Template:Effect of beta on the cdf - Revision history

Lisa Hacker: Redirected page to Weibull Distribution Characteristics

2012-08-07T02:52:59Z

Redirected page to Weibull Distribution Characteristics

← Older revision		Revision as of 02:52, 7 August 2012
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	~~'''The Effect of <span class="texhtml">β</span> on the <math>cdf</math> and Reliability Function'''~~		#REDIRECT [[Weibull Distribution Characteristics]]


	[[~~Image:WB.8 effect of weibull.png\|center\|300px\| Effect on <math>\beta</math> on the <math>cdf</math> on the~~ Weibull ~~probability plot with a fixed value of <math>\eta</math>~~ ]]

	The above figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. The following figure shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.

	~~[[Image:WB.8 weibull reliability.png\|center\|250px\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]~~
	~~<br>~~

	~~:*<span class="texhtml">''R''(''t'')</span> decreases sharply and monotonically for <span class="texhtml">0 < β < 1</span> and is convex.~~
	~~:*For <span class="texhtml">β = 1</span>, <span class="texhtml">''R''(''t'')</span> decreases monotonically but less sharply than for <span class="texhtml">0 < β < 1</span> and is convex.~~
	~~:*For <span class="texhtml">β > 1</span>, <span class="texhtml">''R''(''t'')</span> decreases as increases. As wear-out sets in, the curve goes through an inflection point and decreases sharply.~~

	~~<br>~~

Nicolette Young at 18:01, 25 April 2012

2012-04-25T18:01:18Z

← Older revision		Revision as of 18:01, 25 April 2012
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	[[Image:WB.8 effect of weibull.png\|center\|~~400px~~\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]		[[Image:WB.8 effect of weibull.png\|center\|300px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]

	The above figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. The following figure shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.		The above figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. The following figure shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.

	[[Image:WB.8 weibull reliability.png\|center\|~~400px~~\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]		[[Image:WB.8 weibull reliability.png\|center\|250px\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]
	<br>		<br>

Chris Kahn at 22:59, 24 April 2012

2012-04-24T22:59:03Z

← Older revision		Revision as of 22:59, 24 April 2012
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	[[Image:WB.8 effect of weibull.png\|center\|400px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]		[[Image:WB.8 effect of weibull.png\|center\|400px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]

	The above ~~Figure~~ shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. The ~~followng~~ figure shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.		The above figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. The following figure shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.

	[[Image:WB.8 weibull reliability.png\|center\|400px\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]		[[Image:WB.8 weibull reliability.png\|center\|400px\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]

Nicolette Young at 16:36, 15 March 2012

2012-03-15T16:36:50Z

← Older revision		Revision as of 16:36, 15 March 2012
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	[[Image:~~lda6~~.2.~~gif\|thumb~~\|center\|~~350px~~\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]		[[Image:WB.8 effect of weibull.png\|center\|400px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]

	The above Figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. The followng figure shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.		The above Figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. The followng figure shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.

	[[Image:~~lda6~~.3.~~gif\|thumb~~\|center\|~~350px~~\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]		[[Image:WB.8 weibull reliability.png\|center\|400px\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]
	<br>		<br>

Harry Guo at 21:49, 9 February 2012

2012-02-09T21:49:00Z

← Older revision		Revision as of 21:49, 9 February 2012
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	[[Image:lda6.2.gif\|thumb\|center\|350px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]		[[Image:lda6.2.gif\|thumb\|center\|350px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]

	The above Figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. ~~Figure 6-3~~ shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.		The above Figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. The followng figure shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.

	[[Image:lda6.3.gif\|thumb\|center\|350px\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]		[[Image:lda6.3.gif\|thumb\|center\|350px\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]

Harry Guo at 21:41, 9 February 2012

2012-02-09T21:41:49Z

← Older revision		Revision as of 21:41, 9 February 2012
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	'''The Effect of <span class="texhtml">β</span> on the <math>cdf</math> and Reliability Function''''		'''The Effect of <span class="texhtml">β</span> on the <math>cdf</math> and Reliability Function'''

Harry Guo at 21:41, 9 February 2012

2012-02-09T21:41:34Z

← Older revision		Revision as of 21:41, 9 February 2012
Line 4:		Line 4:
	[[Image:lda6.2.gif\|thumb\|center\|350px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]		[[Image:lda6.2.gif\|thumb\|center\|350px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]

	Figure ~~6-2~~ shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. Figure 6-3 shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.		The above Figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. Figure 6-3 shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.

