Non-Homogeneous Data with Subset IDs Example - Revision history

Lisa Hacker at 18:54, 18 September 2023

2023-09-18T18:54:48Z

← Older revision		Revision as of 18:54, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [~~[Warranty_Data_Analysis#Monitoring_Warranty_Returns_Using_Statistical_Process_Control_(SPC)\|~~Life ~~Data Analysis Reference book]~~]''.		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.

Nicolette Young at 17:24, 23 December 2015

2015-12-23T17:24:40Z

← Older revision		Revision as of 17:24, 23 December 2015
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	To analyze the warranty returns, select the check box in the '''Statistical Process Control''' page of the control panel and set the alpha values to '''0.01''' for the Critical Value and '''0.1''' for the Caution Value. Select to color code the results '''By sales period'''. The following figure shows the analysis settings and results of the analysis.		To analyze the warranty returns, select the check box in the '''Statistical Process Control''' page of the control panel and set the alpha values to '''0.01''' for the Critical Value and '''0.1''' for the Caution Value. Select to color code the results '''By sales period'''. The following figure shows the analysis settings and results of the analysis.

	[[Image:Warranty Example 6 SPC Result.png\|center\|~~600px~~\| ]]		[[Image:Warranty Example 6 SPC Result.png\|center\|650px\| ]]

	As you can see, the November 04 and March 05 sales periods are colored in yellow indicating that they are ''outlier'' sales periods, while the rest are green. One suspected reason for the variation may be the material used in production during these periods. Further analysis confirmed that for these periods, the material was acquired from a different supplier. This implies that the units are not homogenous, and that there are different sub-populations present in the field population.		As you can see, the November 04 and March 05 sales periods are colored in yellow indicating that they are ''outlier'' sales periods, while the rest are green. One suspected reason for the variation may be the material used in production during these periods. Further analysis confirmed that for these periods, the material was acquired from a different supplier. This implies that the units are not homogenous, and that there are different sub-populations present in the field population.
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	Categorized each shipment (using the Subset ID column) based on their material supplier, as shown next. On the control panel, select the '''Use Subsets''' check box. Perform the analysis again using the two-parameter Weibull distribution and the MLE analysis method for both sub-populations.		Categorized each shipment (using the Subset ID column) based on their material supplier, as shown next. On the control panel, select the '''Use Subsets''' check box. Perform the analysis again using the two-parameter Weibull distribution and the MLE analysis method for both sub-populations.

	[[Image:Warranty Example 6 Subpopulation Datat.png\|center\|~~600px~~\| ]]		[[Image:Warranty Example 6 Subpopulation Datat.png\|center\|650px\| ]]

	The new models that describe the data are:		The new models that describe the data are:

Kate Racaza at 23:39, 11 September 2013

2013-09-11T23:39:16Z

← Older revision		Revision as of 23:39, 11 September 2013
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [[Monitoring_Warranty_Returns_Using_Statistical_Process_Control_~~.28SPC.29~~\|Life Data Analysis Reference book]]''.		''This example appears in the [[Warranty_Data_Analysis#Monitoring_Warranty_Returns_Using_Statistical_Process_Control_(SPC)\|Life Data Analysis Reference book]]''.

Kate Racaza at 23:38, 11 September 2013

2013-09-11T23:38:15Z

← Older revision		Revision as of 23:38, 11 September 2013
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [[~~Monitoring Warranty Returns Using Statistical Process Control (SPC)~~\|Life Data Analysis Reference book]]''.		''This example appears in the [[Monitoring_Warranty_Returns_Using_Statistical_Process_Control_.28SPC.29\|Life Data Analysis Reference book]]''.

Richard House at 21:52, 26 September 2012

2012-09-26T21:52:59Z

← Older revision		Revision as of 21:52, 26 September 2012
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	\text{Mar 05} & \text{1105} \\		\text{Mar 05} & \text{1105} \\
	\text{Apr 05} & \text{1110} \\		\text{Apr 05} & \text{1110} \\
	\end{matrix}</math></center>		\end{matrix}\,\!</math></center>


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	Mar 06 & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{2} & \text{12} \\		Mar 06 & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{2} & \text{12} \\
	Apr 06 & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{2} \\		Apr 06 & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{-} & \text{2} \\
	\end{matrix}</math></center>		\end{matrix}\,\!</math></center>


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	& & \beta = & 2.318144 \\		& & \beta = & 2.318144 \\
	& & \eta = & 25.071878		& & \eta = & 25.071878
	\end{align}</math>		\end{align}\,\!</math>

