Weibull Distribution RRX Example - Revision history

Lisa Hacker at 21:46, 18 September 2023

2023-09-18T21:46:14Z

← Older revision		Revision as of 21:46, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This examples also appears in the [~~[The_Weibull_Distribution\|~~Life ~~Data Analysis Reference book]~~].''		''This examples also appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference].''
	</noinclude>		</noinclude>

Richard House at 18:33, 25 September 2012

2012-09-25T18:33:51Z

← Older revision		Revision as of 18:33, 25 September 2012
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	2. The conditional reliability is given by:		2. The conditional reliability is given by:

	::<math>R(t\|T)=\frac{R(T+t)}{R(T)}</math>		::<math>R(t\|T)=\frac{R(T+t)}{R(T)}\,\!</math>

	or:		or:

	::<math>\hat{R}(10hr\|30hr)=\frac{\hat{R}(10+30)}{\hat{R}(30)}=\frac{\hat{R}(40)}{\hat{R}(30)}</math>		::<math>\hat{R}(10hr\|30hr)=\frac{\hat{R}(10+30)}{\hat{R}(30)}=\frac{\hat{R}(40)}{\hat{R}(30)}\,\!</math>

Chris Kahn at 04:31, 23 August 2012

2012-08-23T04:31:39Z

← Older revision		Revision as of 04:31, 23 August 2012
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	</noinclude>		</noinclude>

	Assume that ~~six~~ identical units are being tested. The failure times are: 93, 34, 16, 120, 53 and 75 hours.		Assume that 6 identical units are being tested. The failure times are: 93, 34, 16, 120, 53 and 75 hours.

	1. What is the unreliability of the units for a mission duration of 30 hours, starting the mission at age zero?		1. What is the unreliability of the units for a mission duration of 30 hours, starting the mission at age zero?

Chris Kahn at 04:20, 23 August 2012

2012-08-23T04:20:33Z

← Older revision		Revision as of 04:20, 23 August 2012
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	Select the '''Prob. of Failure''' calculation option and enter 30 hours in the '''Mission End Time''' field.		Select the '''Prob. of Failure''' calculation option and enter 30 hours in the '''Mission End Time''' field.

	[[Image: QCP Result.png\|center\|~~550px~~]]		[[Image: QCP Result.png\|center\|650px]]

	Note that the results in QCP vary according to the parameter estimation method used. The above results are obtained using RRX.		Note that the results in QCP vary according to the parameter estimation method used. The above results are obtained using RRX.
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	Again, the QCP can provide this result directly and more accurately than the plot.		Again, the QCP can provide this result directly and more accurately than the plot.

	[[Image: Conditional R.png\|center\|~~550px~~]]		[[Image: Conditional R.png\|center\|650px]]

	3. To use the QCP to solve for the longest mission that this product should undertake for a reliability of 90%, choose '''Reliable Life''' and enter '''0.9''' for the required reliability. The result is 15.9933 hours.		3. To use the QCP to solve for the longest mission that this product should undertake for a reliability of 90%, choose '''Reliable Life''' and enter '''0.9''' for the required reliability. The result is 15.9933 hours.

	[[Image: Reliable Life.png\|center\|~~550px~~]]		[[Image: Reliable Life.png\|center\|650px]]

Chris Kahn at 04:18, 23 August 2012

2012-08-23T04:18:45Z

← Older revision		Revision as of 04:18, 23 August 2012
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	[[Image: RS Draw.png\|center\|650px]]		[[Image: RS Draw.png\|center\|650px]]

	Using this first method, enter either the screen plot or the printed plot with T = 30 hours, go up vertically to the straight line fitted to the data, then go horizontally to the ordinate, and read off . ~~Then, a~~ good estimate of the ~~sought~~ unreliability is 23%. (Also, the reliability estimate is 1.0 - 0.23 = 0.77 or 77%.)		Using this first method, enter either the screen plot or the printed plot with T = 30 hours, go up vertically to the straight line fitted to the data, then go horizontally to the ordinate, and read off the result. A good estimate of the unreliability is 23%. (Also, the reliability estimate is 1.0 - 0.23 = 0.77 or 77%.)

	The second method involves the use of the Quick Calculation Pad (QCP).		The second method involves the use of the Quick Calculation Pad (QCP).
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	[[Image: Conditional R.png\|center\|550px]]		[[Image: Conditional R.png\|center\|550px]]

	3. ~~Using~~ the QCP ~~again~~, choose '''Reliable Life''' and enter ~~the Required Reliability, 0.90, and click~~ '''~~Calculate~~'''. The result is 15.9933 hours.		3. To use the QCP to solve for the longest mission that this product should undertake for a reliability of 90%, choose '''Reliable Life''' and enter '''0.9''' for the required reliability. The result is 15.9933 hours.

	[[Image: Reliable Life.png\|center\|550px]]		[[Image: Reliable Life.png\|center\|550px]]

Chris Kahn at 04:15, 23 August 2012

2012-08-23T04:15:47Z

← Older revision		Revision as of 04:15, 23 August 2012
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	Then, we investigate several methods of solution for this problem. The first, and more laborious, method is to extract the information directly from the plot. You may do this with either the screen plot in RS Draw or the printed copy of the plot. (When extracting information from the screen plot in '''RS Draw''', note that the translated axis position of your mouse is always shown on the bottom right corner.)		Then, we investigate several methods of solution for this problem. The first, and more laborious, method is to extract the information directly from the plot. You may do this with either the screen plot in RS Draw or the printed copy of the plot. (When extracting information from the screen plot in '''RS Draw''', note that the translated axis position of your mouse is always shown on the bottom right corner.)

