Diluciones ppm
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Publicado: 19 de julio de 2010
Repeatability and Reproducibility
Copyright © 1999 by Engineered Software, Inc.
Repeatability is the variability of the measurements obtained by one person while measuring the same item repeatedly. This is also known as the inherent precision of the measurement equipment. Consider the probability density functions shown in Figure 1. The density functions were constructed from measurements ofthe thickness of a piece of metal with Gage A and Gage B. The density functions demonstrate that Gage B is more repeatable than Gage A.
Gage B
Gage A
Figure 1. Probability density functions for the thickness of 2 gages. Reproducibility is the variability of the measurement system caused by differences in operator behavior. Mathematically, it is the variability of the average valuesobtained by several operators while measuring the same item. Figure 2 displays the probability density functions of the measurements for three operators. The variability of the individual operators are the same, but because each operator has a different bias, the total variability of the measurement system is higher when three operators are used than when one operator is used. Figure 3 also displays theprobability density functions of the measurements for three operators using the same scale as Figure 2. Notice that there is more difference in the means of the measurements shown in Figure 3 than those shown in Figure 2. The reproducibility of the system shown in Figure 3 is higher than the reproducibility of the system shown in Figure 2.
Figure 2. Reproducibility demonstration.
Figure 3.Reproducibility demonstration. The most commonly used method for computing repeatability and reproducibility is the Range and Average method. The ANOVA method is more accurate, but because of the complex mathematics involved it has been shunned historically. With desktop computers there is no excuse for not using the more accurate ANOVA method.
Range & Average Method
The Range & AverageMethod computes the total measurement system variability, and allows the total measurement system variability to be separated into repeatability, reproducibility, and part variation. The ANOVA method, discussed in the next section, is preferred to the average range method. The ANOVA method quantifies the interaction between repeatability and reproducibility, and is considered to be more accurate thanthe average and range method. To quantify repeatability and reproducibility using average and range method, multiple parts, appraisers, and trials are required. The recommended method is to use 10 parts, 3 appraisers and 2 trials, for a total of 60 measurements. The measurement system repeatability is Repeatability = . 515R d2
1
where R is the average of the ranges for all appraisers andparts, and d2 is found in Appendix A with Z = the number of parts times the number of appraisers, and W = the number of trials. The measurement system reproducibility is
5.15X range Repeatability 2 − Reproducibility = nr d2
2
2
where X range is the average of the difference in the average measurements between the appraiser with the highest average measurements, and the appraiserwith the lowest average measurements, for all appraisers and parts, d2 is found in Appendix A with Z = 1 and W = the number of appraisers, n is the number of parts, and r is the number of trials. The measurement system repeatability and reproducibility is
R& R = Repeatability 2 + Reproducibility 2
The part variability is VP = 515R P . d2
3
4
where Rp is the difference between thelargest average part measurement and the smallest average part measurement, where the average is taken for all appraisers and all trials, and d2 is found in Appendix A with Z = 1 and W = the number of parts. The total variability, measurement system variability and part variation combined is VT = R& R 2 + V P2 5
Example 1 The thickness, in millimeters, of 10 parts have been measured by 3...
Copyright © 1999 by Engineered Software, Inc.
Repeatability is the variability of the measurements obtained by one person while measuring the same item repeatedly. This is also known as the inherent precision of the measurement equipment. Consider the probability density functions shown in Figure 1. The density functions were constructed from measurements ofthe thickness of a piece of metal with Gage A and Gage B. The density functions demonstrate that Gage B is more repeatable than Gage A.
Gage B
Gage A
Figure 1. Probability density functions for the thickness of 2 gages. Reproducibility is the variability of the measurement system caused by differences in operator behavior. Mathematically, it is the variability of the average valuesobtained by several operators while measuring the same item. Figure 2 displays the probability density functions of the measurements for three operators. The variability of the individual operators are the same, but because each operator has a different bias, the total variability of the measurement system is higher when three operators are used than when one operator is used. Figure 3 also displays theprobability density functions of the measurements for three operators using the same scale as Figure 2. Notice that there is more difference in the means of the measurements shown in Figure 3 than those shown in Figure 2. The reproducibility of the system shown in Figure 3 is higher than the reproducibility of the system shown in Figure 2.
Figure 2. Reproducibility demonstration.
Figure 3.Reproducibility demonstration. The most commonly used method for computing repeatability and reproducibility is the Range and Average method. The ANOVA method is more accurate, but because of the complex mathematics involved it has been shunned historically. With desktop computers there is no excuse for not using the more accurate ANOVA method.
Range & Average Method
The Range & AverageMethod computes the total measurement system variability, and allows the total measurement system variability to be separated into repeatability, reproducibility, and part variation. The ANOVA method, discussed in the next section, is preferred to the average range method. The ANOVA method quantifies the interaction between repeatability and reproducibility, and is considered to be more accurate thanthe average and range method. To quantify repeatability and reproducibility using average and range method, multiple parts, appraisers, and trials are required. The recommended method is to use 10 parts, 3 appraisers and 2 trials, for a total of 60 measurements. The measurement system repeatability is Repeatability = . 515R d2
1
where R is the average of the ranges for all appraisers andparts, and d2 is found in Appendix A with Z = the number of parts times the number of appraisers, and W = the number of trials. The measurement system reproducibility is
5.15X range Repeatability 2 − Reproducibility = nr d2
2
2
where X range is the average of the difference in the average measurements between the appraiser with the highest average measurements, and the appraiserwith the lowest average measurements, for all appraisers and parts, d2 is found in Appendix A with Z = 1 and W = the number of appraisers, n is the number of parts, and r is the number of trials. The measurement system repeatability and reproducibility is
R& R = Repeatability 2 + Reproducibility 2
The part variability is VP = 515R P . d2
3
4
where Rp is the difference between thelargest average part measurement and the smallest average part measurement, where the average is taken for all appraisers and all trials, and d2 is found in Appendix A with Z = 1 and W = the number of parts. The total variability, measurement system variability and part variation combined is VT = R& R 2 + V P2 5
Example 1 The thickness, in millimeters, of 10 parts have been measured by 3...
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