	To analyze the warranty returns, select the check box in the '''Statistical Process Control''' page of the control panel and set the alpha values to '''0.01''' for the Critical Value and '''0.1''' for the Caution Value. Select to color code the results '''By sales period'''. The following figure shows the analysis settings and results of the analysis.		To analyze the warranty returns, select the check box in the '''Statistical Process Control''' page of the control panel and set the alpha values to '''0.01''' for the Critical Value and '''0.1''' for the Caution Value. Select to color code the results '''By sales period'''. The following figure shows the analysis settings and results of the analysis.
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	\eta =21.282926 \\		\eta =21.282926 \\
	\end{matrix} \\		\end{matrix} \\
	\end{matrix}</math></center>		\end{matrix}\,\!</math></center>

	This analysis uncovered different sub-populations in the data set. Note that if the analysis were performed on the failure and suspension times in a regular standard folio using the mixed Weibull distribution, one would not be able to detect which units fall into which sub-population.		This analysis uncovered different sub-populations in the data set. Note that if the analysis were performed on the failure and suspension times in a regular standard folio using the mixed Weibull distribution, one would not be able to detect which units fall into which sub-population.

Richard House at 07:53, 7 August 2012

2012-08-07T07:53:43Z

← Older revision		Revision as of 07:53, 7 August 2012
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	A manufacturer wants to monitor and analyze the warranty returns for a particular product. They collected the following sales and return data.		A manufacturer wants to monitor and analyze the warranty returns for a particular product. They collected the following sales and return data.


	<center><math>\begin{matrix}		<center><math>\begin{matrix}
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	Analyze the data using the two-parameter Weibull distribution and the MLE analysis method. The parameters are estimated to be:		Analyze the data using the two-parameter Weibull distribution and the MLE analysis method. The parameters are estimated to be:


	::<math>\begin{align}		::<math>\begin{align}
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	& & \eta = & 25.071878		& & \eta = & 25.071878
	\end{align}</math>		\end{align}</math>


	To analyze the warranty returns, select the check box in the '''Statistical Process Control''' page of the control panel and set the alpha values to '''0.01''' for the Critical Value and '''0.1''' for the Caution Value. Select to color code the results '''By sales period'''. The following figure shows the analysis settings and results of the analysis.		To analyze the warranty returns, select the check box in the '''Statistical Process Control''' page of the control panel and set the alpha values to '''0.01''' for the Critical Value and '''0.1''' for the Caution Value. Select to color code the results '''By sales period'''. The following figure shows the analysis settings and results of the analysis.


	[[Image:Warranty Example 6 SPC Result.png\|center\|600px\| ]]		[[Image:Warranty Example 6 SPC Result.png\|center\|600px\| ]]


	As you can see, the November 04 and March 05 sales periods are colored in yellow indicating that they are ''outlier'' sales periods, while the rest are green. One suspected reason for the variation may be the material used in production during these periods. Further analysis confirmed that for these periods, the material was acquired from a different supplier. This implies that the units are not homogenous, and that there are different sub-populations present in the field population.		As you can see, the November 04 and March 05 sales periods are colored in yellow indicating that they are ''outlier'' sales periods, while the rest are green. One suspected reason for the variation may be the material used in production during these periods. Further analysis confirmed that for these periods, the material was acquired from a different supplier. This implies that the units are not homogenous, and that there are different sub-populations present in the field population.

	Categorized each shipment (using the Subset ID column) based on their material supplier, as shown next. On the control panel, select the '''Use Subsets''' check box. Perform the analysis again using the two-parameter Weibull distribution and the MLE analysis method for both sub-populations.		Categorized each shipment (using the Subset ID column) based on their material supplier, as shown next. On the control panel, select the '''Use Subsets''' check box. Perform the analysis again using the two-parameter Weibull distribution and the MLE analysis method for both sub-populations.


	[[Image:Warranty Example 6 Subpopulation Datat.png\|center\|600px\| ]]		[[Image:Warranty Example 6 Subpopulation Datat.png\|center\|600px\| ]]


	The new models that describe the data are:		The new models that describe the data are:
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	\end{matrix} \\		\end{matrix} \\
	\end{matrix}</math></center>		\end{matrix}</math></center>


	This analysis uncovered different sub-populations in the data set. Note that if the analysis were performed on the failure and suspension times in a regular standard folio using the mixed Weibull distribution, one would not be able to detect which units fall into which sub-population.		This analysis uncovered different sub-populations in the data set. Note that if the analysis were performed on the failure and suspension times in a regular standard folio using the mixed Weibull distribution, one would not be able to detect which units fall into which sub-population.

