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Quick reference
Control Limits
Control limits are the limits of normal common cause variation. Control limits are calculated based upon the data set descriptive statistics. Control limits provide indication of special cause variation.
When to use
Control Limits are part of an SPC control chart. If creating a control chart you must calculate control limits. If managing or monitoring a process using a SPC control chart, you must use the control limits to watch for special cause variation.
Instructions
Control limits are an integral part of an SPC control chart. They show the boundaries of normal common cause variation. They are calculated using a combination of descriptive statistics from the data set and constants and formulas that are unique to each type of control chart. A control chart has both an upper control limit and a lower control limit, although on some control charts the lower limit is automatically set at zero and does not change. Generally, the control limits are set near the plus or minus three standard deviation value for the data set.
A good rule of thumb is to not start calculating control limits until you have at least 30 data points. The control limits calculated from fewer points will likely be close, but they don’t become fully stable until approximately that number of points are included.
There are a number of rules that are used for identifying the presence of special cause variation. These rules are similar to those used for the “Run Chart.” However, the values are different. That is because of the statistical nature of the control chart and the inclusion of control limits, which are not calculated for Run Charts.
- Data points that are above the upper control limit or below the lower control limit. These are extreme or astronomical points.
- Nine consecutive data points above or below the mean. This indicates a shift in the mean of the data set.
- Six consecutive data points that are either all increasing or all decreasing. These indicate a trend in the data.
- Fourteen consecutive data points that reverse direction – being up then down as compared to the preceding point. This is a sawtooth pattern and is similar to the “runs” rule used in the Run Chart.
When manually generating the control charts, you will need to apply the rules after each data point is included to see if they have been violated. These rules can be easily set or modified within Minitab. Minitab will then monitor the data and indicate a rule violation by turning the color of the point to red.
Hints & tips
- Be sure to recalculate the control limits after making a process change or removing the root cause of a special cause variation.
- There are alternate schools of thought that usually slightly different levels for the special cause rules. If your organization uses different values (for instance using just eight data points for the “shift” rule instead of nine), modify the level in Minitab. Follow local practice.
- The specific calculation of control limits will be addressed in the module on each of the different types of control charts.
- 00:05 Hi, I'm Ray Sheen.
- 00:06 A critical component of SPC control charts are the control limits.
- 00:11 Let's take a few minutes and explore these.
- 00:13 I'll start with a discussion about how we determine control limits and
- 00:18 then we can move on to how we use them.
- 00:20 As we've said several times,
- 00:22 the control limits are a guide to how we can expect the stable process to perform.
- 00:27 In particular, they are statistically derived limits of common cause variation
- 00:31 occurring within the process.
- 00:33 Control charts have two control limits, an upper and a lower limit.
- 00:37 However, within some types of control charts, the lower limit is always set
- 00:41 zero, because the data can never be less than zero.
- 00:44 In those cases, although there's technically a lower limit,
- 00:47 practically there's only an upper control limit to worry about.
- 00:51 The actual calculation of the control limits varies depending
- 00:54 upon the type of control chart in the data.
- 00:57 In the next section of this course, we'll review eight different types of
- 00:59 control charts and discuss how the control limits are calculated for each.
- 01:04 In all cases they use a combination of descriptive statistics, such as mean,
- 01:08 median and standard deviation, along with some statistically derived constants and
- 01:13 formulas.
- 01:14 I'll give you the constant and the formulas but
- 01:16 the derivation of those are beyond what we can do in this course.
- 01:20 In most cases, you'll find the control limits are close to the three standard
- 01:23 deviation point for each data set.
- 01:26 But keep in mind that when developed this that was his target
- 01:30 of acceptable performance.
- 01:32 In a few cases,
- 01:33 the lower control limit will be bounded by physical impossibilities.
- 01:37 Again, we'll discuss this when we get to those applicable control charts.
- 01:41 Now a great question to ask,
- 01:42 is how many data points do I need before I can calculate my control limits?
