An Investigation of Measurement Uncertainty of Coordinate Measuring Machines (CMMs) by Comparative Analysis

An Investigation of Measurement Uncertainty of Coordinate Measuring Machines (CMMs) by Comparative Analysis

By Jayson Minix, Hans Chapman, Nilesh Joshi, and Ahmad Zargari


Measurement uncertainty is one of the root causes of waste due to variation in industrial manufacturing. This article establishes the impact of certain factors on measurement uncertainty while using coordinate measurement machines as well as its reduction through the usage of recognized Gage R&R methodology to include ANOVA. Measurement uncertainty stemming from equipment and appraiser variation is identified and ranked according to its degree of impact. A comparative analysis is conducted showing how different CMMs of similar design can generate differing amounts of measurement uncertainty. The approach set forth in this paper not only proves effective with CMMs but can also be applied to other complex multivariate measurement systems.

Keywords: coordinate measuring machine, gage repeatability & reproducibility, equipment variation, appraiser variation, measurement system analysis, measurement uncertainty.


Measurement error is one of the root causes of variation, or waste, in any manufacturing process. As such, all measurement errors must be properly identi ed and understood in order to determine the quality of a manufacturing process. This task is accomplished by performing a Measurement System Analysis (MSA) on each measurement system in a given manufacturing process. Perhaps the most well known type of MSA performed is a Gage Repeatability & Reproducibility (R&R) Study.

Gage Repeatability is primarily the variation observed in the measurement gage itself and is often considered to be the equipment variation. Gage Reproducibility is variation introduced into the measurement system when a variable is changed, that is, a different operator using the same gage. The repeatability and reproducibility combined are what determines the total “measurement error,” or “noise” in a given measurement system. This noise is the source of measurement uncertainty in the measurement data ( Kappele, 2005 ).

Typically, a measurement system is considered capable if it has a low amount of uncertainty. Ideally, this is determined by less than 1% noise and a total Gage R&R of less than 10%. The total percentage of Gage R&R is a combination of both the measurement uncertainty as well as part-to-part variation. Systems having more than 10% noise or a combined Gage R&R of more than 30% are considered unacceptable, and every effort should be made to improve the measurement system ( MSA Workgroup, 2010 ).

The three most recognized methods of Gage R&R as set forth in the Measurement Systems Analysis Reference Manual are the Range Method, the Average & Range Method, and the Analysis of Variance (ANOVA) Method. The Measurement Systems Analysis Reference Manual is a publication put together by the Automotive Industry Action Group (AIAG) and  serves as a reference for Gage R&R methodology that has been sanctioned by the Chrysler Group LLC, Ford Motor Company, and General Motors Corporation Supplier Quality Requirements Task Force ( MSA Workgroup, 2010 ).

Coordinate measuring machines are a common measurement device used to secure measurements of high accuracy across various industries. They range in type from table-top bridge-type machines with touch type probes to much more advanced technology using hand-held devices and optical laser type probes. Rather than technically measuring component parts in the traditional sense, CMMs obtain discrete points or hits on a three-dimensional Cartesian plane and generate measurement data through algorithmic mathematical computation.

A number of researchers have made significant progress toward developing methodologies aimed at estimating measurement uncertainty that results in coordinate measurements, particularly using contact-mode probes. Yet, considerable research remains to be performed to fully account for measurement uncertainty and to improve their estimation. For example, techniques to model and estimate task specific uncertainty for contact-probe coordinate measuring machines were developed by Wilhelm et al., ( 2001 ), who reported that for any task specific uncertainty method to gain universal acceptance, standardized inputs would be highly desirable, if not a requirement. In their investigation of measurement uncertainty estimation of CMMs in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM), Fang and Sung ( 2005 ) noted that measurement uncertainties mainly come from the calibration of the CMM and temperature. For a measurement range of 0mm to 400 mm, they estimated an expanded uncertainty of 3.4 µm with a coverage factor of 1.98 at a 95% confidence interval. Their further analysis showed that the measurement uncertainty can be reduced by using a high precision instrument, such as laser interferometer.

