Template:The normal distribution - Revision history

Lisa Hacker: Redirected page to The Normal Distribution

2012-08-03T08:44:58Z

Redirected page to The Normal Distribution

← Older revision		Revision as of 08:44, 3 August 2012
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	~~{{template:LDABOOK\|9\|The Normal (Gaussian) Distribution}}~~		#REDIRECT [[The_Normal_Distribution]]

	~~=The Normal Distribution=~~
	The normal distribution, also known as the Gaussian distribution, is the most widely-used general purpose distribution. It is for this reason that it is included among the lifetime distributions commonly used for reliability and life data analysis. There are some who argue that the normal distribution is inappropriate for modeling lifetime data because the left-hand limit of the distribution extends to negative infinity. This could conceivably result in modeling negative times-to-failure. However, provided that the distribution in question has a relatively high mean and a relatively small standard deviation, the issue of negative failure times should not present itself as a problem. Nevertheless, the normal distribution has been shown to be useful for modeling the lifetimes of consumable items, such as printer toner cartridges.

	~~{{normal probability density function}}~~

	~~{{normal statistical properties}}~~

	~~{{characteristics of the normal distribution}}~~

	~~{{normal distribution estimation of the parameters}}~~

	~~{{normal distribution confidence bounds}}~~

	~~{{normal distribution bayesian confidence bounds}}~~

	~~{{normal distribution general examples}}~~

Nicolette Young at 16:55, 6 March 2012

2012-03-06T16:55:11Z

← Older revision		Revision as of 16:55, 6 March 2012
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	{{template:LDABOOK\|9\|The Normal (Gaussian) Distribution}}		{{template:LDABOOK\|9\|The Normal (Gaussian) Distribution}}

			=The Normal Distribution=
	The normal distribution, also known as the Gaussian distribution, is the most widely-used general purpose distribution. It is for this reason that it is included among the lifetime distributions commonly used for reliability and life data analysis. There are some who argue that the normal distribution is inappropriate for modeling lifetime data because the left-hand limit of the distribution extends to negative infinity. This could conceivably result in modeling negative times-to-failure. However, provided that the distribution in question has a relatively high mean and a relatively small standard deviation, the issue of negative failure times should not present itself as a problem. Nevertheless, the normal distribution has been shown to be useful for modeling the lifetimes of consumable items, such as printer toner cartridges.		The normal distribution, also known as the Gaussian distribution, is the most widely-used general purpose distribution. It is for this reason that it is included among the lifetime distributions commonly used for reliability and life data analysis. There are some who argue that the normal distribution is inappropriate for modeling lifetime data because the left-hand limit of the distribution extends to negative infinity. This could conceivably result in modeling negative times-to-failure. However, provided that the distribution in question has a relatively high mean and a relatively small standard deviation, the issue of negative failure times should not present itself as a problem. Nevertheless, the normal distribution has been shown to be useful for modeling the lifetimes of consumable items, such as printer toner cartridges.

Harry Guo at 22:26, 10 February 2012

2012-02-10T22:26:49Z

← Older revision		Revision as of 22:26, 10 February 2012
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	{{template:LDABOOK\|9\|The Normal (Gaussian) Distribution}}		{{template:LDABOOK\|9\|The Normal (Gaussian) Distribution}}


	The normal distribution, also known as the Gaussian distribution, is the most widely-used general purpose distribution. It is for this reason that it is included among the lifetime distributions commonly used for reliability and life data analysis. There are some who argue that the normal distribution is inappropriate for modeling lifetime data because the left-hand limit of the distribution extends to negative infinity. This could conceivably result in modeling negative times-to-failure. However, provided that the distribution in question has a relatively high mean and a relatively small standard deviation, the issue of negative failure times should not present itself as a problem. Nevertheless, the normal distribution has been shown to be useful for modeling the lifetimes of consumable items, such as printer toner cartridges.		The normal distribution, also known as the Gaussian distribution, is the most widely-used general purpose distribution. It is for this reason that it is included among the lifetime distributions commonly used for reliability and life data analysis. There are some who argue that the normal distribution is inappropriate for modeling lifetime data because the left-hand limit of the distribution extends to negative infinity. This could conceivably result in modeling negative times-to-failure. However, provided that the distribution in question has a relatively high mean and a relatively small standard deviation, the issue of negative failure times should not present itself as a problem. Nevertheless, the normal distribution has been shown to be useful for modeling the lifetimes of consumable items, such as printer toner cartridges.

