Linearity and Bias Study Example - Revision history

Lisa Hacker at 21:07, 18 September 2023

2023-09-18T21:07:29Z

← Older revision		Revision as of 21:07, 18 September 2023
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	<noinclude>{{Banner DOE Examples}}		<noinclude>{{Banner DOE Examples}}
	''This example appears in the [~~[Measurement_System_Analysis#Gage_Linearity_and_Bias_Study\|Experiment Design and Analysis Reference book]~~]''. </noinclude>		''This example appears in the [https://help.reliasoft.com/reference/experiment_design_and_analysis DOE reference]''. </noinclude>

Richard House: /* Results for Bias Study */

2017-08-10T15:27:26Z

Results for Bias Study

← Older revision		Revision as of 15:27, 10 August 2017
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	When there are multiple parts for the same reference value, the standard deviation for that reference value is the pooled standard deviation of all the parts with the same reference value. The standard deviation for the average is calculated from the variance of all the parts.		When there are multiple parts for the same reference value, the standard deviation for that reference value is the pooled standard deviation of all the parts with the same reference value. The standard deviation for the average is calculated from the variance of all the parts.

	There are no clear cut-off values for what percent of linearity and bias are acceptable. Users should make their decision based on their engineering feeling or experience. The results from ~~DOE~~++ is given in the following picture.		There are no clear cut-off values for what percent of linearity and bias are acceptable. Users should make their decision based on their engineering feeling or experience. The results from the Weibull++ DOE folio is given in the following picture.

	[[Image:Doe15_2.png\|center\|700px\|Gage accuracy study example\|link=]]		[[Image:Doe15_2.png\|center\|700px\|Gage accuracy study example\|link=]]

Richard House: /* Results for Bias Study */

2016-01-07T20:33:06Z

Results for Bias Study

← Older revision		Revision as of 20:33, 7 January 2016
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	There are no clear cut-off values for what percent of linearity and bias are acceptable. Users should make their decision based on their engineering feeling or experience. The results from DOE++ is given in the following picture.		There are no clear cut-off values for what percent of linearity and bias are acceptable. Users should make their decision based on their engineering feeling or experience. The results from DOE++ is given in the following picture.

	[[Image:Doe15_2.png\|center\|700px\|Gage accuracy study example]]		[[Image:Doe15_2.png\|center\|700px\|Gage accuracy study example\|link=]]

Richard House: /* Results for Linearity Study */

2016-01-07T20:13:18Z

Results for Linearity Study

← Older revision		Revision as of 20:13, 7 January 2016
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	The calculated R-sq is 55.84% and R-sq(adj) is 54.46%. These values are not very high due to the large variation among the bias values. However, the p value of the lack of fit shows that the linear equation fits the data very well, and the following plot also shows there is a linear relation between reference and bias.		The calculated R-sq is 55.84% and R-sq(adj) is 54.46%. These values are not very high due to the large variation among the bias values. However, the p value of the lack of fit shows that the linear equation fits the data very well, and the following plot also shows there is a linear relation between reference and bias.

	[[Image:doe15_3.png\|center\|~~768px~~\|Clear linearity and bias of a gage.]]		[[Image:doe15_3.png\|center\|650px\|Clear linearity and bias of a gage.\|link=]]

	The estimated coefficients are:		The estimated coefficients are:

Richard House: /* Results for Linearity Study */

2016-01-07T20:03:39Z

Results for Linearity Study

← Older revision		Revision as of 20:03, 7 January 2016
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	If the linearity study shows no linear relation between reference and bias, you need to check the scatter plot of reference and bias to see if there is a non-linear relation. For example, the following plot shows a non-linear relationship between reference and bias.		If the linearity study shows no linear relation between reference and bias, you need to check the scatter plot of reference and bias to see if there is a non-linear relation. For example, the following plot shows a non-linear relationship between reference and bias.

	[[Image:doe15_4.png\|center\|768px\|No clear linearity of a gage.~~\|link=~~]]		[[Image:doe15_4.png\|center\|768px\|No clear linearity of a gage.]]

	Although the slope in the linear equation is almost 0 in the above plot, it does not mean the gage is accurate. The above figure shows an obvious V-shaped pattern between reference and bias. This non-linear pattern requires further analysis to judge whether the gage’s accuracy is acceptable.		Although the slope in the linear equation is almost 0 in the above plot, it does not mean the gage is accurate. The above figure shows an obvious V-shaped pattern between reference and bias. This non-linear pattern requires further analysis to judge whether the gage’s accuracy is acceptable.

Richard House: /* Results for Linearity Study */

2016-01-07T20:02:44Z

Results for Linearity Study

← Older revision		Revision as of 20:02, 7 January 2016
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	The calculated R-sq is 55.84% and R-sq(adj) is 54.46%. These values are not very high due to the large variation among the bias values. However, the p value of the lack of fit shows that the linear equation fits the data very well, and the following plot also shows there is a linear relation between reference and bias.		The calculated R-sq is 55.84% and R-sq(adj) is 54.46%. These values are not very high due to the large variation among the bias values. However, the p value of the lack of fit shows that the linear equation fits the data very well, and the following plot also shows there is a linear relation between reference and bias.

