# Intro to Measurement System Analysis (MSA) of Continuous Data – Part 2: Bias

Measurement System Bias

Tags:
1. This is the second in a series of articles about MSA. The focus of this article will be on measurement bias, sometimes referred to as accuracy.

Bias is the difference between the actual value of a part and the average measured value of that part. In other words, a measurement device that has bias will consistently over or under state the true value of the part.

In most cases, a separate study of measurement bias is not performed if the measurement device has been calibrated. The reason for this is simple. Calibration is intended to detect and correct any measurement bias found. As I stated in Part 1, calibration and measurement uncertainty are outside of the scope of this series and is better left to experts in those fields. However, I will state that all calibration programs are not created equal. Some less equal calibration programs may take a single measurement of a standard and then make a determination on whether there is measureable bias in the gage. This overlooks the fact that taking a second or third measurement could provide different results than found in the first measurement. There are also other less obvious sources of bias from which a calibration system, no matter how well designed and implemented, will not protect you.

I will go through a few examples of bias that you could encounter:

• Measurement device bias – As we discussed in Part 1, all measurements vary to some extent. if the device has sufficient resolution to see it. The failure mode of a weak calibration system is to base the calibration on a single measurement. The solution is to take multiple measurements of the standard and compare the average of these measurements to the standard before making a determination of the magnitude of the bias and making an adjustment. Even better, a 1-sample t-Test may be used to determine the statistical significance of the bias provided the required sample size is established in advance using the maximum allowable bias and desired alpha and beta risks.
• Temperature bias – Many products will change size with changes in temperature. The magnitude of this change in size may or may not add significant bias depending on the materials involved. What may be less commonly known is that the measurement device will also change size with temperature. How often does the appraiser carry the measurement device in a pocket or in their hand warming it up to body temperature? Temperature not only affects mechanical dimensions, but also electrical. Resistance changes with temperature affecting many electrical measurements. An extremely important aspect of calibration performed by internal lab is normalizing both the standard and the gage at standard temperatures before calibration.
• Humidity bias – Certain materials will swell or shrink with changes in moisture content. Critical measurements should be made at standard humidity conditions after a lengthy normalization time.
• Pressure bias – Materials that are compressible such as rubber or foam are notoriously difficult to measure due to the deformation of the part under pressure. But did you realize that the steel shaft diameter that you are measuring may also be understated depending on whether you used the ratchet thimble on the micrometer or not?
• Cosine error bias – Not just for CMMs! Test indicators, less commonly used these days, are also susceptible to cosine error. Did you realize that the ball on the tip of a CMM probe can introduce potential bias? All touches made with the tip must be made perpendicular to the surface of the part. When this is not done the diameter of the sphere will introduce what is called cosine error. The larger the sphere used, the larger the cosine error.
• Measurement procedure bias – Your measurement procedure can also introduce bias. How do you measure the diameter of a shaft (randomly, max, min, average of max-min, using CMM)? What about the location on the shaft (middle, end, multiple locations)? The effect of this bias depends on the application of the part. Does the shaft need to slip into a hole? The average diameter reported by a CMM will understate the effective diameter of the shaft. It may measure in specification and not fit into a ring gage.