Harry Guo at 17:40, 10 February 2012

2012-02-10T17:40:13Z

← Older revision		Revision as of 17:40, 10 February 2012
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	{{normal distribution bayesian confidence bounds}}		{{normal distribution bayesian confidence bounds}}

	~~==General Examples==~~		{{normal distribution general examples}}

	~~'''Example 8:'''~~
	{{~~Example: Normal General Example (RRX Plot)}}~~


	~~'''Example 9:'''~~
	~~{{Example: Normal General Example (RRX QCP)}}~~


	~~'''Example 10:'''~~
	~~{{Example: Normal General Example (RRX Report)}}~~


	~~'''Example 11:'''~~
	~~{{Example: Normal General Example Interval Data}}~~



	~~'''Example 12:'''~~
	~~{{Example: Normal General Example Complete Data}}~~


	~~'''Example 13:'''~~
	~~{{Example: Normal General Example Suspension Data}}~~


	~~'''Example 14:'''~~
	~~{{Example: Normal General Example All Data Type~~}}

Harry Guo at 17:34, 10 February 2012

2012-02-10T17:34:34Z

← Older revision		Revision as of 17:34, 10 February 2012
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	{{normal distribution confidence bounds}}		{{normal distribution confidence bounds}}

	{{nd bayesian confidence bounds}}		{{normal distribution bayesian confidence bounds}}

	==General Examples==		==General Examples==

Harry Guo: /* General Examples */

2012-02-10T17:27:40Z

General Examples

@@ Line 42: / Line 42: @@
 {{Example: Normal General Example Suspension Data}}
-====  Solution to Example 14====
+'''Example 14:'''
-This data set can be entered into Weibull++ by selecting the data type Times to Failure, with Right Censored Data (Suspensions), with Interval and Left Censored Data and with Grouped Observations.
+{{Example: Normal General Example All Data Type}}

Harry Guo: /* General Examples */

2012-02-10T17:26:07Z

General Examples

@@ Line 39: / Line 39: @@
-===  Example 13===
+'''Example 13:'''
-Nineteen units are being reliability tested and the following is a table of their times-to-failure and suspensions.
+{{Example: Normal General Example Suspension Data}}
 ===  Example 14===

Harry Guo: /* General Examples */

2012-02-10T17:23:47Z

General Examples

← Older revision		Revision as of 17:23, 10 February 2012
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	'''Example 12:'''		'''Example 12:'''
	{{{Example: Normal General Example Complete Data}}}		{{Example: Normal General Example Complete Data}}

Harry Guo: /* General Examples */

2012-02-10T17:22:48Z

General Examples

@@ Line 35: / Line 35: @@
-===  Example 12===
+'''Example 12:'''
-Eight units are being reliability tested and the following is a table of their times-to-failure:
+{{{Example: Normal General Example Complete Data}}}
 ===  Example 13===

Harry Guo: /* General Examples */

2012-02-10T17:21:17Z

General Examples

← Older revision		Revision as of 17:21, 10 February 2012
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	{{Example: Normal General Example (RRX Report)}}		{{Example: Normal General Example (RRX Report)}}

	~~===Example 11===~~
	~~Eight units are being reliability tested and the following is a table of their times-to-failure:~~

			'''Example 11:'''
			{{Example: Normal General Example Interval Data}}

	~~{\|align="center" border=1 cellspacing=1~~
	\|-
	~~\|colspan="3" style="text-align:center"\| Table 8.3 - Non-Grouped Data Times-to-Failure with intervals (lnterval and left censored)~~
	\|-
	~~!Data point index~~
	~~!Last Inspected~~
	~~!State End Time~~
	\|-
	~~\|1 \|\|30\|\|32~~
	\|-
	~~\|2 \|\|32\|\|35~~
	\|-
	~~\|3 \|\|35\|\|37~~
	\|-
	~~\|4 \|\|37\|\|40~~
	\|-
	~~\|5 \|\|42\|\|42~~
	\|-
	~~\|6 \|\|45\|\|45~~
	\|-
	~~\|7\|\|50\|\|50~~
	\|-
	~~\|8\|\|55\|\|55~~
	\|}

	~~====Solution to Example 11====~~
	This is a sequence of interval times-to-failure. This data set can be entered into Weibull++ by creating a data sheet that can be used to analyze times-to-failure data with interval and left censored data.

	~~<math></math>~~
	~~[[Image:lastinspected.png\|thumb\|center\|400px\| ]]~~

	~~[[Image:lastinspectedsheet.png\|thumb\|center\|400px]]~~

	~~The computed parameters for maximum likelihood are:~~

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

	~~For rank regression on x:~~

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

	~~For rank regression on y:~~

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


	~~A plot of the MLE solution is shown next.~~

	~~<math></math>~~
	~~[[Image:lastinspectedplot.png\|thumb\|center\|400px\| ]]~~

	=== Example 12===		=== Example 12===