What is the Rule of Tens?

The Rule of Tens is a great tool for checking if the resolution of your measurement system is acceptable. It’s simple, quick, and does not require any advanced statistical knowledge.

What is Resolution?

Resolution can be thought of as the smallest unit that a measurement system can detect. When you look at a data set, the resolution of the measurement system (that created it) is often clear. For example, here are the results of the mens 100 Metres Final at the Beijing Olympics in 2008:

1 Usain Bolt 9.69
2 Richard Thompson 9.89
3 Walter Dix 9.91
4 Churandy Martina 9.93
5 Asafa Powell 9.95
6 Michael Frater 9.97
7 Marc Burns 10.01
8 Darvis Patton 10.03

From these results, it appears that the resolution of this measurement system is 1/100th of a second (0.01). This doesn’t mean that the precision or accuracy of the measurement system is 0.01, it just reflects the smallest unit that the measurement system can (in theory) measure – its resolution!

So, why do you need to check resolution?

If your measurement system does not have sufficient (small enough) resolution, then it is very unlikely to have an acceptable level of precision (GR&R). In other words, its unlikely to be ‘fit for purpose’. So, it is worthwhile checking your resolution first (using the Rule of Tens) before spending time and money completing a full GR&R exercise.

How does the Rule of Tens work?

The Rule of Tens says that the resolution of your measurement system should fit at least ten times into the process variation that you are measuring, as shown on the right.

So, lets look again at the 100 Metres Final results from above. In this case, the measurement system passes the Rule of Tens as follows:

• The Resolution is 0.01 seconds
• The process variation (the difference between the fastest and slowest runners) is 0.34 seconds.
• So, the resolution is 1/34th of the variation between the runners, which is acceptable (from a process measurement perspective).
• In a real life Six Sigma project, you would then continue to check that the Precision and Accuracy of the measurement system are also acceptable.

If the resolution is more than 1/10th of the process variation, then the resolution should be improved before Precision or Accuracy are checked.

More information on the Rule of Tens can be found on page 61 of the Lean Six Sigma and Minitab book.