# Accelerometer Calibration Proficiency Testing

## The Importance of Interlaboratory Comparisons

In past articles, we’ve discussed various contributors to the overall measurement uncertainty of a calibration system. At the end of the uncertainty analysis, it is desirable to test our conclusions to uncover potential errors or oversights and to also learn where improvements can be made. This brings us to the topic of proficiency testing. (Sometimes this is also called: round-robin testing or inter-laboratory comparison.)

Proficiency testing is a comparison between two or more laboratories to check for correlation of results. In accelerometer calibration, this is done by multiple laboratories calibrating the same accelerometer and comparing the results. This can be organized by individual labs which are known to each other or by a third party, such as the system manufacturer, where all participants would remain anonymous. In either case, a sensor with stable sensitivity should be used to minimize effects the sensor has on the study. An accelerometer with quartz design is the ideal material for the sensing element because of its superior long-term stability.

In order to compare the results of two labs, the deviation between the two measured calibration values is divided by the root-sum-squared of the two labs' stated uncertainties.  This provides a number (typically less than 1.0) which is used as an objective method to determine if two labs have statistically “acceptable” results. The calculated value is called the “Normalized Error” - En  (spoken as “E-sub-n”). By convention, if the En value is less than one, the results are considered within acceptable ranges. Skilled calibration laboratories begin investigating practice and uncertainties anytime the normalized error is at 0.8 or above.  Values greater than one are not acceptable and the labs investigating their practice and calculations to find the source of the measurement error.

Most commonly this is done by expanding the proficiency test pool to include additional sensors and another 1 or 2 reputable laboratories to determine the outlying data.  After review of the data, practices and uncertainty calculations of the set, the most common sources of error are reviewed first.  If the unacceptable deviation is occurring at high frequencies then examine the mounting conditions.  Surface flatness, mounting studs, threads and coupling grease can all affect the high frequency response of an accelerometer.  If the deviation occurs at low frequencies, cable force is most often the culprit and can be addressed ensuring the proper grade of cable and by securing the cable with an adequate strain relief loop.   If the deviation is a localized glitch in the sensor frequency response function (either mid or high frequency), then the next culprit is shaker transverse motion.  Flexure based exciters often have lateral resonances in the calibration frequency range of interest which cause transverse input motion in excess of 100% of the primary axis of motion.  Unfortunately, there is no easy cure for excessive transverse motion.  Uncertainties either need to be increased to accommodate measurement errors caused by transverse motion or the shaker needs to be replaced with a calibration grade air bearing exciter.

In addition to evaluating the uncertainty of the measurement uncertainty, the results can also be used to uncover opportunities for improvement in the calibration system itself particularly with contributors that are systemic in nature. If, for example, a proficiency test shows that your lab consistently reported sensitivities that were 1% low compared to other labs, this could indicate that a system component, such as a signal conditioner, is affecting the results and could be improved. As illustrated above, this type of analysis is best done with multiple participating laboratories.

Uncertainty calculation can seem intimidating at first, but they are really just an expression of the understanding of the real world limitations of the measurement equipment/process and acknowledgement that no measurement is perfect.   It's likely that your quality system or your customers require you to be able to knowledgeably and accurately compare and discuss your methods and uncertainties.  If you have questions or would like to discuss the opportunities for inter-laboratory comparisons, contact us here at The Modal Shop and we will be glad to help out.