	[[Image:doe15_3.png\|center\|768px\|Clear linearity and bias of a gage.~~\|link=~~]]		[[Image:doe15_3.png\|center\|768px\|Clear linearity and bias of a gage.]]

	The estimated coefficients are:		The estimated coefficients are:

Richard House: /* Results for Linearity Study */

2016-01-07T19:57:12Z

Results for Linearity Study

← Older revision		Revision as of 19:57, 7 January 2016
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	If the linearity study shows no linear relation between reference and bias, you need to check the scatter plot of reference and bias to see if there is a non-linear relation. For example, the following plot shows a non-linear relationship between reference and bias.		If the linearity study shows no linear relation between reference and bias, you need to check the scatter plot of reference and bias to see if there is a non-linear relation. For example, the following plot shows a non-linear relationship between reference and bias.

	[[Image:doe15_4.png\|center\|~~700px~~\|No clear linearity of a gage.]]		[[Image:doe15_4.png\|center\|768px\|No clear linearity of a gage.\|link=]]

	Although the slope in the linear equation is almost 0 in the above plot, it does not mean the gage is accurate. The above figure shows an obvious V-shaped pattern between reference and bias. This non-linear pattern requires further analysis to judge whether the gage’s accuracy is acceptable.		Although the slope in the linear equation is almost 0 in the above plot, it does not mean the gage is accurate. The above figure shows an obvious V-shaped pattern between reference and bias. This non-linear pattern requires further analysis to judge whether the gage’s accuracy is acceptable.

Richard House: /* Results for Linearity Study */

2016-01-07T19:56:04Z

Results for Linearity Study

← Older revision		Revision as of 19:56, 7 January 2016
Line 149:		Line 149:
	The calculated R-sq is 55.84% and R-sq(adj) is 54.46%. These values are not very high due to the large variation among the bias values. However, the p value of the lack of fit shows that the linear equation fits the data very well, and the following plot also shows there is a linear relation between reference and bias.		The calculated R-sq is 55.84% and R-sq(adj) is 54.46%. These values are not very high due to the large variation among the bias values. However, the p value of the lack of fit shows that the linear equation fits the data very well, and the following plot also shows there is a linear relation between reference and bias.

	[[Image:doe15_3.png\|center\|~~700px~~\|Clear linearity and bias of a gage.]]		[[Image:doe15_3.png\|center\|768px\|Clear linearity and bias of a gage.\|link=]]

	The estimated coefficients are:		The estimated coefficients are:

Richard House: /* Results for Bias Study */

2016-01-06T22:47:41Z

Results for Bias Study

← Older revision		Revision as of 22:47, 6 January 2016
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	There are no clear cut-off values for what percent of linearity and bias are acceptable. Users should make their decision based on their engineering feeling or experience. The results from DOE++ is given in the following picture.		There are no clear cut-off values for what percent of linearity and bias are acceptable. Users should make their decision based on their engineering feeling or experience. The results from DOE++ is given in the following picture.

	[[Image:Doe15_2.png~~\|thumb~~\|center\|~~800px~~\|Gage accuracy study example]]		[[Image:Doe15_2.png\|center\|700px\|Gage accuracy study example]]

Richard House: /* Results for Linearity Study */

2016-01-06T22:45:07Z

Results for Linearity Study

← Older revision		Revision as of 22:45, 6 January 2016
Line 149:		Line 149:
	The calculated R-sq is 55.84% and R-sq(adj) is 54.46%. These values are not very high due to the large variation among the bias values. However, the p value of the lack of fit shows that the linear equation fits the data very well, and the following plot also shows there is a linear relation between reference and bias.		The calculated R-sq is 55.84% and R-sq(adj) is 54.46%. These values are not very high due to the large variation among the bias values. However, the p value of the lack of fit shows that the linear equation fits the data very well, and the following plot also shows there is a linear relation between reference and bias.

	[[Image:doe15_3.png~~\|thumb~~\|center\|700px\|Clear linearity and bias of a gage.]]		[[Image:doe15_3.png\|center\|700px\|Clear linearity and bias of a gage.]]

	The estimated coefficients are:		The estimated coefficients are:
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	If the linearity study shows no linear relation between reference and bias, you need to check the scatter plot of reference and bias to see if there is a non-linear relation. For example, the following plot shows a non-linear relationship between reference and bias.		If the linearity study shows no linear relation between reference and bias, you need to check the scatter plot of reference and bias to see if there is a non-linear relation. For example, the following plot shows a non-linear relationship between reference and bias.

	[[Image:doe15_4.png~~\|thumb~~\|center\|700px\|No clear linearity of a gage.]]		[[Image:doe15_4.png\|center\|700px\|No clear linearity of a gage.]]

	Although the slope in the linear equation is almost 0 in the above plot, it does not mean the gage is accurate. The above figure shows an obvious V-shaped pattern between reference and bias. This non-linear pattern requires further analysis to judge whether the gage’s accuracy is acceptable.		Although the slope in the linear equation is almost 0 in the above plot, it does not mean the gage is accurate. The above figure shows an obvious V-shaped pattern between reference and bias. This non-linear pattern requires further analysis to judge whether the gage’s accuracy is acceptable.