Which type of control chart should be used to monitor the number of defects per unit?

Attributes data arise when classifying or counting observations The Shewhart control chart plots quality characteristics that can be measured and expressed numerically. We measure weight, height, position, thickness, etc. If we cannot represent a particular quality characteristic numerically, or if it is impractical to do so, we then often resort to using a quality characteristic to sort or classify an item that is inspected into one of two "buckets".

An example of a common quality characteristic classification would be designating units as "conforming units" or "nonconforming units". Another quality characteristic criteria would be sorting units into "non defective" and "defective" categories. Quality characteristics of that type are called attributes.

Note that there is a difference between "nonconforming to an engineering specification" and "defective" -- a nonconforming unit may function just fine and be, in fact, not defective at all, while a part can be "in spec" and not fucntion as desired (i.e., be defective).

Examples of quality characteristics that are attributes are the number of failures in a production run, the proportion of malfunctioning wafers in a lot, the number of people eating in the cafeteria on a given day, etc.

Types of attribute control charts Control charts dealing with the number of defects or nonconformities are called c charts (for count).

Control charts dealing with the proportion or fraction of defective product are called  p charts (for proportion).

There is another chart which handles defects per unit, called the u chart (for unit). This applies when we wish to work with the average number of nonconformities per unit of product.

For additional references, see Woodall (1997) which reviews papers showing examples of attribute control charting, including examples from semiconductor manufacturing such as those examining the spatial depencence of defects.

Control charts are simple but very powerful tools that can help you determine whether a process is in control (meaning it has only random, normal variation) or out of control (meaning it shows unusual variation, probably due to a "special cause").

In an earlier post, I wrote about the common elements that all control charts share: upper and lower control limits, an expected variation region, and an unexpected (or special cause) variation region.  But there are many different types of control charts:  P charts, U charts, I-MR charts...how can you know which one is right? 

Which Control Chart Matches Your Data Type? 

The first step in choosing an appropriate control chart is to determine whether you have continuous or attribute data.

Continuous data usually involve measurements, and often include fractions or decimals. Weight, height, width, time, and similar measurements are all continuous data. If you're looking at measurement data for individuals, you would use an I-MR chart. If your data are being collected in subgroups, you would use an Xbar-R chart if the subgroups have a size of 8 or less, or an Xbar-S chart if the subgroup size is larger than 8.  
  

If you have attribute data, you need to determine if you're looking at proportions or counts. If it's proportions, you'll typically be counting the number of defective items in a group, thus coming up with a "pass-fail" percentage. In this case, you would want to use a P chart.  If you're measuring the number of defects per unit, you have count data, which you would display using a U chart.

   Of course, we're just scratching the surface here -- there's a lot more to finding the right control chart for each individual situation than we can fit in a simple blog post.

    But if you're using Minitab Statistical Software, you can choose Assistant > Control Charts... and get step-by-step guidance through the process of creating a control chart, from determining what type of data you have, to making sure that your data meets necessary assumptions, to interpreting the results of your chart.

If you're not using it yet, you can download Minitab and try it for 30 days free.  In addition to guidance for control charts, the new Assistant menu also can guide you through Regression, Hypothesis Tests, Measurement Systems Analysis, and more. As a person who needs to use statistics but isn't naturally inclined toward numbers and math, I find it pretty cool to be able to get that guidance right from the software. 

Which type of control chart should be used to monitor the number of defects per unit attribute variables?

What type of control chart would be used to monitor the number of defects in the output of a process for making reports?

What type of control chart is used for the number of defects?

What type of control chart would be used to monitor the number of defectives in the output of a process for making iron castings?