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There seems to be a lot of confusion, or just colloquially poor usage, of the terms precision, repeatability, and accuracy in the CNC world.  It causes a lot of issues because people often use the terms incorrectly and it causes miscommunication or misunderstandings in conversations.  The simplest answer is that...

Precision + Repeatability = Accuracy

Lets take a minute to review the definition of each term, then we'll go over some examples.

• Precision: Precision of a numerical quantity is a measure of the detail in which the quantity is expressed.  The precision of a value describes the number of digits that are used to express that value. In a scientific setting this would be the total number of digits (sometimes called the significant figures or significant digits).  To a CNC user, this is essentially the smallest movement the machine can make (e.g. a machine that moves 10,000 steps per inch is more precise than one that only moves 1,000 steps per inch).
• Repeatability: Repeatability is the variation in measurements taken by a single person or instrument on the same item and under the same conditions. A measurement may be said to be repeatable when this variation is smaller than some agreed limit. A good synonym to repeatability would be consistency.  To a CNC user, this is essentially the difference in the size of multiple parts cut from the same exact CAD/CAM file (e.g. if repeatability is good, cutting the same part multiple times will yield parts that are extremely close to the same size.)
• Accuracy: The accuracy of a measurement system is the degree of closeness of measurements of a quantity to its actual (true) value.  Accuracy is the combination of precision and repeatability.  To a CNC user, this is essentially the ability to consistently produce parts that are the expected size they were designed to be (e.g. if you cut a file for a 1' part five times, you get five identical parts that are 1' long).

Let's talk about a couple examples that are not correct, and why.  If you cut parts on a machine that is precise, but not repeatable or accurate, you may get parts that do not fit together well because something may have shifted and one side is longer than the other.  If you cut parts on a machine that is repeatable, but not precise or accurate, you may get parts that fit together well but the finished product is the wrong size because they are all 10% smaller than they should be.

To understand better, lets use the analogy of a marksman shooting a gun.

When the marksman is just learning to shoot, he is neither repeatable nor accurate.  He shoots bullets that are all over the target, almost at random.  He is not consistent, and may do things like pull the trigger with different force each shot, or not line the sights up the same way each time.  The gun has the same precision the whole time.

Low Repeatability, Low Accuracy

As the marksman improves his repeatability, and shoots the gun the same exact way every time, the bullet holes get closer and closer together.  This reveals the precision of the gun.  No matter what the marksman does, the precision of the gun will limit how close together he can get the bullet holes (e.g. even if he clamped it in a vice).

High Precision, High Repeatability, Low Accuracy

Now that our marksman is a "good shot", with high repeatability, using his high precision rifle, we still have one more step before we can combine the two to get high accuracy.  The marksman must adjust his sights.  He now knows that he is very consistently missing the target by nearly the same amount (e.g. low and left).  He adjusts his sights to get the benefit of his precision rifle and consistent shooting.

High Precision, High Repeatability, High Accuracy

Our shooter has now attained the high accuracy he desired.

When trying to increase the accuracy of your CNC machine, it is important to understand what factors actually affect which portions of the accuracy equation.  Many people mistakenly try to fix their machine's issues by compensating for the wrong problems, which are often not problems at all.

• Precision: Some things that affect precision, which are things that limit the ability of the machine to make the right sized cut, are...
  • Runout of the router and collet
  • The bit's true diameter being slightly different than the size used to computer CAM toolpaths (e.g. 0.247" vs 0.250")
  • Settings for steps/microsteps on the motor drivers
  • Mechanical ratios in the drive systems (e.g. drive ratio of a sprocket, pulley, screw, or pinion)
  • Wear on, or loose fitting, drive components (e.g. backlash in a lead screw nut)
• Repeatability: Some things that affect repeatability, which are things that cause the machine to cut the same part multiple times at different sizes, or things that keep the machine from moving away and back to the same point multiple times or at different places on the table, are...
  • Loose mechanical linkages (e.g. a shaft coupler or sprocket that is slipping).  This is one of the most common issues!
  • Parts of the drive system that change at different points on the table (e.g. sag in chains that changes while the gantry is in different places)
  • Harmonics in the drive system (e.g. lead screw whip or chain bounce)
  • Expansion/contraction of components (e.g. the table warps as the temperature changes)
  • Losing steps (e.g. running the machine faster than the bit can cut, and it gets pushed back out of place)
• Accuracy: Some things that affect accuracy, which are things that keep the machine from making the proper sized parts consistently, are...
  • Wear on, or change in, drive components (e.g. a chain that stretches over time)
  • Need to calibrate machine (e.g. calibrate steps per inch over the length of the table)
  • Software offsets (e.g. working offsets)
  • Inaccurate zeroing of the machine
  • Software scaling (e.g. a 120% scale increase set in software)
  • Incorrect units used (e.g. cm vs. in)
  • Bad math used to calculate machine's steps per inch settings

This is certainly not an exhaustive list, but should give you some good ideas about where to look for problems.  If you have some more suggestions, leave a comment and I'll add them for everyone to see.

We've examined how precision and repeatability lead to accuracy, and how to use each term correctly.  Simply put, "Accuracy is the result of precision and repeatability, combined correctly."  We also explored some of the root causes of each problem, and how to troubleshoot issues in each area.  Hopefully this will help both new and experienced users understand the terms, and the issues they cause, better.