Template:Grp model - Revision history

Kate Racaza: Redirected page to Recurrent Event Data Analysis

2012-06-29T07:49:01Z

Redirected page to Recurrent Event Data Analysis

← Older revision		Revision as of 07:49, 29 June 2012
Line 1:		Line 1:
	~~=== The GRP Model ===~~		#REDIRECT [[Recurrent Event Data Analysis]]

	In this model, the concept of virtual age is introduced. Let <math>{{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}</math> represent the successive failure times and let <math>{{x}_{1}},{{x}_{2}},\cdots ,{{x}_{n}}</math> represent the time between failures ( <math>{{t}_{i}}=\sum_{j=1}^{i}{{x}_{j}})</math> . Assume that after each event, actions are taken to improve the system performance. Let <span class="texhtml">''q''</span> be the action effectiveness factor. There are two GRP models:

	~~Type I:~~

	~~::<span class="texhtml">''v''<sub>''i''</sub> = ''v''<sub>''i'' − 1</sub> + ''q''''x'''''<b><sub></sub> = </b>''q'''''t''<sub>''i''</sub></span>~~

	~~Type II:~~

	~~::<math>{{v}_{i}}=q({{v}_{i-1}}+{{x}_{i}})={{q}^{i}}{{x}_{1}}+{{q}^{i-1}}{{x}_{2}}+\cdots +{{x}_{i}}</math>~~

	where <span class="texhtml">''v''<sub>''i''</sub></span> is the virtual age of the system right after <span class="texhtml">''i''</span> th repair. The Type I model assumes that the <span class="texhtml">''i''</span> th repair cannot remove the damage incurred before the ith failure. It can only reduce the additional age <span class="texhtml">''x''<sub>''i''</sub></span> to <span class="texhtml">''q''''x'''''<b><sub>''i''</sub></b></span> . The Type II model assumes that at the <span class="texhtml">''i''</span> th repair, the virtual age has been accumulated to <span class="texhtml">''v''<sub>''i'' − 1</sub> + ''x''<sub>''i''</sub></span> . The <span class="texhtml">''i''</span> th repair will remove the cumulative damage from both current and previous failures by reducing the virtual age to <span class="texhtml">''q''(''v''<sub>''i'' − 1</sub> + ''x''<sub>''i''</sub>)</span> .

	~~The power law function is used to model the rate of recurrence, which is:~~

	~~::<span class="texhtml">λ(''t'') = λβ''t''<sup>β − 1</sup></span>~~

	~~The conditional <span class="texhtml">''pdf''</span> is:~~

	~~::<math>f({{t}_{i}}\|{{t}_{i-1}})=\lambda \beta {{({{x}_{i}}+{{v}_{i-1}})}^{\beta -1}}{{e}^{-\lambda \left~~[ ~~{{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i-1}^{\beta } \right]}}</math>~~

	~~MLE method is used to estimate the model parameters. The log likelihood function is [[Appendix: Weibull References\|[28]]]:~~

	~~::<math>\begin{align}~~
	~~& \ln (L)= n(\ln \lambda +\ln \beta )-\lambda \left~~[ ~~{{\left( T-{{t}_{n}}+{{v}_{n}} \right)}^{\beta }}-v_{n}^{\beta } \right~~] \\
	~~& -\lambda \underset{i=1}{\overset{n}{\mathop \sum }}\,\left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i}^{\beta } \right~~]~~+(\beta -1)\underset{i=1}{\overset{n}{\mathop \sum }}\,\ln ({{x}_{i}}+{{v}_{i-1}})~~
	~~\end{align}</math>~~

	where <span class="texhtml">''n''</span> is the total number of events during the entire observation period. <span class="texhtml">''T''</span> is the stop time of the observation. <span class="texhtml">''T'' = ''t''<sub>''n''</sub></span> if the observation stops right after the last event.

Kate Racaza at 17:25, 8 March 2012

2012-03-08T17:25:46Z

← Older revision		Revision as of 17:25, 8 March 2012
Line 17:		Line 17:
	::<span class="texhtml">λ(''t'') = λβ''t''<sup>β − 1</sup></span>		::<span class="texhtml">λ(''t'') = λβ''t''<sup>β − 1</sup></span>

	The conditional <span class="texhtml">''~~p''''d''''f~~''</span> is:		The conditional <span class="texhtml">''pdf''</span> is:

	::<math>f({{t}_{i}}\|{{t}_{i-1}})=\lambda \beta {{({{x}_{i}}+{{v}_{i-1}})}^{\beta -1}}{{e}^{-\lambda \left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i-1}^{\beta } \right]}}</math>		::<math>f({{t}_{i}}\|{{t}_{i-1}})=\lambda \beta {{({{x}_{i}}+{{v}_{i-1}})}^{\beta -1}}{{e}^{-\lambda \left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i-1}^{\beta } \right]}}</math>

Kate Racaza at 16:21, 8 March 2012

2012-03-08T16:21:49Z

← Older revision		Revision as of 16:21, 8 March 2012
Line 5:		Line 5:
	Type I:		Type I:

	::<span class="texhtml">''v''<sub>''i''</sub> = ''v''<sub>''i'' − 1</sub> + ''q''''x'''''<b><sub>~~''i''~~</sub> = ''q'''~~</b>~~''t''<sub>''i''</sub></span>		::<span class="texhtml">''v''<sub>''i''</sub> = ''v''<sub>''i'' − 1</sub> + ''q''''x'''''<b><sub></sub> = </b>''q'''''t''<sub>''i''</sub></span>

