# Rule of Tens/Ten to 1 Rule in Measurement and Inspection

I'm trying to clarify my understanding about the requirements [read: best practices] for measurement resolution and measurement confidence.

The "Rule of 10s" is a commonly tossed around guideline for measurement resolution that, to the best of my understanding and searching, suggests the following:

• That your measurement systems should be able to resolve to a level of 10% of your total tolerance.

However, regardless of whether you consider "tolerance" to refer to the product or process tolerance, there still seems to be some confusion among those I've talked with.

As an example, take the following dimension:

125mm +/- 10mm

In this case, the total tolerance range is 20mm. Ten percent of 20mm would be 2mm. Therefore your measurement system should be able to resolve down to a 2mm level which would get you roughly 10 distinct "categories" into which your results fall.

An alternate theory that I've come across however, is:

• That the measurement resolution should be "ten times greater than your specification/tolerance as written.
• This is the "move the decimal place" approach and is more a "significant figures" discussion.

Taking the same previous example where the tolerance is +/- 10mm, increasing the resolution 10X would imply that measurements should be obtained at the 1mm level.

I don't believe this latter approach is the intent of the "10 to 1" rule, but I'm looking for some general consensus.

To complicate this question slightly, consider a scenario with an engineering drawing which defines a length as follows:

468.2mm +/- 6.48mm

(THIS is where the team arguments begin.)

The total tolerance is 12.96mm (6.48mm x 2), of which 10% would be 1.296mm. Being a good inspector, and dropping the decimal places to utilize a 1mm resolution measurement method, this still seems to be contradictory to the intent of the dimension.

Where the dimension or tolerance is specified out to multiple decimal places, should the "move the decimal place" method be invoked? If a dimension is specified out two decimal places, it would only make sense to be able to resolve it to 3 decimals.

Appreciate anyone who takes the time to read through this and give your thoughts!

• The measurement uncertainty of a measuring device is 1/2 the tick marks. Period. Rules of thumb are as objective as the range of variations that we find in the size of thumbs in a crowd of people. – Jeffrey J Weimer Sep 20 '18 at 13:49

Remember that a rule of thumb is just that, a rule of thumb. It is not a hard specification, so in some sense there really is no right answer here. It is a good starting point, but to determine what is acceptable for your system you need to balance three things

1) What is the cost of a false positive? i.e. what is the consequence if a perfectly acceptable +9 mm part is flagged as +11 mm and thrown away? Does that cost you 2 cents or a million dollars?

2) What is the consequence of a missed negative? i.e. what is the consequence if an unacceptable +11 mm part is marked as acceptable? Does it cost you 2 cents or a million dollars?

3) What is the cost of various levels of resolution?

For example, if missed negatives are costing your company \$1,000 per year, and upgrading from 2 mm resolution to 1 mm resolution costs$1 million, well then just stick with 2 mm.

If, on the other hand, if missed negatives are costing you a million dollars per year, and and upgrading resolution only costs $10,000 then you should upgrade as quick as you can. Correct. The rule of thumb is multiply your tolerance range by 10% (or divide by 10) to get the minumum resolution of your measuring device. Regarding the 12.96 tolerance range because more precision is applied to the dimension, two decimal places, or .01mm precision, you need a measuring device 10x that precision to be accurate. So a device with .001mm precision would be correct. Now, my opinion on the +-6.48 tolerance is that it lacks consideration for design for manufacturing and inspection. • @JeffreyJWeimer A ruler with 1/10 mm graduations is impractical. It may be used on an optical comparator, but now you are using those graduations at a magnified level which would yield more accuracy. That said, in the context of measuring a physical dimension there are several other precision devices which are much more accurate than a ruler. – GisMofx Sep 20 '18 at 13:58 • @JeffreyJWeimer We are getting off topic. I’m not disagreeing with you and I’m well aware of the difference between accuracy and precision. If you have an alternative answer, please submit it. Rule of 10 is a real concept in metrology, but not a hard and fast rule. – GisMofx Sep 20 '18 at 15:54 • Done. Removed my comments to post in an answer instead. – Jeffrey J Weimer Sep 20 '18 at 16:30 The best metric of confidence in making measurements is the overall relative uncertainty of the measurement. Two factors contribute to uncertainty for a measuring device. One is the calibration uncertainty. This is an offset or bias. The other is the device or scale uncertainty (precision). Consider a force-gauge with a spring. The spring constant depends on temperature. Readings taken at different temperatures will be different. This is an example of a calibration uncertainty. Device uncertainties are$\pm$half the tick mark spacings whether the ruler is a millimeter ruler (where such markings are impractical) or a football field marked in 10 yard increments (where the best we can then reliable measure is$\pm$5 yards). By example, consider a perfect 1 m beam. A ruler that expands$\pm 100$microns over the temperature range of measurements will have a relative calibration uncertainty of$100/10^6$= 100 ppm. A ruler that is marked in millimeters will have a relative scale uncertainty of$0.5/10^3\$ = 0.05%.

The "Rule of 10ths" is subjective. It is never to be used to define a consistent statement about the precision of a measurement. When you need a component to have a specific size at a specific tolerance level, use a measuring device that has at least that relative uncertainty or better.

ACCURACY and PRECISION are two different terms. The former is not defined by the measurement device, the latter is.