Normal Distribution Examples - Revision history

Lisa Hacker at 21:45, 18 September 2023

2023-09-18T21:45:45Z

← Older revision		Revision as of 21:45, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}{{Navigation box}}		<noinclude>{{Banner Weibull Examples}}{{Navigation box}}
	''These examples appear in the [~~[The_Normal_Distribution\|~~Life ~~Data Analysis Reference book]~~].''		''These examples appear in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference].''
	</noinclude>		</noinclude>
	The following examples illustrate the different types of life data that can be analyzed in Weibull++ using the normal distribution. For more information on the different types of life data, see [[Life Data Classification]].		The following examples illustrate the different types of life data that can be analyzed in Weibull++ using the normal distribution. For more information on the different types of life data, see [[Life Data Classification]].

Nicolette Young: /* Interval Censored Data Example */

2015-12-21T22:43:26Z

Interval Censored Data Example

← Older revision		Revision as of 22:43, 21 December 2015
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	[[Image:lastinspectedplot.png\|center\|~~550px~~\| ]]		[[Image:lastinspectedplot.png\|center\|600px\| ]]

	===Mixed Data Types Example===		===Mixed Data Types Example===

Nicolette Young: /* Complete Data Example */

2015-12-21T22:42:56Z

Complete Data Example

← Older revision		Revision as of 22:42, 21 December 2015
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	[[Image:Normal Distribution Example 8 Data.png\|center\|~~550px~~\| ]]		[[Image:Normal Distribution Example 8 Data.png\|center\|650px\| ]]


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	[[Image:folio^E.png\|center\|550px]]		[[Image:folio^E.png\|center\|550px]]


	===Suspension Data Example===		===Suspension Data Example===

Richard House at 20:43, 25 September 2012

2012-09-25T20:43:34Z

← Older revision		Revision as of 20:43, 25 September 2012
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	:1. Find the parameters for the data set, using the Rank Regression on X (RRX) parameter estimation method		:1. Find the parameters for the data set, using the Rank Regression on X (RRX) parameter estimation method
	:2. Obtain the probability plot for the data with 90%, two-sided Type 1 confidence bounds.		:2. Obtain the probability plot for the data with 90%, two-sided Type 1 confidence bounds.
	:3. Obtain the ~~<math>~~pdf~~</math>~~ plot for the data.		:3. Obtain the ''pdf'' plot for the data.
	:4. Using the Quick Calculation Pad (QCP), determine the reliability for a mission of 11,000 hours, as well as the upper and lower two-sided 90% confidence limit on this reliability.		:4. Using the Quick Calculation Pad (QCP), determine the reliability for a mission of 11,000 hours, as well as the upper and lower two-sided 90% confidence limit on this reliability.
	:5. Using the QCP, determine the MTTF, as well as the upper and lower two-sided 90% confidence limit on this MTTF.		:5. Using the QCP, determine the MTTF, as well as the upper and lower two-sided 90% confidence limit on this MTTF.
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	& \widehat{\mu }= & 48.07 \\		& \widehat{\mu }= & 48.07 \\
	& {{{\hat{\sigma }}}_{T}}= & 28.41.		& {{{\hat{\sigma }}}_{T}}= & 28.41.
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 46.40 \\		& \widehat{\mu }= & 46.40 \\
	& {{{\hat{\sigma }}}_{T}}= & 28.64.		& {{{\hat{\sigma }}}_{T}}= & 28.64.
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 47.34 \\		& \widehat{\mu }= & 47.34 \\
	& {{{\hat{\sigma }}}_{T}}= & 29.96.		& {{{\hat{\sigma }}}_{T}}= & 29.96.
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 41.40 \\		& \widehat{\mu }= & 41.40 \\
	& {{{\hat{\sigma }}}_{T}}= & 7.740.		& {{{\hat{\sigma }}}_{T}}= & 7.740.
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 41.40 \\		& \widehat{\mu }= & 41.40 \\
	& {{{\hat{\sigma }}}_{T}}= & 9.03.		& {{{\hat{\sigma }}}_{T}}= & 9.03.
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 41.39 \\		& \widehat{\mu }= & 41.39 \\
	& {{{\hat{\sigma }}}_{T}}= & 9.25.		& {{{\hat{\sigma }}}_{T}}= & 9.25.
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 48.11 \\		& \widehat{\mu }= & 48.11 \\
	& {{{\hat{\sigma }}}_{T}}= & 26.42		& {{{\hat{\sigma }}}_{T}}= & 26.42
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 49.99 \\		& \widehat{\mu }= & 49.99 \\
	& {{{\hat{\sigma }}}_{T}}= & 30.17		& {{{\hat{\sigma }}}_{T}}= & 30.17
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 51.61 \\		& \widehat{\mu }= & 51.61 \\
	& {{{\hat{\sigma }}}_{T}}= & 33.07		& {{{\hat{\sigma }}}_{T}}= & 33.07
	\end{align}</math>		\end{align}\,\!</math>
	===Comparison of Analysis Methods===		===Comparison of Analysis Methods===
	8 units are being reliability tested, and the following is a table of their failure times:		8 units are being reliability tested, and the following is a table of their failure times:
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	& \widehat{\mu }= & 26.13 \\		& \widehat{\mu }= & 26.13 \\
	& {{{\hat{\sigma }}}_{T}}= & 18.57		& {{{\hat{\sigma }}}_{T}}= & 18.57
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 26.13 \\		& \widehat{\mu }= & 26.13 \\
	& {{{\hat{\sigma }}}_{T}}= & 21.64		& {{{\hat{\sigma }}}_{T}}= & 21.64
	\end{align}</math>		\end{align}\,\!</math>


