, we will be constructing a control
chart for R (or an R-chart) from raw data.
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Control charts are used to monitor how a process
changes over time.
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They reveal the stability or variability in
a process.
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They help us to distinguish between random
and assignable variations.
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Random Variations, also called Natural Variations,
are present in every system.
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Assignable Variations on the other hand are
Special Causes of Variation.
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So the objective of statistical process control
is to identify and eliminate these external
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causes of variation.
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Here is an example of a control chart.
It comprises of a lower control limit (LCL),
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centre line (CL), and an upper control limit
(UCL).
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If a process is operating within acceptable
limits, we say that the process is “in statistical
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control” or stable. Otherwise, the process
is “out of control.”
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For the purpose of this video, we will just
say that a process is in control if
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1. There are no sample points outside the
lower or upper limits;
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2. The sample points appear randomly distributed.
That is, there is no trend, or other unusual
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behavior.
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Here is a control chart that shows the process
is out of control because there is a point
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above the upper control limit. There is also
one below the lower control limit. Either
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of these show us that the process is not in
control.
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Here is another process out-of-control as
there is a positive trend in the process values.
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This process here will also be considered
out of control because of increasing variation
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between the values over time.
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In this SPC series, we will be discussing
the R-chart, the x-bar chart, the p-chart,
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and the c-chart.
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The R and x-bar charts are used to monitor
quantitative variables (that is, variability
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and central tendency), while the p and c charts
are used to monitor qualitative variables
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(that is, attributes or characteristics).
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In constructing a control chart for the range,
R, we will be using this process data, consisting
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of weights of a snack pack specified as 500
grams. Samples of size 5 are collected every
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day for 10 days.
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Our objective is to determine if the process
variability is in control.
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The R-chart is used to monitor sample ranges
and it thus provides us with some information
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about the process variability.
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The Range is the numerical difference between
the largest and smallest value in a sample.
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Therefore the range for the first sample is
509 minus 496 which gives 13.
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For the second sample the range is 521 minus
492 which gives 29.
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Continuing in that fashion we have the ranges
for all the samples.
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Next we calculate the centerline, R-bar. That
is, the average of the ranges.
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The sum of these ranges is 231. Therefore
the mean of the ranges, R-bar, is 231/10 which
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gives 23.1.
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The formula for the lower control limit, LCL
is D3 R-bar
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And the formula for the upper control limit,
UCL, is D4 R-bar.
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D3 and D4 are obtained from the table of control
limit constants.
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Here is the first 9 rows of the table.
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For Ranges, we look to the right here for
our D3 and D4 values.
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Remember that the sample size is 5 per day.
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As you can see that in this table; each sample
has 5 values while the number of samples is
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10.
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So going back to the control limit table,
sample size is 5, our D3 will be 0 and D4
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2.114.
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So the lower control limit, LCL, will be 0(23.1)
which is 0.
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And the upper control limit, UCL, will be
2.114(23.1) which gives 48.83.
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For the chart, we can first draw the control
limits.
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Next, the sample ranges as points.
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And finally we join the points with lines.
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The R-chart is now complete. The sample points
appear random and there are no points beyond
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the lower and upper control limits.
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We can say that the process is within statistical
control.
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If you plan drawing the control chart in Excel,
I have posted a few useful links in the description
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below.
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Thanks for watching.
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