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.