Measurement System Analysis - Revision history

Richard House: /* Precision Agreement Study */

2017-08-10T15:34:58Z

Precision Agreement Study

← Older revision		Revision as of 15:34, 10 August 2017
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	::<math>\text{Lower bound}={{F}_{ratio}}/{{f}_{U}}</math>		::<math>\text{Lower bound}={{F}_{ratio}}/{{f}_{U}}</math>

	For this example <math>{f_U}=2.6733</math> and <math>{{f}_{L}}=0.374069</math>. Therefore, the upper bound is 1.5799 and the lower bound is 0.22101. Since the bounds include 1, it means the two gages have the same repeatability. The results from DOE++ are given below.		For this example <math>{f_U}=2.6733</math> and <math>{{f}_{L}}=0.374069</math>. Therefore, the upper bound is 1.5799 and the lower bound is 0.22101. Since the bounds include 1, it means the two gages have the same repeatability. The results from the DOE folio are given below.

	[[Image: Doe15_19.png\|center\|750px\|Gage agreement study results from DOE++\|link=]]		[[Image: Doe15_19.png\|center\|750px\|Gage agreement study results from DOE++\|link=]]

Richard House: /* X-bar and R Charts in Gage R&R */

2017-08-10T15:34:30Z

X-bar and R Charts in Gage R&R

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	==X-bar and R Charts in Gage R&R==		==X-bar and R Charts in Gage R&R==
	X-bar and R charts are often used in gage R&R studies. Although ~~DOE~~++ ~~does~~ not use them to estimate repeatability and reproducibility, they are included in the plot to visually display the data. Along with X-bar and R charts, other plots are also used in DOE++. For example, the following is a run chart for the example of gage R&R study using crossed design.		X-bar and R charts are often used in gage R&R studies. Although Weibull++ DOE folios do not use them to estimate repeatability and reproducibility, they are included in the plot to visually display the data. Along with X-bar and R charts, other plots are also used in DOE folios. For example, the following is a run chart for the example of gage R&R study using crossed design.

	[[Image: Doe15_11.png\|center\|650px\|Run chart for the gage R&R study using crossed design.\|link=]]		[[Image: Doe15_11.png\|center\|650px\|Run chart for the gage R&R study using crossed design.\|link=]]

Richard House: /* Example: Gage R&R Study for Crossed Experiment */

2017-08-10T15:33:32Z

Example: Gage R&R Study for Crossed Experiment

← Older revision		Revision as of 15:33, 10 August 2017
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	<div class="noprint">		<div class="noprint">
	{{Examples Box\|DOE++ Examples\|<p> A variation of the example that demonstrates how to obtain the results using the gage R&R folio is available in the [http://help.synthesisplatform.net/~~doe10~~/gage_r_r_folio__example.htm ~~DOE~~++ Help file].</p>}}		{{Examples Box\|DOE++ Examples\|<p> A variation of the example that demonstrates how to obtain the results using the gage R&R folio is available in the [http://help.synthesisplatform.net/weibull_alta11/gage_r_r_folio__example.htm Weibull++/ALTA Help file].</p>}}
	</div>		</div>

Richard House: /* Gage R&R Study for Crossed Experiments */

2017-08-10T15:29:38Z

Gage R&R Study for Crossed Experiments

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	A model that has only fixed effect factors is called a fixed effect model; a model that has only random effect factors is called a random effect model; a model that has both random and fixed effect factors is called a mixed effect model.		A model that has only fixed effect factors is called a fixed effect model; a model that has only random effect factors is called a random effect model; a model that has both random and fixed effect factors is called a mixed effect model.

	For random and mixed effect models, variance components can be estimated using least squares estimation, maximum likelihood estimation (MLE), and restricted MLE (RMLE) methods. The general calculations for variance components and F test in the ANOVA table are beyond the discussion of this chapter. For detail, readers are referred to [[DOE References\|Searl 1971 and 1997]]. However, when the design is balanced, variance components can be estimated using the regular linear regression method discussed in the general level factorial design chapter [http://reliawiki.org/index.php/General_Full_Factorial_Designs]. ~~DOE~~++ ~~uses~~ this method for balanced designs.		For random and mixed effect models, variance components can be estimated using least squares estimation, maximum likelihood estimation (MLE), and restricted MLE (RMLE) methods. The general calculations for variance components and F test in the ANOVA table are beyond the discussion of this chapter. For detail, readers are referred to [[DOE References\|Searl 1971 and 1997]]. However, when the design is balanced, variance components can be estimated using the regular linear regression method discussed in the general level factorial design chapter [http://reliawiki.org/index.php/General_Full_Factorial_Designs]. Weibull++ DOE folios use this method for balanced designs.