The principal factors that impact measurement uncertainty have been studied extensively. Barini et al. ( 2010 ) investigated the source and effects of differing uncertainty contributors by point-by-point sampling of complex surface measurements using tactile CMMs. By carrying out a four-factor (machine, probe, operator, and procedure), two-level randomized factorial experiment and choosing adequate process parameter settings, a subsequent decrease of the measurement uncertainty from 34 µm to 8 µm was observed.

Other researchers have used other approaches. In their work, Phillips et al. ( 2010 ) utilized a computer simulation software approach to investigate the validation of CMM measurement uncertainty. All the measurement errors found in the physical measurements were well inside their corresponding uncertainty intervals. From their investigation, Phillips et al. suggested a well-documented list of reference value tests as a useful tool to employ before starting the more expensive aspect of real physical measurements of calibrated parts.


Data for this study was collected using two separate CMMs; the first is located in the CMM Laboratory of the School of Engineering and Information Systems, Morehead State University and the second from a CMM Lab located in a Tier 1 Original Equipment Manufacturer (OEM) facility. Both machines were similar in design, utilizing a bridge type table design with Direct Computer Control (DCC) capability.

The primary differences of the two machines were that they are manufactured by different companies and each functions with a different operating software. The machine used in the university laboratory was manufactured by Brown & Sharpe and is operated by PC•DMIS 2014 software; while the second machine was manufactured by the Zeiss company and operated by Calypso 4.8 software.

As many controls as possible were maintained during the study to ensure a quality comparative analysis between the two machines. For example, the same participants were used to collect measurement data on each of the CMMs. Additionally, all data were collected by measuring the same three sample parts with each machine. The DCC mode was utilized on each machine in lieu of a third operator to provide baseline data.


The overall methodology of this research is based on the American Automotive Industry standard requirement for Gauge R&R studies. One of the challenges faced by quality professionals who supply products to customers in the American Automotive Industry (AAI) is not only complying with an extensive list of customer specific requirements, but also complying with those requirements in the specific manner prescribed by the customer as well. An especially good example of this challenge is encountered when attempting to comply with customer requirements pertaining to MSAs and the documentation of the measurement variation present with each gage used to release product to the customer.

While the core tools reference manuals contain good practices and methods this is not the same as being “best” method across the board in every instance. As the name implies these manuals were originally created as “reference” guides, but over the years the AAI requirements have evolved to the point that these guides have changed from references to requirements for the entire automotive supply chain. This phenomenon in and of itself poses its own set of unique obstacles and challenges to those in the field of quality due to the fact that “not all measurements systems are created alike.” The result is a tendency to analyze a measurement system through the lens of the required method for the purpose of compliance to the requirement, rather than analyzing a measurement system with the intent of truly understanding the capability and uncertainty of the system itself.

Rationale of the Four Factors Selected for Analysis

Dimensional type:

The three separate dimensional measurement types selected are referred to in the CMM operator’s manual as ‘geometric features’. They were selected due to the way a CMM generates three-dimensional measurements differently than two-dimensional measurements. When three-dimensional objects are measured, probe radius compensation is made perpendicular to the surface of the object as opposed to the active work plane used in two-dimensional objects.

Operation type:

The decision between a manually operated CMM versus a DCC type is typically determined by the type of operation in a given organization. Most production-oriented environments choose a DCC type, while companies specializing in prototype development and reverse engineering are more likely to prefer a manual CMM ( Meredith, 1999 ). However this does not mean to imply that a CMM with DCC capability is always being utilized in DCC mode. DCC CMMs can still be operated in manual mode.

Set-up type:

The two different CMM setup types that are under investigation are those of manual setup and CAD setup. Both setup types are directly linked to a DCC operation type. The integration of advanced CAD inspection programs has provided yet another layer of part inspection versatility to the realm of metrology. Through the usage of CAD enhanced CMM software, it is now possible to graphically test and debug inspection routines before executing a new part program with the CMM ( PC•DMIS, 2014 ).