Competing Failure Modes - Revision history

Kate Racaza at 16:21, 28 September 2015

2015-09-28T16:21:54Z

← Older revision		Revision as of 16:21, 28 September 2015
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	{{Reference Example}}		{{Reference Example}}

	This example ~~compares~~ the competing failure mode calculations.		This example validates the competing failure mode calculations in Weibull++ standard folios.

Kate Racaza at 16:36, 9 June 2014

2014-06-09T16:36:58Z

← Older revision		Revision as of 16:36, 9 June 2014
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	The data is from ~~the~~ Table 15.1 on page 383 in the book ''Statistical Methods for Reliability Data'' by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.		The data set is from Table 15.1 on page 383 in the book ''Statistical Methods for Reliability Data'' by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.


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	In the book, ~~parameter~~ <math>\mu\,\!</math> and <math>\sigma\,\!</math> are used for the Weibull distribution. They are defined by <math>\mu = ln(\eta)\,\!</math> and <math>\sigma = \frac{1}{\beta}\,\!</math>. The results are:		In the book, parameters <math>\mu\,\!</math> and <math>\sigma\,\!</math> are used for the Weibull distribution. They are defined by <math>\mu = ln(\eta)\,\!</math> and <math>\sigma = \frac{1}{\beta}\,\!</math>. The results are:

	* For failure mode s, the log-likelihood value is -101.36.		* For failure mode s, the log-likelihood value is -101.36.
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	* The ML estimates and the variance covariance matrix for each failure mode ~~are:~~		* The following picture shows the ML estimates and the variance covariance matrix for each failure mode.


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	* The 95% confidence intervals for the parameters of each failure mode ~~are:~~		* The following picture shows the 95% confidence intervals for the parameters of each failure mode.

Kate Racaza at 20:24, 5 June 2014

2014-06-05T20:24:05Z

← Older revision		Revision as of 20:24, 5 June 2014
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	[[Image:CFM_results.png\|center~~\|550px\|~~]]		[[Image:CFM_results.png\|center]]


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

Kate Racaza: Created page with '{{Reference Example}} This example compares the competing failure mode calculations. {{Reference_Example_Heading1}} The data is from the Table 15.1 on page 383 in the book ''…'

2014-06-05T20:23:06Z

Created page with '{{Reference Example}} This example compares the competing failure mode calculations. {{Reference_Example_Heading1}} The data is from the Table 15.1 on page 383 in the book ''…'

New page

{{Reference Example}}

This example compares the competing failure mode calculations.

{{Reference_Example_Heading1}}

The data is from the Table 15.1 on page 383 in the book ''Statistical Methods for Reliability Data'' by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.

{{Reference_Example_Heading2}}

{| {{table}}
!State F/S
!Time to F/S
!Failure Mode
|-
| F||275||w
|-
| F||13||s
|-
| F||147||w
|-
| F||23||s
|-
| F||181||w
|-
| F||30||s
|-
| F||65||s
|-
| F||10||s
|-
| S||300||
|-
| F||173||s
|-
| F||106||s
|-
| S||300||
|-
| S||300||
|-
| F||212||w
|-
| S||300||
|-
| S||300||
|-
| S||300||
|-
| F||2||s
|-
| F||261||s
|-
| F||293||w
|-
| F||88||s
|-
| F||247||s
|-
| F||28||s
|-
| F||143||s
|-
| S||300||
|-
| F||23||s
|-
| S||300||
|-
| F||80||s
|-
| F||245||w
|-
| F||266||w
|-
|
|}

{{Reference_Example_Heading3}}

In the book, parameter <math>\mu\,\!</math> and <math>\sigma\,\!</math> are used for the Weibull distribution. They are defined by <math>\mu = ln(\eta)\,\!</math> and <math>\sigma = \frac{1}{\beta}\,\!</math>. The results are:

* For failure mode s, the log-likelihood value is -101.36.
* For failure mode s, <math>\mu_{s}\,\!</math> = 6.11 and its approximated 95% confidence interval are [5.27, 6.95].
* For failure mode s, <math>\sigma_{s}\,\!</math> = 1.49 and its approximated 95% confidence interval are [0.94, 2.36].
* For failure mode w, the log-likelihood value is -47.16.
* For failure mode w, <math>\mu_{w}\,\!</math> = 5.83 and its approximated 95% confidence interval are [5.62, 6.04].
* For failure mode w, <math>\sigma_{s}\,\!</math> = 0.23 and its approximated 95% confidence interval are [0.12, 0.44].

{{Reference_Example_Heading4}}

* The ML estimates and the variance covariance matrix for each failure mode are:

[[Image:CFM_results.png|center|550px|]]

* The 95% confidence intervals for the parameters of each failure mode are:

[[Image:CFM_bounds.png|center|550px|]]

* In terms of <math>\mu\,\!</math> and <math>\sigma\,\!</math>, the results are:

:* For failure mode s, <math>\mu_{s} = ln(\eta_{s})\,\!</math> = 6.11 and its approximated 95% confidence interval are [5.27, 6.95].
:* For failure mode s, <math>\sigma_{s} = \frac{1}{\beta_{s}}\,\!</math> = 1.49 and its approximated 95% confidence interval are [0.94, 2.36].
:* For failure mode w, <math>\mu_{w} = ln(\eta_{w})\,\!</math> = 5.83 and its approximated 95% confidence interval are [5.62, 6.04].
:* For failure mode w, <math>\sigma_{s} = \frac{1}{\beta_{s}}\,\!</math> = 0.23 and its approximated 95% confidence interval are [0.12, 0.44].

The above results are exactly the same as the results in the book.