Richard House at 07:17, 6 August 2012

2012-08-06T07:17:29Z

← Older revision		Revision as of 07:17, 6 August 2012
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	[[Image:Warranty Example 6 SPC Result.png~~\|thumb~~\|center\|600px\| ]]		[[Image:Warranty Example 6 SPC Result.png\|center\|600px\| ]]


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	[[Image:Warranty Example 6 Subpopulation Datat.png~~\|thumb~~\|center\|600px\| ]]		[[Image:Warranty Example 6 Subpopulation Datat.png\|center\|600px\| ]]

Kate Racaza: updated example

2012-07-26T09:01:47Z

updated example

← Older revision		Revision as of 09:01, 26 July 2012
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	''~~'Discovering Subpopulations~~ Using ~~Warranty Return Montoring Example'~~''		<noinclude>{{Banner Weibull Examples}}
			''This example appears in the [[Monitoring Warranty Returns Using Statistical Process Control (SPC)\|Life Data Analysis Reference book]]''.

	The SPC (warranty monitoring) methodology explained in this section can also be used to detect different subpopulations. The different subpopulations can reflect different use conditions, different material, etc. In this methodology, one can use different IDs to ~~differentiate between subpopulations,~~ and ~~obtain models that are distinct to each subpopulation~~. ~~The following example illustrates this concept.~~
	~~A manufacturer~~ collected the following sales and return data.		</noinclude>'''Using Subset IDs with Statistical Process Control'''

			A manufacturer wants to monitor and analyze the warranty returns for a particular product. They collected the following sales and return data.


	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	Period & Quantity In-Service \\		Period & Quantity In-Service \\
	\text{Sep 05} & \text{1150} \\		\text{Sep 04} & \text{1150} \\
	\text{Oct 05} & \text{1100} \\		\text{Oct 04} & \text{1100} \\
	\text{Nov 05} & \text{1200} \\		\text{Nov 04} & \text{1200} \\
	\text{Dec 05} & \text{1155} \\		\text{Dec 04} & \text{1155} \\
	\text{Jan 06} & \text{1255} \\		\text{Jan 05} & \text{1255} \\
	\text{Feb 06} & \text{1150} \\		\text{Feb 05} & \text{1150} \\
	\text{Mar 06} & \text{1105} \\		\text{Mar 05} & \text{1105} \\
	\text{Apr 06} & \text{1110} \\		\text{Apr 05} & \text{1110} \\
	\end{matrix}</math></center>		\end{matrix}</math></center>


	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	{} & Oct 05 & Nov 05 & Dec 05 & Jan 06 & Feb 06 & Mar 06 & Apr 06 & May 06 \\		{} & Oct 04 & Nov 04 & Dec 04 & Jan 05 & Feb 05 & Mar 05 & Apr 05 & May 05 \\
	Sep 05 & \text{2} & \text{4} & \text{5} & \text{7} & \text{12} & \text{13} & \text{16} & \text{17} \\		Sep 05 & \text{2} & \text{4} & \text{5} & \text{7} & \text{12} & \text{13} & \text{16} & \text{17} \\
	Oct 05 & \text{-} & \text{3} & \text{4} & \text{5} & \text{3} & \text{8} & \text{11} & \text{14} \\		Oct 05 & \text{-} & \text{3} & \text{4} & \text{5} & \text{3} & \text{8} & \text{11} & \text{14} \\
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	~~The~~ data ~~were analyzed~~ using the two-parameter Weibull distribution and the MLE analysis method. The parameters are estimated to be:		'''Solution'''

			Analyze the data using the two-parameter Weibull distribution and the MLE analysis method. The parameters are estimated to be:


	::<math>\begin{align}		::<math>\begin{align}
	& & \beta = & 2.31 \\		& & \beta = & 2.318144 \\
	& & \eta = & 25.07		& & \eta = & 25.071878
	\end{align}</math>		\end{align}</math>

	~~The SPC's <math>\alpha </math> value are set at 0.01 for the Critical Value and 0.1 for the Caution Value. When analyzed and color coded in Weibull++ the following window is obtained:~~

	~~[[Image:Warranty Example 6 SPC Result~~.~~png\|thumb\|center\|250px\| ]]~~		To analyze the warranty returns, select the check box in the '''Statistical Process Control''' page of the control panel and set the alpha values to '''0.01''' for the Critical Value and '''0.1''' for the Caution Value. Select to color code the results '''By sales period'''. The following figure shows the analysis settings and results of the analysis.

	Here the Nov. 05 and Mar 06 sales periods are colored in yellow indicating that they are `outlier' sales periods, while the rest are green. One suspected reason for the variation may be the material used in production in this period. Further analysis confirmed that for these periods the material was acquired from a different supplier. This then implies that the units are not homogenous, and that there are different subpopulations present in the field populations.