- 01:46 That is a good question.
- 01:47 And if you read the literature, you will hear a variety of different values.
- 01:52 So I decided to just see for
- 01:53 myself how the number of data points affected the control limits.
- 01:57 I did a study using the simplest of the control charts, the C Chart.
- 02:01 In this study I collected 500 data points and then I started to calculate the mean
- 02:05 and the control limits of various sizes of a data set.
- 02:09 I compared the calculator values to the value that I had when I included all
- 02:13 500 data points in the set, to see how close they were to those limits.
- 02:17 You can see my results in this table.
- 02:20 I started the calculation with just five data points,
- 02:23 because the formula would work with data sets that were that small.
- 02:26 And you can see, even with the small data sets such as 5,10, or 15,
- 02:31 the values were not very far from the 500 data point base line values.
- 02:36 The mean was different by less than 2% and it was spread between the upper limit and
- 02:39 lower control limits was less than 1%.
- 02:43 By the time I had 30 data points in my data set, the differences were very small
- 02:48 and remained roughly the same for the rest of the data set size.
- 02:51 So I would say you are definitely safe with 30 data points and
- 02:55 even less than that, should not be too bad for most control charts.
- 02:59 I would recommend that you always recalculate your control limits
- 03:02 after a process change.
- 03:04 The new process will likely have different common cause variation effects.
- 03:08 And also, recalculate your control limits after the removal of a special cause.
- 03:13 Special causes can affect both the mean and the standard deviation.
- 03:16 So there won't be an impact on the control limits.
- 03:19 Once they are gone, the impact needs to be removed.
- 03:22 Let's look at some of the rules for identifying special cause variation.
- 03:26 Most of these will be based upon the control limits and the mean.
- 03:30 I do want to highlight that these rules are different than the rules that we used
- 03:33 with the run chart.
- 03:35 Those of you who are taking one of the Lean Six Sigma belt courses,
- 03:38 will recall that we discussed the run chart already.
- 03:41 It too is a sequential plot of processed data.
- 03:44 But it does not include control limits.
- 03:46 The first rule is the easiest.
- 03:48 An extreme point that is beyond control limits.
- 03:51 This is often called an astronomical point.
- 03:54 The second rule is nine consecutive data points above or below the mean.
- 03:59 These indicate a shift in the process performance due to a special cause and
- 04:03 it needs to be investigated to determine if it is a permanent shift or
- 04:06 a temporary shift.
- 04:08 The third rule is six consecutive data points that are either increasing or
- 04:12 decreasing.
- 04:13 The data may have a start on one side of the mean and end on the other.
- 04:17 That doesn't matter.
- 04:18 It still indicates a trend in the data.
- 04:20 Again, it is a special cause that needs to be investigated.
- 04:24 The final rule is 14 consecutive data points that alternate up and down.
- 04:28 This is similar to the run calculation that was done with the run chart.
- 04:32 A violation of any of these rules is an indication
- 04:35 that a special cause is present, so investigate it.
- 04:40 Now if you're plotting these control charts by hand or doing it with Excel,
- 04:44 you will need to apply these rules every time you add a data point.
- 04:48 If using Minitab, it will you do the thinking for you.
- 04:51 If you're using Minitab you can just turn the rule on and
- 04:54 Minitab automatically identify any data point that violates the rule and
- 04:58 change the color of that data point to red on the chart.
- 05:02 And you can turn these rules on or even modify them if you want to,
- 05:05 by going to the Tools menu and selecting Options.
- 05:09 Then selecting Control Charts and Quality Tools.
- 05:12 Finally, selecting Tests.
- 05:14 That would bring up the panel you see on this slide.
- 05:17 Now just check which rules you want to include and if you want,
- 05:21 you can change the limits.
- 05:23 The control limits on an SPC control chart
- 05:26 show us the expected level of common cause variation.
- 05:30 And of course that's why they're so helpful for
- 05:33 determining when we have special cause variation.
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