	When a design is balanced, the expected mean squares for each effect in the above random effect model for gage R&R study using crossed design are:		When a design is balanced, the expected mean squares for each effect in the above random effect model for gage R&R study using crossed design are:

Richard House: /* Gage Repeatability and Reproducibility Study */

2017-08-10T15:28:44Z

Gage Repeatability and Reproducibility Study

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	[[Image:doe15_7.png\|center\|600px\|Gage R&R study - nested design.\|link=]]		[[Image:doe15_7.png\|center\|600px\|Gage R&R study - nested design.\|link=]]

	The X-bar and R chart methods and the ANOVA method have been used to provide an estimation of the variance for each variation source in a measurements system. The X-bar and R chart methods cannot calculate the variance of operator by part interaction. In ~~DOE~~++, we use the ANOVA method as discussed by Montgomery and Runger. The ANOVA method is the classical method for estimating variance components in designed experiments. It is more accurate than the X-bar and R chart methods.		The X-bar and R chart methods and the ANOVA method have been used to provide an estimation of the variance for each variation source in a measurements system. The X-bar and R chart methods cannot calculate the variance of operator by part interaction. In Weibull++ DOE folios, we use the ANOVA method as discussed by Montgomery and Runger. The ANOVA method is the classical method for estimating variance components in designed experiments. It is more accurate than the X-bar and R chart methods.

	In order to estimate variance, each part needs to be measured multiple times. For destructive testing, this is impossible. Therefore, some assumptions have to be made. Usually, for destructive testing, we need to assume that all the parts within the same batch are identical enough to claim that they are the same part. Nested design is the first option for destructive testing since each operator measures unique parts. If a part can be measured multiple times by different operators, then you would use crossed design.		In order to estimate variance, each part needs to be measured multiple times. For destructive testing, this is impossible. Therefore, some assumptions have to be made. Usually, for destructive testing, we need to assume that all the parts within the same batch are identical enough to claim that they are the same part. Nested design is the first option for destructive testing since each operator measures unique parts. If a part can be measured multiple times by different operators, then you would use crossed design.

Richard House: /* Precision Agreement Study */

2016-01-07T22:07:22Z

Precision Agreement Study

← Older revision		Revision as of 22:07, 7 January 2016
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	For this example <math>{f_U}=2.6733</math> and <math>{{f}_{L}}=0.374069</math>. Therefore, the upper bound is 1.5799 and the lower bound is 0.22101. Since the bounds include 1, it means the two gages have the same repeatability. The results from DOE++ are given below.		For this example <math>{f_U}=2.6733</math> and <math>{{f}_{L}}=0.374069</math>. Therefore, the upper bound is 1.5799 and the lower bound is 0.22101. Since the bounds include 1, it means the two gages have the same repeatability. The results from DOE++ are given below.

	[[Image: Doe15_19.png\|center\|~~800px~~\|Gage agreement study results from DOE++]]		[[Image: Doe15_19.png\|center\|750px\|Gage agreement study results from DOE++\|link=]]

	=General Guidelines on Measurement System Analysis=		=General Guidelines on Measurement System Analysis=

Richard House: /* Example: Compare the Accuracy of Two Gages Using Linear Regression */

2016-01-07T21:54:00Z

Example: Compare the Accuracy of Two Gages Using Linear Regression

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	The difference vs. mean plot shows a clear linear pattern, although all the points are within the control limits.		The difference vs. mean plot shows a clear linear pattern, although all the points are within the control limits.

	[[Image: Doe15_17.png\|center\|~~600px~~\|Difference vs Mean plot for gage agreement study with a linear trend]]		[[Image: Doe15_17.png\|center\|650px\|Difference vs Mean plot for gage agreement study with a linear trend\|link=]]

	The paired t-test results are:		The paired t-test results are:

Richard House: /* Example: Compare the Accuracy of Two Gages Using a Paired t-Test */

2016-01-07T21:38:14Z

Example: Compare the Accuracy of Two Gages Using a Paired t-Test

← Older revision		Revision as of 21:38, 7 January 2016
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	The difference vs. mean plot is shown next.		The difference vs. mean plot is shown next.

	[[Image: Doe15_16.png\|center\|~~600px~~\|Difference vs Mean plot for gage agreement study]]		[[Image: Doe15_16.png\|center\|650px\|Difference vs Mean plot for gage agreement study\|link=]]

	The above plot shows that all the values are within the control limits (significant level = 0.05) except for one point, and are evenly distributed around the central 0 line.		The above plot shows that all the values are within the control limits (significant level = 0.05) except for one point, and are evenly distributed around the central 0 line.

