Exponential Distribution Characteristics - Revision history

Lisa Hacker at 21:41, 18 September 2023

2023-09-18T21:41:12Z

← Older revision		Revision as of 21:41, 18 September 2023
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	<noinclude>{{Navigation box}}		<noinclude>{{Navigation box}}
	''This article also appears in the [~~[The_Exponential_Distribution\|~~Life ~~Data Analysis Reference]~~] and [~~[Distributions_Used_in_Accelerated_Testing\|~~Accelerated ~~Life Testing Data Analysis Reference]~~] ~~books~~.'' </noinclude>		''This article also appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference] and [https://help.reliasoft.com/reference/accelerated_life_testing_data_analysis Accelerated life testing reference].'' </noinclude>

	The primary trait of the exponential distribution is that it is used for modeling the behavior of items with a constant failure rate. It has a fairly simple mathematical form, which makes it fairly easy to manipulate. Unfortunately, this fact also leads to the use of this model in situations where it is not appropriate. For example, it would not be appropriate to use the exponential distribution to model the reliability of an automobile. The constant failure rate of the exponential distribution would require the assumption that the automobile would be just as likely to experience a breakdown during the first mile as it would during the one-hundred-thousandth mile. Clearly, this is not a valid assumption. However, some inexperienced practitioners of reliability engineering and life data analysis will overlook this fact, lured by the siren-call of the exponential distribution's relatively simple mathematical models.		The primary trait of the exponential distribution is that it is used for modeling the behavior of items with a constant failure rate. It has a fairly simple mathematical form, which makes it fairly easy to manipulate. Unfortunately, this fact also leads to the use of this model in situations where it is not appropriate. For example, it would not be appropriate to use the exponential distribution to model the reliability of an automobile. The constant failure rate of the exponential distribution would require the assumption that the automobile would be just as likely to experience a breakdown during the first mile as it would during the one-hundred-thousandth mile. Clearly, this is not a valid assumption. However, some inexperienced practitioners of reliability engineering and life data analysis will overlook this fact, lured by the siren-call of the exponential distribution's relatively simple mathematical models.

Nicolette Young: /* The Effect of lambda and gamma on the Failure Rate Function */

2015-12-17T15:14:03Z

The Effect of lambda and gamma on the Failure Rate Function

← Older revision		Revision as of 15:14, 17 December 2015
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	:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.		:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.

	[[Image: effect_on_failure_rate_new.png\|center\|~~550px~~\|]]		[[Image: effect_on_failure_rate_new.png\|center\|525px\|]]

Nicolette Young: /* The Effect of lambda and gamma on the Failure Rate Function */

2015-12-17T15:13:08Z

The Effect of lambda and gamma on the Failure Rate Function

← Older revision		Revision as of 15:13, 17 December 2015
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	:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.		:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.

	[[Image: effect_on_failure_rate_new.png\|center\|~~500px~~\|]]		[[Image: effect_on_failure_rate_new.png\|center\|550px\|]]

Lisa Hacker: /* The Effect of lambda and gamma on the Failure Rate Function */

2014-02-10T23:19:21Z

The Effect of lambda and gamma on the Failure Rate Function

← Older revision		Revision as of 23:19, 10 February 2014
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	:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.		:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.

	[[Image: effect_on_failure_rate_new.png\|center\|~~400px~~\|]]		[[Image: effect_on_failure_rate_new.png\|center\|500px\|]]

Lisa Hacker at 23:19, 10 February 2014

2014-02-10T23:19:07Z

← Older revision		Revision as of 23:19, 10 February 2014
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	:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.		:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.

	[[Image: effect_on_failure_rate_new.png\|center\|~~600px~~\|]]		[[Image: effect_on_failure_rate_new.png\|center\|400px\|]]

Harry Guo: /* The Effect of lambda and gamma on the Failure Rate Function */

2014-02-10T18:28:11Z

The Effect of lambda and gamma on the Failure Rate Function

← Older revision		Revision as of 18:28, 10 February 2014
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	:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.		:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.

	[[Image: ~~effect_on_failure_rate~~.png\|center\|600px\|]]		[[Image: effect_on_failure_rate_new.png\|center\|600px\|]]

Harry Guo: /* The Effect of lambda and gamma on the Failure Rate Function */

2014-02-10T18:26:13Z

The Effect of lambda and gamma on the Failure Rate Function

← Older revision		Revision as of 18:26, 10 February 2014
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	:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.		:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.

	[[Image: effect_on_failure_rate.png\|center\|~~400px~~\|]]		[[Image: effect_on_failure_rate.png\|center\|600px\|]]

Harry Guo: /* The Effect of lambda and gamma on the Failure Rate Function */

2014-02-10T18:25:25Z

The Effect of lambda and gamma on the Failure Rate Function

← Older revision		Revision as of 18:25, 10 February 2014
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	:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.		:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.

	Image: effect_on_failure_rate.png\|center\|400px\|]]		[[Image: effect_on_failure_rate.png\|center\|400px\|]]

Harry Guo: /* The Effect of lambda and gamma on the Failure Rate Function */

2014-02-10T18:25:09Z

The Effect of lambda and gamma on the Failure Rate Function

← Older revision		Revision as of 18:25, 10 February 2014
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	:*The 1-parameter exponential failure rate function is constant and starts at <math>t=0\,\!</math>.		:*The 1-parameter exponential failure rate function is constant and starts at <math>t=0\,\!</math>.
	:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.		:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.

			Image: effect_on_failure_rate.png\|center\|400px\|]]

Harry Guo at 18:13, 10 February 2014

2014-02-10T18:13:51Z

← Older revision		Revision as of 18:13, 10 February 2014
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	===The Effect of lambda and gamma on the Failure Rate Function===		===The Effect of lambda and gamma on the Failure Rate Function===
	:*The 1-parameter exponential failure rate function is constant and starts at <math>t=0\,\!</math>.		:*The 1-parameter exponential failure rate function is constant and starts at <math>t=0\,\!</math>.
	:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\~~labmda~~\,\!</math>.		:*The 2-parameter exponential failure rate function remains at the value of 0 for <math>t=0\,\!</math> up to <math>t=\gamma \,\!</math>, and then keeps at the constant value of <math>\lambda\,\!</math>.