ACME Example - Revision history

Kate Racaza at 04:08, 15 August 2012

2012-08-15T04:08:02Z

← Older revision		Revision as of 04:08, 15 August 2012
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	~~===ACME Example===~~		<noinclude>{{Banner ALTA Examples}}</noinclude>
	ACME manufacturing has implemented an accelerated testing program for their new design. A total of 40 units were tested at four different pressure levels. The operating stress level is 170 psi.		ACME manufacturing has implemented an accelerated life testing program for their new product design. A total of 40 units were tested at four different pressure levels. The operating stress level is 170 psi. The following table shows the data from the test. Determine the parameters of the inverse power law Weibull model and obtain the use level probability plot with 90% 2-sided confidence bounds on time.


	{\|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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	\|}		\|}

	~~Do the following:~~

	~~1) Determine the parameters of the inverse power law Weibull model.~~

	~~2) Obtain the use level probability plot with 90% 2-sided confidence bounds on time.~~

	~~3) Obtain the Life vs. Stress plot with 90% 2-sided confidence bounds.~~

	~~====Solution====~~		The parameters of the IPL-Weibull model are estimated to be:

	~~1) The parameters of the IPL-Weibull model are estimated to be:~~

	::<math>\begin{align}		::<math>\begin{align}
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	\end{align}</math>		\end{align}</math>

	~~2) The use level probability plot is shown next.~~

	[[Image:new_7.gif~~\|thumb~~\|center\|550px\|The probability plot at a use stress level.]]		The use level probability plot is shown next.


			[[Image:new_7.gif\|center\|550px\|The probability plot at a use stress level.]]


	~~The~~ confidence bounds on time are the Type 1 bounds (Time Bounds) ~~in ALTA~~.		In ALTA, the confidence bounds on time are the Type 1 bounds (Time Bounds).

	~~[[Image:new_9.gif\|thumb\|center\|550px\|The probability plot at a use stress level with 90% Type I confidence bounds.]]~~

	~~3) Similarly, the Life vs~~. ~~Stress~~ plot with ~~the~~ confidence bounds ~~can be obtained~~.		[[Image:new_9.gif\|center\|550px\|The probability plot at a use stress level with 90% Type I confidence bounds.]]

Kate Racaza: moved Template:ACME Example to ACME Example: incorrect namespace

2012-08-15T04:03:55Z

moved Template:ACME Example to ACME Example: incorrect namespace

← Older revision	Revision as of 04:03, 15 August 2012
(No difference)

Richard House at 07:01, 9 August 2012

2012-08-09T07:01:11Z

← Older revision		Revision as of 07:01, 9 August 2012
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	ACME manufacturing has implemented an accelerated testing program for their new design. A total of 40 units were tested at four different pressure levels. The operating stress level is 170 psi.		ACME manufacturing has implemented an accelerated testing program for their new design. A total of 40 units were tested at four different pressure levels. The operating stress level is 170 psi.

	~~<br>~~		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	{\|~~style=~~ border="1" align="center"
	\|-		\|-
	!Stress Level, psi		!Stress Level, psi
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	\| \|\|544\|\|288\|\|228\|\|140		\| \|\|544\|\|288\|\|228\|\|140
	\|}		\|}


	Do the following:		Do the following:


	1) Determine the parameters of the inverse power law Weibull model.		1) Determine the parameters of the inverse power law Weibull model.


	2) Obtain the use level probability plot with 90% 2-sided confidence bounds on time.		2) Obtain the use level probability plot with 90% 2-sided confidence bounds on time.


	3) Obtain the Life vs. Stress plot with 90% 2-sided confidence bounds.		3) Obtain the Life vs. Stress plot with 90% 2-sided confidence bounds.

	~~<br>~~
	====Solution====		====Solution====


	1) The parameters of the IPL-Weibull model are estimated to be:		1) The parameters of the IPL-Weibull model are estimated to be:


	::<math>\begin{align}		::<math>\begin{align}
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	\end{align}</math>		\end{align}</math>

			2) The use level probability plot is shown next.