Richard House: /* X-bar and R Charts in Gage R&R */

2016-01-07T21:18:31Z

X-bar and R Charts in Gage R&R

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	A2 is from the above constant value table. The X-bar chart for this example is:		A2 is from the above constant value table. The X-bar chart for this example is:

	[[Image: Doe15_15.png\|center\|~~600px~~\|X-Bar chart by operator for the crossed design example.]]		[[Image: Doe15_15.png\|center\|650px\|X-Bar chart by operator for the crossed design example.\|link=]]

	When the sample size (the reading of the same part by the same operator) is greater than 10, the more accurate s chart is used to replace the R chart. The calculation for the UCL and LCL in the X-bar chart is also updated using the sample standard deviation s.		When the sample size (the reading of the same part by the same operator) is greater than 10, the more accurate s chart is used to replace the R chart. The calculation for the UCL and LCL in the X-bar chart is also updated using the sample standard deviation s.

Richard House: /* X-bar and R Charts in Gage R&R */

2016-01-07T21:13:53Z

X-bar and R Charts in Gage R&R

← Older revision		Revision as of 21:13, 7 January 2016
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	X-bar and R charts are often used in gage R&R studies. Although DOE++ does not use them to estimate repeatability and reproducibility, they are included in the plot to visually display the data. Along with X-bar and R charts, other plots are also used in DOE++. For example, the following is a run chart for the example of gage R&R study using crossed design.		X-bar and R charts are often used in gage R&R studies. Although DOE++ does not use them to estimate repeatability and reproducibility, they are included in the plot to visually display the data. Along with X-bar and R charts, other plots are also used in DOE++. For example, the following is a run chart for the example of gage R&R study using crossed design.

	[[Image: Doe15_11.png\|center\|~~600px~~\|Run chart for the gage R&R study using crossed design.]]		[[Image: Doe15_11.png\|center\|650px\|Run chart for the gage R&R study using crossed design.\|link=]]

	Each column in the above figure is the 9 measurements of a part by all the operators. In the above plot, we see that all readings by operator C (the blue points) are above the mean line. This indicates that operator C’s readings are different from the calculated mean. Part 3 (the last column in the plot) has the least variation among these 3 parts. These two conclusions also can be inferred from the following two plots.		Each column in the above figure is the 9 measurements of a part by all the operators. In the above plot, we see that all readings by operator C (the blue points) are above the mean line. This indicates that operator C’s readings are different from the calculated mean. Part 3 (the last column in the plot) has the least variation among these 3 parts. These two conclusions also can be inferred from the following two plots.

	[[Image: Doe15_12.png\|center\|~~600px~~\|measurement by operator for the gage R&R study using crossed design.]]		[[Image: Doe15_12.png\|center\|650px\|measurement by operator for the gage R&R study using crossed design.\|link=]]

	The above plot shows that operator C’s readings are much higher than the other two operators.		The above plot shows that operator C’s readings are much higher than the other two operators.
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	The above plot shows part 3 has less variation compared to parts 1 and 2.		The above plot shows part 3 has less variation compared to parts 1 and 2.

	[[Image: Doe15_13.png\|center\|~~600px~~\|measurement by part for the gage R&R study using crossed design.]]		[[Image: Doe15_13.png\|center\|650px\|measurement by part for the gage R&R study using crossed design.\|link=]]

	Now let’s talk about X-bar and R charts. The X-bar chart is used to see how the mean reading changes among the parts; the R chart is used to check the repeatability. When the number of readings of each part by the same operator is greater than 10, an s chart is used to replace the R chart. The R chart is accurate only when the sample size is small (<10). For this example, the sample size is 3, so the R chart is used, as shown next.		Now let’s talk about X-bar and R charts. The X-bar chart is used to see how the mean reading changes among the parts; the R chart is used to check the repeatability. When the number of readings of each part by the same operator is greater than 10, an s chart is used to replace the R chart. The R chart is accurate only when the sample size is small (<10). For this example, the sample size is 3, so the R chart is used, as shown next.

	[[Image: Doe15_14.png\|center\|~~600px~~\|R chart by operator for the gage R&R study using crossed design.]]		[[Image: Doe15_14.png\|center\|650px\|R chart by operator for the gage R&R study using crossed design.\|link=]]

	In the above plot, the x-axis is operator and the y-axis is the range for each part measured by each operator.		In the above plot, the x-axis is operator and the y-axis is the range for each part measured by each operator.