Appendix A: Brief Statistical Background - Revision history

Lisa Hacker at 19:22, 15 September 2023

2023-09-15T19:22:42Z

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	{{template:ALTABOOK ~~SUB~~\|Appendix A\|Brief Statistical Background}}		{{template:ALTABOOK\|Appendix A\|Brief Statistical Background}}
	In this appendix, we attempt to provide a brief elementary introduction to the most common and fundamental statistical equations and definitions used in reliability engineering and life data analysis. The equations and concepts presented in this appendix are used extensively throughout this reference.		In this appendix, we attempt to provide a brief elementary introduction to the most common and fundamental statistical equations and definitions used in reliability engineering and life data analysis. The equations and concepts presented in this appendix are used extensively throughout this reference.
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Lisa Hacker: /* Basic Statistical Definitions */

2012-08-01T09:42:34Z

Basic Statistical Definitions

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	In this appendix, we attempt to provide a brief elementary introduction to the most common and fundamental statistical equations and definitions used in reliability engineering and life data analysis. The equations and concepts presented in this appendix are used extensively throughout this reference.		In this appendix, we attempt to provide a brief elementary introduction to the most common and fundamental statistical equations and definitions used in reliability engineering and life data analysis. The equations and concepts presented in this appendix are used extensively throughout this reference.
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	~~=Basic Statistical Definitions=~~
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	{{:Brief Statistical Background}}		{{:Brief Statistical Background}}

Lisa Hacker: Replaced content with '{{template:ALTABOOK SUB|Appendix A|Brief Statistical Background}} In this appendix, we attempt to provide a brief elementary introduction to the most common and fundamental s…'

2012-08-01T09:42:13Z

Replaced content with '{{template:ALTABOOK SUB|Appendix A|Brief Statistical Background}} In this appendix, we attempt to provide a brief elementary introduction to the most common and fundamental s…'

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Lisa Hacker at 09:17, 1 August 2012

2012-08-01T09:17:41Z

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Kate Racaza at 11:44, 2 July 2012

2012-07-02T11:44:17Z

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	{{template:ALTABOOK\|A}}		{{template:ALTABOOK SUB\|Appendix A\|Brief Statistical Background}}

	In this appendix we attempt to provide a brief elementary introduction to the most common and fundamental statistical equations and definitions used in reliability engineering and life data analysis. The equations and concepts presented in this appendix are used extensively throughout this reference.		In this appendix we attempt to provide a brief elementary introduction to the most common and fundamental statistical equations and definitions used in reliability engineering and life data analysis. The equations and concepts presented in this appendix are used extensively throughout this reference.

Athanasios Gerokostopoulos: /* Approximate Confidence Intervals on the Parameters */

2012-02-27T23:10:10Z

Approximate Confidence Intervals on the Parameters

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	The same procedure can be repeated for the case of a two or more parameter distribution. Lloyd and Lipow [24] elaborate on this procedure.		The same procedure can be repeated for the case of a two or more parameter distribution. Lloyd and Lipow [[Reference Appendix D: References\|[24]]] elaborate on this procedure.
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Athanasios Gerokostopoulos: /* Confidence Limits Determination */

2012-02-27T23:09:40Z

Confidence Limits Determination

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	=Confidence Limits Determination=		=Confidence Limits Determination=
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	This section presents an overview of the theory on obtaining approximate confidence bounds on suspended (multiply censored) data. The methodology used is the so-called Fisher Matrix Bounds, described in Nelson [27] and Lloyd and Lipow [24].		This section presents an overview of the theory on obtaining approximate confidence bounds on suspended (multiply censored) data. The methodology used is the so-called Fisher Matrix Bounds, described in Nelson [[Reference Appendix D: References\|[27]]] and Lloyd and Lipow [[Reference Appendix D: References\|[24]]].
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Athanasios Gerokostopoulos: /* Most Commonly Used Distributions */

2012-02-27T23:08:30Z

Most Commonly Used Distributions

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	==Most Commonly Used Distributions==		==Most Commonly Used Distributions==
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	There are many different lifetime distributions that can be used. ReliaSoft [31] presents a thorough overview of lifetime distributions. Leemis [22] and others also present good overviews of many of these distributions. The three distributions used in ALTA, the 1-parameter exponential, 2-parameter Weibull, and the lognormal, are presented in greater detail [[Distributions used in Accelerated Testing\|here]].		There are many different lifetime distributions that can be used. ReliaSoft [[Reference Appendix D: References\|[31]]] presents a thorough overview of lifetime distributions. Leemis [[Reference Appendix D: References\|[22]]] and others also present good overviews of many of these distributions. The three distributions used in ALTA, the 1-parameter exponential, 2-parameter Weibull, and the lognormal, are presented in greater detail [[Distributions used in Accelerated Testing\|here]].

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Athanasios Gerokostopoulos: /* The Failure Rate Function */

2012-02-27T23:07:51Z

The Failure Rate Function

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	==The Failure Rate Function==		==The Failure Rate Function==
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	The failure rate function enables the determination of the number of failures occurring per unit time. Omitting the derivation, see [18; Ch. 4], the failure rate is mathematically given as:		The failure rate function enables the determination of the number of failures occurring per unit time. Omitting the derivation, see [[Reference Appendix D: References\|[18; Ch. 4]]], the failure rate is mathematically given as:

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Athanasios Gerokostopoulos at 18:35, 23 February 2012

2012-02-23T18:35:33Z

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	Reliability bounds (Type 2) return the confidence bounds by determining the confidence intervals around <math>\widehat{\lambda }</math> and substituting into the above equation.		Reliability bounds (Type 2) return the confidence bounds by determining the confidence intervals around <math>\widehat{\lambda }</math> and substituting into the above equation.

			[[Category: Completed Theoretical Review]]