Control charts are the most difficult of the seven basic quality tools to use. They are seldom the method of choice. When a process step is important, we would prefer that the step not vary at all. ONLY when this can not be accomplished in an economical way does one choose to use a control chart.

In any process, pieces vary from each other.

But as they vary, they form a pattern.

And if that pattern is stable, it can be described as a distribution. These distributions can differ in location, spread, and shape.

If this variation that is present is, only common caused variation the process output forms a distribution that is stable **and** predictable over time.

If this variation that is present is special caused variation, the process is unstable over time producing varying distributions and thus is not predictable.

Control charts are only useful if the step (operation or function), over time, exhibits measurable random variation. Control charts display the data over time.

The Control Chart above (Time is on the x axis above listed as sample). Control Limits (the red lines) are displayed on control charts, where data falling within the control limits are considered common caused or “normal” variation. Any point outside the control limits are considered “special caused” variation and need to be look at and corrected through an action plan. If you create a control chart, you must also have with it an action plan.

Besides control limits for control charts, there are several other type of trends (runs) that can indicate an out-of-control process before any defective parts are produced. Remember that with common cause I can predict what will happen next. This means that if I have several things happen in a row it could tell me something has changed.

What I have shown above is only one type a control chart and one of the simplest to use but there are several others types of control charts available.

As mentioned in other articles, there are two types of data and we have control charts for both. There is what we call variables data and attribute data. Variables data is data that you can measure and attribute data is data that we count. So let me give you a brief description of the most commonly used Control Charts we have for each data type.

## Variables Data Control Charts (Measurable)

### The Individuals and Moving Range Chart (X-MR)

Individual and Moving range charts are used when taking more than one is expensive or the data is collected in a destructive test. If this is not your situation use one of the other types of variable control charts. One of the main reasons why you should use a different variables control chart is that with individual control charts the data need to be normally distributed. If it is not normally distributed, the chart will not work properly for you. The other charts below use averages and the distribution of averages are normal (Central Limit Theorem).

### Average and Range Chart ( Xbar – R)

This is the most popular of the variables control charts. This is because it is uses a small sample size and the range of that sample. With this chart, it is easiest to calculate the average (Xbar) of the sample and Range of the sample by hand. As mentioned above using the averages of samples in this chart assures you that the data plotted will be normal and all the trends can be predicted.

### Average and Standard Deviation Chart (Xbar – s)

This chart is used a lot when there is a computer associated with the work area that can calculate and plot the statistics needed for this chart (Xbar and s). Here we have to calculate and plot the sample average (Xbar) and the sample standard deviation (s).

### Other Variable Control Charts

There are several other types of variables control charts all used for very special conditions. These are the three that are used 95% of the time.

## Attribute Data Control Charts (Count)

### Proportion Defective (p)

p charts measure the proportion defective over time. It is important that each item (part, component or document) being check is either conforming (good) or defective (bad) as a whole. This means even if an item has several defects in it, it is still counted as 1 defective item. It is also important that the inspection of these items is grouped in some meaningful way. In this chart, the groups do not always have to be equal, but because of the varying group sizes, the control limits vary for group to group. This way the defective items can be expressed as a decimal fraction (percentage) of the grouping.

### Number Defective (np)

np charts also measure the proportion defective over time. It is important that each item (part, component or document) being check is either conforming (good) or defective (bad) as a whole. This means even if an item has several defects in it, it is still counted as 1 defective item.

The difference between the p and the np chart is in the grouping. Here in the np charts all of the groups being inspected need to always be the same size and never vary. This having the grouping (sample size) always the same make the control limits always the same an easier to calculate. These groupings, like the p chart, should be grouped in some meaningful way. This way the defective items can be expressed as a decimal fraction (percentage) of the grouping

### Number of Defects (c)

c charts measure the number of defects over time. Here we are counting defect in each item (part, component or document), so an item can have more than one defect in it. It is also important that the inspection of these items is grouped in some meaningful way. In this chart, the groups do not always have to be equal, but because of the varying group sizes, the control limits vary for group to group. This way the defective items can be expressed as a decimal fraction (percentage) of the grouping.

### Defects per unit (u)

u charts also measure the number of defects over time. . Here, just like c charts, we are counting defect in each item (part, component or document), so an item can have more than one defect in it. The difference between the c and the u chart is in the grouping. Here in the u charts all of the groups being inspected need to always be the same size and never vary. This having the grouping (sample size) always the same make the control limits always the same an easier to calculate. These groupings, like the p chart, should be grouped in some meaningful way. This way the defective items can be expressed as a decimal fraction (percentage) of the grouping.

## Selecting the Correct Control Chart

Below is a Decision Tree Diagram of the different type and there use. In this chart “n” is your grouping size or what is called sample size. Be sure you understand the application of each control chart or get help if you plan to use one of these.

## The Control Systems

I have talked to you about control charts, but to make them useful and not just a pretty picture on the wall you have to have a “Reaction Plan”. What is a Reaction Plan; a plan so when an out-of-control condition does occur you have a plan of action for the operator (person that plots the points) to follow to correct the condition NOW before another item is produced. Without this, the chart is a waste of time to build and maintain.

Well there you have a short article on Control Charts. Check back on my website blog to find videos on how to build each one of these in Minitab. If, you have questions or comments please feel free to contact me by leaving a comment below, emailing me, calling me, or leaving a comment on my website.

Bersbach Consulting

Peter Bersbach

Six Sigma Master Black Belt

http://sixsigmatrainingconsulting.com

peter@bersbach.com

1.520.829.0090