Distributions Used in Accelerated Testing - Revision history

Lisa Hacker at 21:39, 18 September 2023

2023-09-18T21:39:01Z

← Older revision		Revision as of 21:39, 18 September 2023
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	In this chapter, we will briefly present three lifetime distributions commonly used in accelerated life test analysis: the exponential, the Weibull and the lognormal distributions. Note that although all forms are mentioned below, ALTA uses the 1-parameter form of the exponential distribution and the 2-parameter form of the Weibull distribution.		In this chapter, we will briefly present three lifetime distributions commonly used in accelerated life test analysis: the exponential, the Weibull and the lognormal distributions. Note that although all forms are mentioned below, ALTA uses the 1-parameter form of the exponential distribution and the 2-parameter form of the Weibull distribution.

	Readers who are interested in a more rigorous overview of these distributions (or for information about other life distributions) can refer to ~~ReliaSoft's~~ Life ~~Data Analysis Reference~~ . For information about the parameter estimation methods, see [[Appendix_B:_Parameter_Estimation\|Appendix B]].<br>		Readers who are interested in a more rigorous overview of these distributions (or for information about other life distributions) can refer to the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]. For information about the parameter estimation methods, see [[Appendix_B:_Parameter_Estimation\|Appendix B]].<br>

	=The Exponential Distribution=		=The Exponential Distribution=

Lisa Hacker at 22:14, 15 September 2023

2023-09-15T22:14:52Z

← Older revision		Revision as of 22:14, 15 September 2023
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	In this chapter, we will briefly present three lifetime distributions commonly used in accelerated life test analysis: the exponential, the Weibull and the lognormal distributions. Note that although all forms are mentioned below, ALTA uses the 1-parameter form of the exponential distribution and the 2-parameter form of the Weibull distribution.		In this chapter, we will briefly present three lifetime distributions commonly used in accelerated life test analysis: the exponential, the Weibull and the lognormal distributions. Note that although all forms are mentioned below, ALTA uses the 1-parameter form of the exponential distribution and the 2-parameter form of the Weibull distribution.

	Readers who are interested in a more rigorous overview of these distributions (or for information about other life distributions) can refer to ReliaSoft's [[Life Data Analysis Reference ~~Book\|Life Data Analysis Reference]]~~. For information about the parameter estimation methods, see [[Appendix_B:_Parameter_Estimation\|Appendix B]].<br>		Readers who are interested in a more rigorous overview of these distributions (or for information about other life distributions) can refer to ReliaSoft's Life Data Analysis Reference . For information about the parameter estimation methods, see [[Appendix_B:_Parameter_Estimation\|Appendix B]].<br>

	=The Exponential Distribution=		=The Exponential Distribution=

Lisa Hacker at 03:30, 7 August 2012

2012-08-07T03:30:14Z

← Older revision		Revision as of 03:30, 7 August 2012
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	{{template:ALTABOOK\|3}}		{{template:ALTABOOK\|3}}
	In this chapter, we will briefly present three lifetime distributions commonly used in accelerated life test analysis: the exponential, the Weibull and the lognormal distributions. Note that ALTA uses the 1-parameter form of the exponential distribution and the 2-parameter form of the Weibull distribution.		In this chapter, we will briefly present three lifetime distributions commonly used in accelerated life test analysis: the exponential, the Weibull and the lognormal distributions. Note that although all forms are mentioned below, ALTA uses the 1-parameter form of the exponential distribution and the 2-parameter form of the Weibull distribution.

	Readers who are interested in a more rigorous overview of these distributions (or for information about other life distributions) can refer to ReliaSoft's [[Life Data Analysis Reference Book\|Life Data Analysis Reference]]. For information about the parameter estimation methods, see [[Appendix_B:_Parameter_Estimation\|Appendix B]].<br>		Readers who are interested in a more rigorous overview of these distributions (or for information about other life distributions) can refer to ReliaSoft's [[Life Data Analysis Reference Book\|Life Data Analysis Reference]]. For information about the parameter estimation methods, see [[Appendix_B:_Parameter_Estimation\|Appendix B]].<br>

Lisa Hacker at 03:29, 7 August 2012

2012-08-07T03:29:42Z

← Older revision		Revision as of 03:29, 7 August 2012
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	{{template:ALTABOOK\|3}}		{{template:ALTABOOK\|3}}
	In this chapter, we will briefly present three lifetime distributions commonly used in accelerated life test analysis: the 1-parameter exponential, the 2-parameter Weibull ~~and the lognormal distributions~~. Readers who are interested in a more rigorous overview (or ~~in different forms of these and~~ other life distributions) can refer to ReliaSoft's [[Life Data Analysis Reference Book\|Life Data Analysis Reference]]. For information about the parameter estimation methods, see [[Appendix_B:_Parameter_Estimation\|Appendix B]].<br>		In this chapter, we will briefly present three lifetime distributions commonly used in accelerated life test analysis: the exponential, the Weibull and the lognormal distributions. Note that ALTA uses the 1-parameter form of the exponential distribution and the 2-parameter form of the Weibull distribution.

