Six Sigma

Control Charts – Part 2

By Ron Updated on March 23rd, 2008

Welcome back. This is part 2 of the 3 part series on control charts. As promised we will discuss the p, c, and u charts this evening. These control charts are used when we are dealing with attribute data, which is sometimes referred to as discrete data.

Attribute Data

Before discussing these 3 control charts I wanted to say a few words about attribute data. Whenever we count things like defects or scratches (1, 2, 3, etc.) or categorize them (pass/fail, boy/girl, etc.) we are dealing with attribute data.

OK, let me get all statistical on you for a second… when we count things we are dealing with what we call “Poisson Data” and when we categorize them we are dealing with “Binomial Data.” That bit of info may serve you well in a game of trivial pursuit one day – or not.

So, the first thing we need to understand before attempting to create a control chart is what type of data we have. If it we are counting or categorizing things it is attribute and the main control charts for this type of data are the p, c, and u chart.

Defects and Defectives

Next we must discuss an extremely important topic – the difference between a defect and a defective. Here is an easy way to understand the difference.

I want you to imagine how the cover on your mobile phone was made. When the nice manufacturing operator had finished the last process they probably did some type of inspection since they probably don’t trust their batch and queue painting process (kidding… sort of).

If the cover had even one tiny scratch or blemish it was likely marked as “defective” and thrown in the trash bin. Upon further examination of this defective cover someone may want to count the number of blemishes in order to quantify how bad the situation is. Each blemish would count as 1 “defect.” So, a “defective” cover can have multiple “defects.” Clear as mud? Good. Let us continue.

p chart

Now then, let’s talk about the p chart. These charts are used when we are dealing with the proportion of “defective” product. We may use the p chart to track the ratio of “defective to total” covers produced in the aforementioned example. The p chart is finicky about sample sizes and works really well when the sample size is over 50. Grab your local Black Belt or shoot me an email if you are ever concerned about your sample size.

c chart

Next we have the c chart. It is used to chart the number of “defects” in each subgroup. We use the c chart when our subgroup size is constant (i.e. the same). So in this case we are charting the number of blemishes (defects) but the subgroup size (i.e. number of covers) must be the same.

u chart

Last, but certainly not least of the attribute control charts, is the u chart. The rules for when to use the u chart are almost identical to that of the c chart, with one exception. The exception is that we use the u chart when our subgroup size is not the same. So, we are still counting the blemishes (defects) but the subgroup size (number of covers) does not have to be the same.

Well that about sums things up for this evening. There are a few other attribute control charts out there but these 3 will get you through most battles.

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Ron

Anonymous
August 5, 2010 - 12:42 pm
Reply

One common problem I encounter when working with p-charts is what to do when the sample size is so large that it compresses the interval between control limits to a degree that renders UCL/LCL useless. Should we use an I-MR chart even though it’s discreet data which I have seen done?