In lesson 1 we discovered why we need control charts. Now we are going to learn how to draw the control charts.
We use different types of control charts for different types of data. Data can be divided into two major categories, variables and attributes.

Variable data is any measurement which has a continuous scale. For example:
Length, weight, temperature and pressure.

Attribute data is based on discrete counts. For example:
The number of blemishes on a surface, the number of faulty products and the number of unpaid invoices.

With variable data we can measure to any accuracy that we want, for example 12.5, 3.075 etc. Attribute data, on the other hand, can only have whole number values like 1, 3, 12 etc. In this lesson we are going to look at a process where we have been given a preferred target value for a variable measurement. Our job is to try to get results as close as possible to that target.

The process is a tennis ball launcher and we are trying to shoot balls at a target distance. The target is 500 and the specifications are 300 to 700. The location of the previous shots fired are given in the screen.

Imagine that you are the operator of a machine – the launcher. Your job is to fire balls at the target and get them to land as close as possible to the ideal value of 500. First we need to ‘center’ the process.
When we fire one ball from the launcher we find the value is 415.
The customer of this process wants the landing position to be 500, so what do we do now? Should we compensate for the error by moving the launcher?

The answer is NO because we don’t know the process yet. There is always a certain amount of variation in every process and if we only have common cause variation and we are trying to adjust for this variation we will actually cause more variation on the output.

Look at the display of Landing positions at the right of the launcher. Each landing position is different and the variation may be due to common causes which are always present in this process.
We now have more information to get an idea how the process is performing. We can calculate the average of the shots which is 413 (Rounded).
If we fire 45 more shots we will get a better estimate of the real average of the process. After 50 shots the process average is 419 (Rounded)
We can now move the launcher so future shots will center around 500. Assuming that nothing changes in this process, future output should now be centered on 500.
“Assuming that nothing changes” is a big assumption. At this stage we do not know very much about our process and we do not know if things are likely to change over time. So, we need to find out if the process is “statistically stable”. We fire off another 100 shots then we will create a control chart.
The landing position is a continuous scale. We are actually using complete numbers for the results (423, 657 etc.) but there is nothing to stop us using more accurate measurements if we wanted to (423.45, 657.09 etc.)
This type of data is called variable data. We will use an Xbar and Range chart as the control chart for this process. In an Xbar and Range chart, the data is arranged into subgroups.

Let’s take a quick look at the data table.

Notice that there are 5 columns with “Landing position ( )” at the top. The number in brackets means that the column is part of a subgroup. For each row of the table, the data in these five columns represents one subgroup. Look at subgroup 25.
Look at the row with the number 25 in the grey column at the left. This subgroup starts at shot number 121. The subgroup columns contain the results of shots 121, 122, 123, 124 and 125.

Now let’s look at the control chart of this data:

An Xbar and range chart contains two graphs. For each row in the data table, the subgroup average is plotted (Xbar) along with the largest value in the subgroup minus the smallest value (Range). Let’s confirm this:
The last subgroup is highlighted and on the right side we see that Xbar = 533.2 and the Range = 69.
The 5 measurements of subgroup 30 are 499,567,550,498 and 552.
We can confirm that the value on the Range chart 168 is the highest value (567) – the smallest value (498) and the average is the sum of values/5.
The point at which the launcher was moved is shown on the chart. This is the equivalent of a written note on a paper chart and this is the sort of information an operator should record on a control chart.
Next we will calculate the control limits and draw control lines on the chart. The purpose of these lines is to show when we should suspect that something has changed which affects the process (in other words, a special cause of variation has occurred).

We calculate the control limits from a section of the data. Of course we know that the launcher has been moved and moving the launcher is a special cause of variation, so we should calculate the limits with results which come after the launcher move. For now, we will not worry about how the calculations are made.

All the results after moving the launcher are within the control limits, so the process is probably stable or “in statistical control”. This means that all the variation comes from common causes. Common cause variation is just the normal random variation which is inherent in the process.

If we want to be in full control of a process we must use the charts to identify when special cause variation occurs, determine if things were better before or after the change, then make one of these situations permanent.

Let’s carry on producing. We fire off another 100 shots.

Look at the control chart. All we need to know now is whether there has been any change in the process since the lines were calculated. Is the output stable?
Look to see if any of the points are outside the control limits. It looks as if something unusual happened around subgroup 40 (launcher shot 200). Subgroup average drops below the control line so a special cause of variation has occurred. As an operator, your job is to produce results as close as possible to 500 but the average landing position has suddenly changed.

You could, of course re-centre the process (move the launcher). This might help in the short term, but you have no idea whether things might suddenly change back to normal. The only really satisfactory solution is to carry out an investigation, find the source of the special cause of variation, learn from what happened, then make sure that this kind of change does not occur again.

A word now about specification or tolerance limits. In most industrial processes, the operator is given specification or tolerance limits as well as the target value. However, these specification limits should always be looked on as representing the MINIMUM acceptable quality from the process. World class quality does not come from treating everything within the specification limits as equally acceptable. We must try to produce as close as we can to the target value. This is what the customer really wants.

In our bouncing ball process, an unknown special cause of variation made the subgroup average fall at around subgroup 40 (shot 200). It might be that the individual results are still within the specified tolerance limits, but our customer would prefer the results to be 500. So we must make efforts to produce with the average output at 500 and the minimum variation that our process is capable of. So we must investigate and remove special causes of variation even if we are still producing within the specification or tolerance limits.

When we did the investigations we found out that one batch of balls has slightly less bounce than normal. We discard this batch and demand from our supplier that they supply us with statistically stable product (they can only be sure of doing this by using control charts).

We have removed this special cause of variation so things should return to normal from shot 256. We fire off another 50 shots.

The control chart should show clearly that a change occurred around subgroup 40 and things returned to normal around subgroup 53.

Now we will look at how the control limits were calculated.

The mathematics are not difficult. You need to find the average Xbar (average subgroup average) and the average range for the section of the data that you use to calculate the limits. You also need to look up a table to find constants called “A2” “D3” and “D4” for the subgroup size that you are using.
By distinguishing between special cause variation and common cause variation, control charts can help operators and managers to run processes which produce on-target with minimum variation.

If special cause variation is present, we must find the root cause and stop this from occurring again in the future. We ask the questions:

“What happened at approximately that point to change the results?” and “How can we prevent this from happening again?”

If no special causes are present and we want to get better results, we ask different questions:
“Looking at all the results, is the average off-target?” and “Looking at all the results, why is there so much variation?”

To reduce common cause variation we might need better machinery, more frequent maintenance or less common cause variation within raw materials.

Summary Lesson 2:

  1. When we are given a target or ideal value for something, we should always try to get results with the Average on target and with the minimum amount of variation. We should not just try to get results within the specification limits.
  2. Control charts can help to distinguish between common cause variation and special cause variation.
  3. A good type of control chart for variables is the Xbar and Range chart. Xbar and Range charts use data arranged into small subgroups.
  4. It is not enough just to react to special causes of variation by adjusting the process to compensate. World class quality comes from removing the special causes of variation and preventing them from returning. Because this often requires management action, SPC will only work properly when managers understand the role they have to play in creating stability and reducing variation.