			[[Image:new_7.gif\|thumb\|center\|550px\|The probability plot at a use stress level.]]

	~~2) The use level probability plot is shown next.~~
	~~<br>~~
	~~<br>~~
	~~[[Image:new_7.gif\|thumb\|center\|500px\|The probability plot at a use stress level.]]~~
	~~<br>~~
	The confidence bounds on time are the Type 1 bounds (Time Bounds) in ALTA.		The confidence bounds on time are the Type 1 bounds (Time Bounds) in ALTA.

	~~<br>~~		[[Image:new_9.gif\|thumb\|center\|550px\|The probability plot at a use stress level with 90% Type I confidence bounds.]]
	[[Image:new_9.gif\|thumb\|center\|~~500px~~\|The probability plot at a use stress level with 90% Type I confidence bounds.]]
	~~<br>~~

	3) Similarly, the Life vs. Stress plot with the confidence bounds can be obtained.		3) Similarly, the Life vs. Stress plot with the confidence bounds can be obtained.

	~~<br>~~

Chris Kahn: /* Solution */

2012-06-25T13:21:29Z

Solution

← Older revision		Revision as of 13:21, 25 June 2012
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	<br>		<br>
	<br>		<br>
	[[Image:new_7.gif\|thumb\|center\|~~300px~~\|The probability plot at a use stress level.]]		[[Image:new_7.gif\|thumb\|center\|500px\|The probability plot at a use stress level.]]
	<br>		<br>
	The confidence bounds on time are the Type 1 bounds (Time Bounds) in ALTA.		The confidence bounds on time are the Type 1 bounds (Time Bounds) in ALTA.

	<br>		<br>
	[[Image:new_9.gif\|thumb\|center\|~~300px~~\|The probability plot at a use stress level with 90% Type I confidence bounds.]]		[[Image:new_9.gif\|thumb\|center\|500px\|The probability plot at a use stress level with 90% Type I confidence bounds.]]
	<br>		<br>

Athanasios Gerokostopoulos: Created page with '===ACME Example=== ACME manufacturing has implemented an accelerated testing program for their new design. A total of 40 units were tested at four different pressure levels. The …'

2012-03-21T17:43:44Z

Created page with '===ACME Example=== ACME manufacturing has implemented an accelerated testing program for their new design. A total of 40 units were tested at four different pressure levels. The …'

New page

===ACME Example===
ACME manufacturing has implemented an accelerated testing program for their new design. A total of 40 units were tested at four different pressure levels. The operating stress level is 170 psi.

 
{|style= border="1" align="center"
|-
!Stress Level, psi
!220 psi
!230 psi
!240 psi
!250 psi
|-
| ||165||93||72||26
|-
| ||177||106||73||44
|-
| ||238||156||99||63
|-
| ||290||170||124||68
|-
|''Times-to-failure, hr''||320||185||134||69
|-
| ||340||214||150||72
|-
| ||341||220||182||77
|-
| ||380||236||186||96
|-
| ||449||252||190||131
|-
| ||544||288||228||140
|}

Do the following:

1) Determine the parameters of the inverse power law Weibull model.

2) Obtain the use level probability plot with 90% 2-sided confidence bounds on time.

3) Obtain the Life vs. Stress plot with 90% 2-sided confidence bounds.

 
====Solution====

1) The parameters of the IPL-Weibull model are estimated to be:

::<math>\begin{align}

\beta =\ & 3.009236 \\

K=\ & 3.267923E-27 \\

n=\ & 10.218104

\end{align}</math>

2) The use level probability plot is shown next.
 
 
[[Image:new_7.gif|thumb|center|300px|The probability plot at a use stress level.]]
 
The confidence bounds on time are the Type 1 bounds (Time Bounds) in ALTA.

 
[[Image:new_9.gif|thumb|center|300px|The probability plot at a use stress level with 90% Type I confidence bounds.]]
 

3) Similarly, the Life vs. Stress plot with the confidence bounds can be obtained.