	[[Image: RS Draw.png\|center\|~~450px~~]]		[[Image: RS Draw.png\|center\|650px]]

	Using this first method, enter either the screen plot or the printed plot with T = 30 hours, go up vertically to the straight line fitted to the data, then go horizontally to the ordinate, and read off . Then, a good estimate of the sought unreliability is 23%. (Also, the reliability estimate is 1.0 - 0.23 = 0.77 or 77%.)		Using this first method, enter either the screen plot or the printed plot with T = 30 hours, go up vertically to the straight line fitted to the data, then go horizontally to the ordinate, and read off . Then, a good estimate of the sought unreliability is 23%. (Also, the reliability estimate is 1.0 - 0.23 = 0.77 or 77%.)

Chris Kahn at 04:15, 23 August 2012

2012-08-23T04:15:13Z

← Older revision		Revision as of 04:15, 23 August 2012
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	3. What is the longest mission that this product should undertake for a reliability of 90%?		3. What is the longest mission that this product should undertake for a reliability of 90%?


	'''Solution'''		'''Solution'''

Chris Kahn at 04:14, 23 August 2012

2012-08-23T04:14:58Z

Chris Kahn at 01:11, 23 August 2012

2012-08-23T01:11:23Z

@@ Line 3: / Line 3: @@
 </noinclude>
-Assume that 6 identical units are being tested. The failure times are: 93, 34, 16, 120, 53 and 75. What is the unreliability of the units for a mission duration of 30 hours, starting the mission at age zero? To replicate the results in this reference with Weibull++, choose RRX (Rank Regression on X) as the calculation method.
+Assume that 6 identical units are being tested. The failure times are: 93, 34, 16, 120, 53 and 75.
 '''Solution'''
-First, we use Weibull++ to obtain the parameters using RRX.
+. First, we use Weibull++ to obtain the parameters using RRX.
 Then, we investigate several methods of solution for this problem. The first, and more laborious, method is to extract the information directly from the plot. You may do this with either the screen plot in RS Draw or the printed copy of the plot. (When extracting information from the screen plot in '''RS Draw''', note that the translated axis position of your mouse is always shown on the bottom right corner.)
@@ Line 22: / Line 28: @@
 Note that the results in QCP vary according to the parameter estimation method used. The above results are obtained using RRX.

Chris Kahn: moved Weibull Distribution Unreliability RRX Example to Weibull Distribution RRX Example

2012-08-23T00:49:12Z

moved Weibull Distribution Unreliability RRX Example to Weibull Distribution RRX Example

← Older revision	Revision as of 00:49, 23 August 2012
(No difference)

← Older revision		Revision as of 04:14, 23 August 2012
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	</noinclude>		</noinclude>

	Assume that 6 identical units are being tested. The failure times are: 93, 34, 16, 120, 53 and 75.		Assume that six identical units are being tested. The failure times are: 93, 34, 16, 120, 53 and 75 hours.

	1. What is the unreliability of the units for a mission duration of 30 hours, starting the mission at age zero? ~~(To replicate the results in this reference with Weibull++, choose RRX (Rank Regression on X) as the calculation method.)~~		1. What is the unreliability of the units for a mission duration of 30 hours, starting the mission at age zero?

	2. What is the reliability for a ~~new~~ mission of ~~t =~~ 10 hours ~~duration~~, starting the new mission at the age of T = 30 hours?		2. What is the reliability for a mission duration of 10 hours, starting the new mission at the age of T = 30 hours?

	3. What is the longest mission that this ~~equipment~~ should undertake for a reliability of 90%?		3. What is the longest mission that this product should undertake for a reliability of 90%?

	'''Solution'''		'''Solution'''
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	The second method involves the use of the Quick Calculation Pad (QCP).		The second method involves the use of the Quick Calculation Pad (QCP).

	Select '''Prob. of Failure''' calculation option and enter 30 hours in the Mission End Time ~~box. Click~~ '''~~Calculate''' to get the result~~.		Select the '''Prob. of Failure''' calculation option and enter 30 hours in the '''Mission End Time''' field.

	[[Image: QCP Result.png\|center\|550px]]		[[Image: QCP Result.png\|center\|550px]]
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	Again, the ~~'''Quick Calculation Pad'''~~ can provide this result directly and more accurately than the plot.		Again, the QCP can provide this result directly and more accurately than the plot.

	[[Image: Conditional R.png\|center\|550px]]		[[Image: Conditional R.png\|center\|550px]]

	3. Using the ~~'''~~QCP~~'''~~ again, choose '''Reliable Life''' and enter the Required Reliability, 0.90, and click '''Calculate'''. The result is 15.9933 hours.		3. Using the QCP again, choose '''Reliable Life''' and enter the Required Reliability, 0.90, and click '''Calculate'''. The result is 15.9933 hours.

	[[Image: Reliable Life.png\|center\|550px]]		[[Image: Reliable Life.png\|center\|550px]]