	[[Image:lda6.3.gif\|thumb\|center\|350px\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]		[[Image:lda6.3.gif\|thumb\|center\|350px\| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]
	<br>		<br>

	:*<span class="texhtml">''R''(''T'')</span> decreases sharply and monotonically for <span class="texhtml">0 < β < 1</span> and is convex.		:*<span class="texhtml">''R''(''t'')</span> decreases sharply and monotonically for <span class="texhtml">0 < β < 1</span> and is convex.
	:*For <span class="texhtml">β = 1</span>, <span class="texhtml">''R''(''T'')</span> decreases monotonically but less sharply than for <span class="texhtml">0 < β < 1</span> and is convex.		:*For <span class="texhtml">β = 1</span>, <span class="texhtml">''R''(''t'')</span> decreases monotonically but less sharply than for <span class="texhtml">0 < β < 1</span> and is convex.
	:*For <span class="texhtml">β > 1</span>, <span class="texhtml">''R''(''T'')</span> decreases as increases. As wear-out sets in, the curve goes through an inflection point and decreases sharply.		:*For <span class="texhtml">β > 1</span>, <span class="texhtml">''R''(''t'')</span> decreases as increases. As wear-out sets in, the curve goes through an inflection point and decreases sharply.

	<br>		<br>

Harry Guo: /* The Effect of β on the cdf and Reliability Function */

2012-02-09T21:08:33Z

The Effect of β on the cdf and Reliability Function

← Older revision		Revision as of 21:08, 9 February 2012
Line 1:		Line 1:
	~~====~~ The Effect of <span class="texhtml">β</span> on the <math>cdf</math> and Reliability Function ~~====~~		'''The Effect of <span class="texhtml">β</span> on the <math>cdf</math> and Reliability Function''''


	[[Image:lda6.2.gif\|thumb\|center\|350px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]		[[Image:lda6.2.gif\|thumb\|center\|350px\| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]

Nicolette Young: Created page with '==== The Effect of $β$ on the $cdf$ and Reliability Function ==== [[Image:lda6.2.gif|thumb|center|350px| Effect on $\beta$ on t…'

2012-02-08T19:43:08Z

Created page with '==== The Effect of β on the <math>cdf</math> and Reliability Function ==== [[Image:lda6.2.gif|thumb|center|350px| Effect on <math>\beta</math> on t…'

New page

==== The Effect of β on the <math>cdf</math> and Reliability Function ====

[[Image:lda6.2.gif|thumb|center|350px| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]

Figure 6-2 shows the effect of the value of β on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of η. Figure 6-3 shows the effects of these varied values of β on the reliability plot, which is a linear analog of the probability plot.

[[Image:lda6.3.gif|thumb|center|350px| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]
 

:*''R''(''T'') decreases sharply and monotonically for 0 < β < 1 and is convex.
:*For β = 1, ''R''(''T'') decreases monotonically but less sharply than for 0 < β < 1 and is convex.
:*For β > 1, ''R''(''T'') decreases as increases. As wear-out sets in, the curve goes through an inflection point and decreases sharply.

Template:Effect of beta on the cdf - Revision history

Lisa Hacker: Redirected page to Weibull Distribution Characteristics

Nicolette Young at 18:01, 25 April 2012

Chris Kahn at 22:59, 24 April 2012

Nicolette Young at 16:36, 15 March 2012

Harry Guo at 21:49, 9 February 2012

Harry Guo at 21:41, 9 February 2012

Harry Guo at 21:41, 9 February 2012

Harry Guo: /* The Effect of β on the cdf and Reliability Function */

Nicolette Young: Created page with '==== The Effect of β on the cdf and Reliability Function ==== [[Image:lda6.2.gif|thumb|center|350px| Effect on \beta on t…'

Nicolette Young: Created page with '==== The Effect of $β$ on the $cdf$ and Reliability Function ==== [[Image:lda6.2.gif|thumb|center|350px| Effect on $\beta$ on t…'