Logistic Distribution Example - Revision history

Lisa Hacker at 21:39, 18 September 2023

2023-09-18T21:39:55Z

← Older revision		Revision as of 21:39, 18 September 2023
Line 1:		Line 1:
	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [~~[The_Logistic_Distribution#General_Example\|~~Life ~~Data Analysis Reference book]~~]''.</noinclude>		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.</noinclude>

	The lifetime of a mechanical valve is known to follow a logistic distribution. 10 units were tested for 28 months and the following months-to-failure data were collected.		The lifetime of a mechanical valve is known to follow a logistic distribution. 10 units were tested for 28 months and the following months-to-failure data were collected.

Lisa Hacker at 00:40, 10 March 2023

2023-03-10T00:40:29Z

← Older revision		Revision as of 00:40, 10 March 2023
Line 4:		Line 4:
	The lifetime of a mechanical valve is known to follow a logistic distribution. 10 units were tested for 28 months and the following months-to-failure data were collected.		The lifetime of a mechanical valve is known to follow a logistic distribution. 10 units were tested for 28 months and the following months-to-failure data were collected.

			{\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
			\|- align="center"
			!Data Point Index
			!State F or S
			!State End Time
			\|- align="center"
			\|1 \|\|F \|\| 8
			\|- align="center"
			\|2 \|\|F \|\| 10
			\|- align="center"
			\|3 \|\|F \|\| 15
			\|- align="center"
			\|4 \|\|F \|\| 17
			\|- align="center"
			\|5 \|\|F \|\| 19
			\|- align="center"
			\|6 \|\|F \|\| 26
			\|- align="center"
			\|7 \|\|F \|\| 27
			\|- align="center"
			\|8 \|\|S \|\| 28
			\|- align="center"
			\|9 \|\|S \|\| 28
			\|- align="center"
			\|10 \|\|S \|\| 28
			\|}

	~~<!--<center><math>\overset{{}}{\mathop{\text{Times-to-Failure Data with Suspensions}}}\,\,\!</math></center>~~
	~~<center><math>\begin{matrix}~~
	~~\text{Data Point Index} & \text{State F or S} & \text{State End Time} \\~~
	~~\text{1} & \text{F} & \text{8} \\~~
	~~\text{2} & \text{F} & \text{10} \\~~
	~~\text{3} & \text{F} & \text{15} \\~~
	~~\text{4} & \text{F} & \text{17} \\~~
	~~\text{5} & \text{F} & \text{19} \\~~
	~~\text{6} & \text{F} & \text{26} \\~~
	~~\text{7} & \text{F} & \text{27} \\~~
	~~\text{8} & \text{S} & \text{28} \\~~
	~~\text{9} & \text{S} & \text{28} \\~~
	~~\text{10} & \text{S} & \text{28} \\~~
	~~\end{matrix}\,\!</math></center>-->~~

	* Determine the valve's design life if specifications call for a reliability goal of 0.90.		* Determine the valve's design life if specifications call for a reliability goal of 0.90.

Lisa Hacker at 00:36, 10 March 2023

2023-03-10T00:36:08Z

← Older revision		Revision as of 00:36, 10 March 2023
Line 5:		Line 5:


	<center><math>\overset{{}}{\mathop{\text{Times-to-Failure Data with Suspensions}}}\,\,\!</math></center>		<!--<center><math>\overset{{}}{\mathop{\text{Times-to-Failure Data with Suspensions}}}\,\,\!</math></center>
	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	\text{Data Point Index} & \text{State F or S} & \text{State End Time} \\		\text{Data Point Index} & \text{State F or S} & \text{State End Time} \\
Line 18:		Line 18:
	\text{9} & \text{S} & \text{28} \\		\text{9} & \text{S} & \text{28} \\
	\text{10} & \text{S} & \text{28} \\		\text{10} & \text{S} & \text{28} \\
	\end{matrix}\,\!</math></center>		\end{matrix}\,\!</math></center>-->

	* Determine the valve's design life if specifications call for a reliability goal of 0.90.		* Determine the valve's design life if specifications call for a reliability goal of 0.90.

Nicolette Young at 17:11, 23 December 2015

2015-12-23T17:11:29Z

← Older revision		Revision as of 17:11, 23 December 2015
Line 25:		Line 25:
	Enter the data set in a Weibull++ standard folio, as follows:		Enter the data set in a Weibull++ standard folio, as follows:

	[[Image:Logistic Distribution Exmaple 1 Data.png\|center\|~~600px~~\| ]]		[[Image:Logistic Distribution Exmaple 1 Data.png\|center\|650px\| ]]

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

Richard House at 16:23, 26 September 2012

2012-09-26T16:23:31Z

← Older revision		Revision as of 16:23, 26 September 2012
Line 5:		Line 5:


	<center><math>\overset{{}}{\mathop{\text{Times-to-Failure Data with Suspensions}}}\,</math></center>		<center><math>\overset{{}}{\mathop{\text{Times-to-Failure Data with Suspensions}}}\,\,\!</math></center>
	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	\text{Data Point Index} & \text{State F or S} & \text{State End Time} \\		\text{Data Point Index} & \text{State F or S} & \text{State End Time} \\
Line 18:		Line 18:
	\text{9} & \text{S} & \text{28} \\		\text{9} & \text{S} & \text{28} \\
	\text{10} & \text{S} & \text{28} \\		\text{10} & \text{S} & \text{28} \\
	\end{matrix}</math></center>		\end{matrix}\,\!</math></center>

