Today, let’s discuss the types of Control Chart, and how to decide which one you should use.
[Intro Video]
Hi, this is Mike Negami, LeanSigma Black Belt.
Today’s topic is from this request: “Could you please make a video
about what the difference between an Xbar-R Control Chart and Xbar-S Control Chart is
and what an R Control Chart, X Bar Control Chart, P Control Chart are?”
Tuan, thank you for your request. I totally understand why he made this request. There
are many types of Control Charts and there are very few learning materials that easily
explain this topic out there. I’ll tell you beforehand that while I won’t show you
any formulas, I’ll explain the differences between the eight Control Charts in an easy-to-understand
way. By the way, I made a template of an Xbar-R Control Chart and a video about how to interpret
the result after creating a Control Chart. You may want to watch that video first to
understand the basics. I’ll answer the first question about the
difference between the Xbar-R and Xbar-S Control Charts. The left chart is the Xbar-R Control
Chart and the right shows the Xbar-S Control Chart as examples. Each of the Control Chart
consists of two Control Charts. Both of the upper halves are Xbar Control
Charts with the averages of the data groups dotted in chronological order. You can see
a big flow of data with this chart. The lower half of the Xbar-R is the R Control Chart.
R stands for ‘Range’ and it’s the difference between the maximum value and the minimum
value of each data group. The R chart dots the range values in chronological order. On
the other hand, the lower half of the Xbar-S is the S Control Chart, which stands for standard
deviation and dots the standard deviations of each data group. Both have the same purpose
and you can see the variation of the data group with them.
Now, how can you use the Xbar-R and the Xbar-S Control Charts differently? It depends on
sample size. In practice, we periodically measure data as samples. The sample size is
how many samples you take at that time. Actually, I’ll show you the source data of the two
Control Charts. This is the Xbar-R Control Chart and its source
data. Its sample size is 5. As the sample size of the data group increases, the R Control
Chart loses its accuracy. If so, the S Control Chart is better for larger sample sizes.
Although there is no global standard, in general, if the sample size is 9 or less, we use the
R Control Chart. If it’s more than 9, we use the S Control Chart. This is the source
data of the Xbar-S Control Chart. In this example the sample size is 12.
The answer was quite easy. The Xbar-R is a Control Chart with the Xbar and the R Control
Charts. The Xbar-S is a Control Chart with the Xbar and the S Control Charts. It becomes
a little challenging the next question. How do you use the other Control Charts differently?
There is one answer. It depends on the data you use.
I made a quick reference table. The Control Charts are divided into two groups according
to the type of data we use. The first group is ‘Variable’. It has measured values
such as length, weight, temperature, voltage, etc. This data type is continuous numbers
and it can have decimal numbers and negative values. Then, we’ll divide the group more.
The next checkpoint is their sample conditions. As I mentioned earlier, if the sample size
is consistent and more than 9, use the Xbar-S Control Chart, 9 or less, use the Xbar-R Control
Chart. When data is very biased, it may be better to use the median rather than the average,
so you may rather want to use a Me-R Control Chart. Sometimes you may not have a consistent
sample size for some reason. Then, the sample size would be 1 and we would dot each data
value. That Control Chart is an X-R Control Chart.
The other data type has counted value. We call it an ‘Attribute’. We usually count
the number of defects or defectives. Since this is counting numbers, it cannot have decimal
numbers or negative values, and the Control Chart to be used depends on whether you’re
targeting defects or defectives. What’s the difference between the two? For
example, if there are three scratches on one manufactured part, the number of defects is
3 and the number of defectives is one. The next checkpoint is the sample condition. However,
unlike before, the difference in size doesn’t matter, but whether the sample size can be
consistent or not matters. From these two checkpoints, the following
four Control Charts will come out. If you want to manage the numbers of defects and
can keep the sample size consistent, record only the number of defects and use the c Chart.
‘c’ stands for ‘Count’. You simply dot the numbers of defects.
When the sample size is not consistent, you can’t compare the face values, so it’s
necessary to record the number of samples each time as well. Then, use a u Chart. ‘u’
stands for ‘Unit’. You dot the defect percentages per unit, which are the number
of defects divided by the number of samples. Next is the case where you want to manage
the number of Defectives. Like the u Chart, if you can’t have the sample size consistent,
record the number of Defectives and the number of samples, then use a p Chart. ‘p’ stands
for ‘Proportion’. You’ll dot the Defective’s percentages, which are the number of Defectives
divided by the number of samples. Lastly, when you want to manage the number
of Defectives and can make the sample size consistent, record only the numbers of Defectives
and use an np Chart. ‘n’ stands for ‘Number’ and p stands
for ‘Proportion’. The total ‘Number’ x ‘Proportion’ % = # of Defectives and
you dot the numbers of Defectives. The conclusion is very simple. The type of
your Control Chart will be decided naturally depending on what you want to manage, what
kind of data you can get and if you can have a consistent sample size or not. It’s better
to rely on software to create Control Charts these days. For example, the software I use
is QI Macros, which is an Excel add-in. After you prepare appropriate data, this software
determines the type of Control Chart and makes it automatically.
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