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