			Readers who are interested in a more rigorous overview of these distributions (or for information about other life distributions) can refer to ReliaSoft's [[Life Data Analysis Reference Book\|Life Data Analysis Reference]]. For information about the parameter estimation methods, see [[Appendix_B:_Parameter_Estimation\|Appendix B]].<br>

	=The Exponential Distribution=		=The Exponential Distribution=

Lisa Hacker: /* The Exponential Distribution */

2012-08-07T03:26:22Z

The Exponential Distribution

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 =The Exponential Distribution=
+{{Exponential Distribution Definition}}
 ==Exponential Distribution Functions==
 {{:Exponential Distribution Functions}}
 == Characteristics of the Exponential Distribution==
 {{:Exponential Distribution Characteristics}}

Lisa Hacker: /* The Lognormal Distribution */

2012-08-07T03:15:04Z

The Lognormal Distribution

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 = The Lognormal Distribution =
+{{Lognormal Distribution Definition}}
 ==Lognormal Distribution Functions==
 {{:Lognormal Distribution Functions}}
 ==Characteristics of the Lognormal Distribution==
 {{:Lognormal Distribution Characteristics}}

Lisa Hacker: /* The Weibull Distribution */

2012-08-07T03:13:23Z

The Weibull Distribution

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 = The Weibull Distribution  =
+{{Weibull Distribution Definition}}
 ==Weibull Distribution Functions==
 {{:Weibull Distribution Functions}}
 ==Characteristics of the Weibull Distribution==
 {{:Weibull Distribution Characteristics}}

Lisa Hacker: /* Characteristics */

2012-08-07T02:48:36Z

Characteristics

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 {{:Weibull Distribution Functions}}
-==Characteristics==
+==Characteristics of the Weibull Distribution==
-The characteristics of the 2-parameter Weibull distribution can be exemplified by examining the two parameters, beta,  <math>\beta ,</math>  and eta,  <math>\eta ,</math>  and the effect they have on the  <math>pdf,</math>  reliability and failure rate functions.
+{{:Weibull Distribution Characteristics}}
 = The Lognormal Distribution =

Lisa Hacker: /* Characteristics */

2012-08-07T02:47:24Z

Characteristics

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	==Characteristics==		==Characteristics of the Lognormal Distribution==
	~~:* The lognormal distribution is a distribution skewed to the right.~~		{{:Lognormal Distribution Characteristics}}
	~~:* The <math>pdf</math> starts at zero, increases to its mode, and decreases thereafter.~~
	~~<br>~~
	~~[[Image:chp4pdf.png\|center\|400px\|''Pdf'' of the lognormal distribution.]]~~
	~~<br>~~
	~~<br>~~
	The characteristics of the lognormal distribution can be exemplified by examining the two parameters, the log-mean <math>({{\overline{T}}^{\prime }})</math> and the log-std (<math>{{\sigma }_{{{T}'}}}</math>), and the effect they have on the <math>pdf</math>.
	~~<br>~~
	~~'''Looking at the Log-Mean''' <math>({{\overline{T}}^{\prime }})</math>~~
	:* The parameter, <math>\bar{{T}'}</math>, or the log-mean life, or the <math>MTT{F}'</math> in terms of the logarithm of the <math>{T}'s</math> is also the scale parameter and a unitless number.
	~~:* For the same <math>{{\sigma }_{{{T}'}}}</math> the <math>pdf</math> 's skewness increases as <math>\bar{{T}'}</math> increases.~~
	~~<br>~~
	~~<br>~~
	~~[[Image:chp4pdf2.png\|center\|400px\|''Pdf''~~ of the ~~lognormal distribution with different log-mean values.]]~~
	~~<br>~~


	~~====Looking at the Log-STD <math>({{\sigma }_{{{T}'}}})</math>~~====
	:* The parameter <math>{{\sigma }_{{{T}'}}}</math>, or the standard deviation of the <math>{T}'s</math> in terms of their logarithm or of their <math>{T}'</math>, is also the shape parameter, and not the scale parameter as in the normal <math>pdf</math>. It is a unitless number and assumes only positive values.
	~~:* The degree of skewness increases as <math>{{\sigma }_{{{T}'}}}</math> increases, for a given <math>\bar~~{{~~T}'}</math>.~~
	:* For <math>{{\sigma }~~_{{{T~~}'}}}</math> values significantly greater than 1, the <math>pdf</math> rises very sharply in the beginning (i.e., for very small values of <math>T</math> near zero), and essentially follows the ordinate axis, peaks out early, and then decreases sharply like an exponential <math>pdf</math> or a Weibull <math>pdf</math> with <math>0<\beta <1</math>.
	~~<br>~~
	~~[[Image:chp4pdf3.png\|center\|400px\|''Pdf'' of the lognormal distribution with different log-std values.]]~~
	~~<br>~~

Lisa Hacker: /* Characteristics */

2012-08-07T02:37:18Z

Characteristics

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-== Characteristics  ==
+== Characteristics of the Exponential Distribution==
+{{:Exponential Distribution Characteristics}}
 = The Weibull Distribution  =