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	& \widehat{\mu }= & 26.13 \\		& \widehat{\mu }= & 26.13 \\
	& {{{\hat{\sigma }}}_{T}}= & 22.28.		& {{{\hat{\sigma }}}_{T}}= & 22.28.
	\end{align}</math>		\end{align}\,\!</math>

Chris Kahn: /* Interval Censored Data Example */

2012-08-23T22:42:39Z

Interval Censored Data Example

← Older revision		Revision as of 22:42, 23 August 2012
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	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|-		\|-
	\|colspan="3" style="text-align:center"\| Non-Grouped Interval Data		\|colspan="3" style="text-align:center"\| '''Non-Grouped Interval Data'''
	\|-		\|-
	!Data point index		!Data point index
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	[[Image:lastinspectedplot.png\|center\|550px\| ]]		[[Image:lastinspectedplot.png\|center\|550px\| ]]


	===Mixed Data Types Example===		===Mixed Data Types Example===

Chris Kahn at 05:53, 23 August 2012

2012-08-23T05:53:22Z

Show changes

Chris Kahn at 05:52, 23 August 2012

2012-08-23T05:52:09Z

← Older revision		Revision as of 05:52, 23 August 2012
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	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|-		\|-
	\|colspan="3" style="text-align:center"\| Non-Grouped Data Times-to-Failure Data with Suspensions		\|colspan="3" style="text-align:center"\| '''Non-Grouped Data Times-to-Failure Data with Suspensions'''
	\|-		\|-
	!Data point index		!Data point index

Chris Kahn at 05:51, 23 August 2012

2012-08-23T05:51:21Z

← Older revision		Revision as of 05:51, 23 August 2012
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	===Interval Censored Data Example===		===Interval Censored Data Example===
	~~Eight~~ units are being reliability tested, and the following is a table of their times~~-to-failure~~:		8 units are being reliability tested, and the following is a table of their failure times:

	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
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	& {{{\hat{\sigma }}}_{T}}= & 7.740.		& {{{\hat{\sigma }}}_{T}}= & 7.740.
	\end{align}</math>		\end{align}</math>


	For rank regression on x:		For rank regression on x:
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	===Suspension Data Example===		===Suspension Data Example===
	~~Nineteen~~ units are being reliability tested and the following is a table of their times-to-failure and suspensions.		19 units are being reliability tested and the following is a table of their times-to-failure and suspensions.

	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
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	& {{{\hat{\sigma }}}_{T}}= & 21.64		& {{{\hat{\sigma }}}_{T}}= & 21.64
	\end{align}</math>		\end{align}</math>


	For the rank regression on y (RRY) method, the parameters are:		For the rank regression on y (RRY) method, the parameters are:
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	& {{{\hat{\sigma }}}_{T}}= & 22.28.		& {{{\hat{\sigma }}}_{T}}= & 22.28.
	\end{align}</math>		\end{align}</math>


	===Mixed Data Types Example===		===Mixed Data Types Example===
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	& {{{\hat{\sigma }}}_{T}}= & 26.42		& {{{\hat{\sigma }}}_{T}}= & 26.42
	\end{align}</math>		\end{align}</math>


	If we analyze the data set with the rank regression on x (RRX) method, the computed parameters are:		If we analyze the data set with the rank regression on x (RRX) method, the computed parameters are:
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	& {{{\hat{\sigma }}}_{T}}= & 30.17		& {{{\hat{\sigma }}}_{T}}= & 30.17
	\end{align}</math>		\end{align}</math>


	For the rank regression on y (RRY) method, the parameters are:		For the rank regression on y (RRY) method, the parameters are:

Chris Kahn at 05:47, 23 August 2012

2012-08-23T05:47:18Z

← Older revision		Revision as of 05:47, 23 August 2012
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	To obtain tabulated values for the failure rate, use the Analysis Workbook or General Spreadsheet features that are included in Weibull++. (For more information on these features, please refer to the Weibull++ User's Guide. For a step-by-step example on creating Weibull++ reports, please see the [http://www.~~synthesis8~~.~~com~~/~~WeibullALTA~~/en/~~QS_WeibullALTA~~.~~pdf~~ Quick Start Guide]). The following worksheet shows the mission times and the corresponding failure rates.		To obtain tabulated values for the failure rate, use the Analysis Workbook or General Spreadsheet features that are included in Weibull++. (For more information on these features, please refer to the Weibull++ User's Guide. For a step-by-step example on creating Weibull++ reports, please see the [http://www.reliasoft.tv/weibull/startguide/weibull_qsg_2.html Quick Start Guide]). The following worksheet shows the mission times and the corresponding failure rates.

Chris Kahn at 05:43, 23 August 2012

2012-08-23T05:43:11Z

← Older revision		Revision as of 05:43, 23 August 2012
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	To obtain tabulated values for the failure rate, use the Analysis Workbook or General Spreadsheet features that are included in Weibull++. (For more information on these features, please refer to the Weibull++ User's Guide. For a step-by-step example on creating Weibull++ reports, please see the [[http://www.synthesis8.com/WeibullALTA/en/QS_WeibullALTA.pdf Quick Start Guide). The following worksheet shows the mission times and the corresponding failure rates.		To obtain tabulated values for the failure rate, use the Analysis Workbook or General Spreadsheet features that are included in Weibull++. (For more information on these features, please refer to the Weibull++ User's Guide. For a step-by-step example on creating Weibull++ reports, please see the [http://www.synthesis8.com/WeibullALTA/en/QS_WeibullALTA.pdf Quick Start Guide]). The following worksheet shows the mission times and the corresponding failure rates.