Quality Progress - July 2013 - 44

Measure For Measure BY Dilip Shah Into the unknown A guide to estimating Type A measurement uncertainty data For estimation of measurement un- • Actual, statistical analysis of monitored (reproducibility) and within groups certainty,1-4 both Type A and B uncertainty data of environmental conditions (tem- (repeatability) data. It determines this by contributors may need to be considered, perature and relative humidity). looking at the F-critical value (2.86626) depending on the parameter that is being • Long-term drift of equipment that is from the F-distribution table (degrees of estimated. ISO/IEC Guide 99:2007—In- characterized statistically. freedom numerator of three and degrees ternational vocabulary of metrology— When collecting Type A data for analy- of freedom denominator of 36 at 95% con- Basic and general concepts and associ- sis, ensure that the data collected takes fidence interval) and comparing it with the ated terms defines Type A evaluation of into account the instrument resolution. F-calculated value, which is the between measurement uncertainty as: “Evaluation If the instrument reads to a 0.001 resolu- groups mean square (MS)-value divided by of a component of measurement uncer- tion, ensure that the data collected also within groups MS-value (see Online Figure tainty by a statistical analysis of measured reports to a 0.001 resolution. For example, 1 and Online Table 1 on this column’s quantity values obtained under defined a 0.500 reading on display is reported as webpage at www.qualityprogress.com for measurement conditions.”5 0.500. There should not be any premature more on the F-distribution). The MS-value rounding of data. When data get collected is derived by dividing the sum of squares Type A measurement uncertainty data is by automated data acquisition systems, value by degrees of freedom. It also is the by taking a series of measurements and ensure that it is capable of collecting and variance value. calculating its appropriate standard devia- reporting to the appropriate resolution. tion. For example, if you took 10 measure- In most cases, a laboratory has more One of the quickest ways of estimating 7 The decision rules are: 1. If the F-value is less than the ments, as shown in Table 1, its standard than one technician that is capable of F-critical value, then the data are deviation would be calculated by using the making the measurements for that param- considered statistically insignificant. sample standard deviation formula. This is eter. Depending on the availability of the In this case, reproducibility may be also classified as repeatability data in the technician, either one may be assigned ignored if it does not make a significant measurement uncertainty budgets. to the task of making the measurement. One of the reasons ISO/IEC 170256 ac- In that case, it is important to know that crediting bodies require accredited labora- measurements made by either of the tories to estimate Type A contributors to technicians are statistically insignificant their measurement uncertainty budget is (reproducible) or if they are significant, to ensure that the laboratory is capable of the reproducibility of the technicians need making measurements with the equipment to be taken into account and listed as the that they list in their scope of accredita- second Type A uncertainty contributor tion. This validates the competence of the with its degrees of freedom. Calculating standard deviation / Table 1 laboratory and the personnel making the measurements. The repeatability of measurements is usually the minimum requirement for Conducting such a study may require each of the technicians to make 10 or more measurements on a single artifact, as shown in Table 2, and employing appro- a 1 0.997 2 1.002 3 1.008 4 0.995 5 1.009 0.995 listing Type A uncertainty contribution priate statistical analysis. One-way analy- 6 to the measurement uncertainty budget. sis of variance (ANOVA) is one technique 7 1.005 However, any uncertainty contributor that that can be used. ANOVA is available in 8 0.992 is estimated by statistical means should be popular spreadsheets and statistical soft- 9 1.003 listed as Type A data with its appropriate ware packages. It uses the F-distribution 10 1.003 degrees of freedom. Examples include: to determine if there is a statistically significant difference in the between groups standard deviation 0.0058 • Reproducibility. 44 QP • www.qualityprogress.com i=n s= – ∑ ( x – xi ) i=1 n–1 2 http://www.qualityprogress.com http://www.qualityprogress.com

Table of Contents for the Digital Edition of Quality Progress - July 2013

Up Front
LogOn
Expert Answers
Keeping Current
Mr. Pareto Head
Feeling Connected
Take Charge
Full View
Reinventing Excellence
Innovation Imperative
Measure for Measure
Quality in the First Person
Standards Outlook
Career Corner
Statistics Roundtable
ASQ's Continuing Education and Professional Development Directory
QP Toolbox
QP Reviews
One Good Idea

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