	~~Based on this, the data is re-analyzed after categorizing the different shipments (using the ID column) based on their material supplier. The data as entered are shown next~~.		[[Image:Warranty Example 6 SPC Result.png\|thumb\|center\|600px\| ]]

	~~[[Image:Warranty Example 6 Subpopulation Datat.png\|thumb\|center\|250px\| ]]~~

			As you can see, the November 04 and March 05 sales periods are colored in yellow indicating that they are ''outlier'' sales periods, while the rest are green. One suspected reason for the variation may be the material used in production during these periods. Further analysis confirmed that for these periods, the material was acquired from a different supplier. This implies that the units are not homogenous, and that there are different sub-populations present in the field population.

	~~The new models that describe~~ the ~~data are (assuming a~~ two-parameter Weibull distribution and ~~using~~ MLE ~~as the~~ analysis method for both sub-populations):		Categorized each shipment (using the Subset ID column) based on their material supplier, as shown next. On the control panel, select the '''Use Subsets''' check box. Perform the analysis again using the two-parameter Weibull distribution and the MLE analysis method for both sub-populations.


			[[Image:Warranty Example 6 Subpopulation Datat.png\|thumb\|center\|600px\| ]]


			The new models that describe the data are:

	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	Supplier 1 & Supplier 2 \\		Supplier 1 & Supplier 2 \\
	\begin{matrix}		\begin{matrix}
	\beta =2.38 \\		\beta =2.381905 \\
	\eta =25.39 \\		\eta =25.397633 \\
	\end{matrix} & \begin{matrix}		\end{matrix} & \begin{matrix}
	\beta =2.32 \\		\beta =2.320696 \\
	\eta =21.28 \\		\eta =21.282926 \\
	\end{matrix} \\		\end{matrix} \\
	\end{matrix}</math></center>		\end{matrix}</math></center>

	This analysis ~~helped~~ in ~~uncovering different subpopulations as well as allowing us to compute different distributions for each subpopulation~~. Note that if the analysis were performed on the failure and suspension times in a regular ~~Standard Folio,~~ using the mixed Weibull distribution, one would not be able to detect which units fall into which ~~subpopulation~~.
			This analysis uncovered different sub-populations in the data set. Note that if the analysis were performed on the failure and suspension times in a regular standard folio using the mixed Weibull distribution, one would not be able to detect which units fall into which sub-population.

Kate Racaza: moved Template:Example: Discovering Subpopulations Using Warranty Return Montoring Example to Non-Homogeneous Data with Subset IDs Example: incorrect namespace

2012-07-26T08:01:15Z

moved Template:Example: Discovering Subpopulations Using Warranty Return Montoring Example to Non-Homogeneous Data with Subset IDs Example: incorrect namespace

← Older revision	Revision as of 08:01, 26 July 2012
(No difference)

Nicolette Young at 22:33, 25 April 2012

2012-04-25T22:33:45Z

← Older revision		Revision as of 22:33, 25 April 2012
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	The SPC's <math>\alpha </math> value are set at 0.01 for the Critical Value and 0.1 for the Caution Value. When analyzed and color coded in Weibull++ the following window is obtained:		The SPC's <math>\alpha </math> value are set at 0.01 for the Critical Value and 0.1 for the Caution Value. When analyzed and color coded in Weibull++ the following window is obtained:

	[[Image:Warranty Example 6 SPC Result.png\|thumb\|center\|~~400px~~\| ]]		[[Image:Warranty Example 6 SPC Result.png\|thumb\|center\|250px\| ]]

	Here the Nov. 05 and Mar 06 sales periods are colored in yellow indicating that they are `outlier' sales periods, while the rest are green. One suspected reason for the variation may be the material used in production in this period. Further analysis confirmed that for these periods the material was acquired from a different supplier. This then implies that the units are not homogenous, and that there are different subpopulations present in the field populations.		Here the Nov. 05 and Mar 06 sales periods are colored in yellow indicating that they are `outlier' sales periods, while the rest are green. One suspected reason for the variation may be the material used in production in this period. Further analysis confirmed that for these periods the material was acquired from a different supplier. This then implies that the units are not homogenous, and that there are different subpopulations present in the field populations.
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	Based on this, the data is re-analyzed after categorizing the different shipments (using the ID column) based on their material supplier. The data as entered are shown next.		Based on this, the data is re-analyzed after categorizing the different shipments (using the ID column) based on their material supplier. The data as entered are shown next.

	[[Image:Warranty Example 6 Subpopulation Datat.png\|thumb\|center\|~~400px~~\| ]]		[[Image:Warranty Example 6 Subpopulation Datat.png\|thumb\|center\|250px\| ]]