	* Determine the valve's design life if specifications call for a reliability goal of 0.90.		* Determine the valve's design life if specifications call for a reliability goal of 0.90.
Line 32:		Line 32:
	& \widehat{\mu }= & 22.34 \\		& \widehat{\mu }= & 22.34 \\
	& \hat{\sigma }= & 6.15		& \hat{\sigma }= & 6.15
	\end{align}</math>		\end{align}\,\!</math>

	The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:		The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:

Chris Kahn at 01:13, 20 August 2012

2012-08-20T01:13:32Z

← Older revision		Revision as of 01:13, 20 August 2012
Line 2:		Line 2:
	''This example appears in the [[The_Logistic_Distribution#General_Example\|Life Data Analysis Reference book]]''.</noinclude>		''This example appears in the [[The_Logistic_Distribution#General_Example\|Life Data Analysis Reference book]]''.</noinclude>

	The lifetime of a mechanical valve is known to follow a logistic distribution. ~~Ten~~ units were tested for 28 months and the following months-to-failure data ~~was~~ collected.		The lifetime of a mechanical valve is known to follow a logistic distribution. 10 units were tested for 28 months and the following months-to-failure data were collected.

Chris Kahn: moved Example: Logistic Distribution to Logistic Distribution Example

2012-08-20T01:12:22Z

moved Example: Logistic Distribution to Logistic Distribution Example

← Older revision	Revision as of 01:12, 20 August 2012
(No difference)

Richard House at 07:49, 7 August 2012

2012-08-07T07:49:02Z

← Older revision		Revision as of 07:49, 7 August 2012
Line 20:		Line 20:
	\end{matrix}</math></center>		\end{matrix}</math></center>


	* Determine the valve's design life if specifications call for a reliability goal of 0.90.		* Determine the valve's design life if specifications call for a reliability goal of 0.90.
	* The valve is to be used in a pumping device that requires 1 month of continuous operation. What is the probability of the pump failing due to the valve?		* The valve is to be used in a pumping device that requires 1 month of continuous operation. What is the probability of the pump failing due to the valve?
Line 34:		Line 33:
	& \hat{\sigma }= & 6.15		& \hat{\sigma }= & 6.15
	\end{align}</math>		\end{align}</math>


	The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:		The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:

	[[Image:Logistic Distribution Exmaple 1 QCP Reliable Life.png\|center\|500px\| ]]		[[Image:Logistic Distribution Exmaple 1 QCP Reliable Life.png\|center\|500px\| ]]


	The probability, along with 90% two sided confidence bounds, that the pump fails due to a valve failure during the first month is obtained as follows:		The probability, along with 90% two sided confidence bounds, that the pump fails due to a valve failure during the first month is obtained as follows:


	[[Image:Logistic Distribution Exmaple 1 QCP Reliability.png\|center\|500px\| ]]		[[Image:Logistic Distribution Exmaple 1 QCP Reliability.png\|center\|500px\| ]]

Richard House at 05:58, 6 August 2012

2012-08-06T05:58:56Z

← Older revision		Revision as of 05:58, 6 August 2012
Line 23:		Line 23:
	* Determine the valve's design life if specifications call for a reliability goal of 0.90.		* Determine the valve's design life if specifications call for a reliability goal of 0.90.
	* The valve is to be used in a pumping device that requires 1 month of continuous operation. What is the probability of the pump failing due to the valve?		* The valve is to be used in a pumping device that requires 1 month of continuous operation. What is the probability of the pump failing due to the valve?


	Enter the data set in a Weibull++ standard folio, as follows:		Enter the data set in a Weibull++ standard folio, as follows:

Richard House at 05:58, 6 August 2012

2012-08-06T05:58:39Z

← Older revision		Revision as of 05:58, 6 August 2012
Line 27:		Line 27:
	Enter the data set in a Weibull++ standard folio, as follows:		Enter the data set in a Weibull++ standard folio, as follows:

	[[Image:Logistic Distribution Exmaple 1 Data.png~~\|thumb~~\|center\|600px\| ]]		[[Image:Logistic Distribution Exmaple 1 Data.png\|center\|600px\| ]]

	The computed parameters for maximum likelihood are:		The computed parameters for maximum likelihood are:
Line 39:		Line 39:
	The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:		The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:

	[[Image:Logistic Distribution Exmaple 1 QCP Reliable Life.png~~\|thumb~~\|center\|500px\| ]]		[[Image:Logistic Distribution Exmaple 1 QCP Reliable Life.png\|center\|500px\| ]]


Line 45:		Line 45:


	[[Image:Logistic Distribution Exmaple 1 QCP Reliability.png~~\|thumb~~\|center\|500px\| ]]		[[Image:Logistic Distribution Exmaple 1 QCP Reliability.png\|center\|500px\| ]]