	Type II:		Type II:
Line 11:		Line 11:
	::<math>{{v}_{i}}=q({{v}_{i-1}}+{{x}_{i}})={{q}^{i}}{{x}_{1}}+{{q}^{i-1}}{{x}_{2}}+\cdots +{{x}_{i}}</math>		::<math>{{v}_{i}}=q({{v}_{i-1}}+{{x}_{i}})={{q}^{i}}{{x}_{1}}+{{q}^{i-1}}{{x}_{2}}+\cdots +{{x}_{i}}</math>

	where <span class="texhtml">''v''<sub>''i''</sub></span> is the virtual age of the system right after <span class="texhtml">''i''</span> th repair. The Type I model assumes that the <span class="texhtml">''i''</span> th repair cannot remove the damage incurred before the ith failure. It can only reduce the additional age <span class="texhtml">''x''<sub>''i''</sub></span> to <span class="texhtml">''q''''x'''''<b><sub>''i''</sub></b></span> . The Type II model assumes that at the <span class="texhtml">''i''</span> th repair, the virtual age has been accumulated to <span class="texhtml">''v''<sub>''i'' − 1</sub> + ''x''<sub>''i''</sub></span> . The <span class="texhtml">''i''</span> th repair will remove the cumulative damage from both current and previous failures by reducing the virtual age to <span class="texhtml">''q''(''v''<sub>''i'' − 1</sub> + ''x''<sub>''i''</sub>)</span> .		where <span class="texhtml">''v''<sub>''i''</sub></span> is the virtual age of the system right after <span class="texhtml">''i''</span> th repair. The Type I model assumes that the <span class="texhtml">''i''</span> th repair cannot remove the damage incurred before the ith failure. It can only reduce the additional age <span class="texhtml">''x''<sub>''i''</sub></span> to <span class="texhtml">''q''''x'''''<b><sub>''i''</sub></b></span> . The Type II model assumes that at the <span class="texhtml">''i''</span> th repair, the virtual age has been accumulated to <span class="texhtml">''v''<sub>''i'' − 1</sub> + ''x''<sub>''i''</sub></span> . The <span class="texhtml">''i''</span> th repair will remove the cumulative damage from both current and previous failures by reducing the virtual age to <span class="texhtml">''q''(''v''<sub>''i'' − 1</sub> + ''x''<sub>''i''</sub>)</span> .

	The power law function is used to model the rate of recurrence, which is:		The power law function is used to model the rate of recurrence, which is:
Line 21:		Line 21:
	::<math>f({{t}_{i}}\|{{t}_{i-1}})=\lambda \beta {{({{x}_{i}}+{{v}_{i-1}})}^{\beta -1}}{{e}^{-\lambda \left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i-1}^{\beta } \right]}}</math>		::<math>f({{t}_{i}}\|{{t}_{i-1}})=\lambda \beta {{({{x}_{i}}+{{v}_{i-1}})}^{\beta -1}}{{e}^{-\lambda \left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i-1}^{\beta } \right]}}</math>

	MLE method is used to estimate the model parameters. The log likelihood function is [[[Appendix: Weibull References\|28]]]:		MLE method is used to estimate the model parameters. The log likelihood function is [[Appendix: Weibull References\|[28]]]:

	::<math>\begin{align}		::<math>\begin{align}

Kate Racaza at 16:21, 8 March 2012

2012-03-08T16:21:02Z

← Older revision		Revision as of 16:21, 8 March 2012
Line 1:		Line 1:
	===The GRP Model===		=== The GRP Model ===
	In this model, the concept of virtual age is introduced. ~~Denote by~~ <math>{{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}</math> the successive failure times and let <math>{{x}_{1}},{{x}_{2}},\cdots ,{{x}_{n}}</math> represent the time between failures ( <math>{{t}_{i}}=\sum_{j=1}^{i}{{x}_{j}})</math> . Assume that after each event, actions are taken to improve the system performance. Let <~~math~~>q</~~math~~> be the action effectiveness factor. There are two GRP models.
			In this model, the concept of virtual age is introduced. Let <math>{{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}</math> represent the successive failure times and let <math>{{x}_{1}},{{x}_{2}},\cdots ,{{x}_{n}}</math> represent the time between failures ( <math>{{t}_{i}}=\sum_{j=1}^{i}{{x}_{j}})</math> . Assume that after each event, actions are taken to improve the system performance. Let <span class="texhtml">''q''</span> be the action effectiveness factor. There are two GRP models:

	Type I:		Type I:
	~~::<math>{{v}_{i}}={{v}_{i-1}}+q{{x}_{i}}=q{{t}_{i}}</math>~~

	Type II:		::<span class="texhtml">''v''<sub>''i''</sub> = ''v''<sub>''i'' − 1</sub> + ''q''''x'''''<b><sub>''i''</sub> = ''q'''</b>''t''<sub>''i''</sub></span>

			Type II:

	::<math>{{v}_{i}}=q({{v}_{i-1}}+{{x}_{i}})={{q}^{i}}{{x}_{1}}+{{q}^{i-1}}{{x}_{2}}+\cdots +{{x}_{i}}</math>		::<math>{{v}_{i}}=q({{v}_{i-1}}+{{x}_{i}})={{q}^{i}}{{x}_{1}}+{{q}^{i-1}}{{x}_{2}}+\cdots +{{x}_{i}}</math>

	where <~~math~~>{{v~~}_{~~i}}</~~math~~> is the virtual age of the system right after <~~math~~>i</~~math~~> th repair. The Type I model assumes that the <~~math~~>i</~~math~~> th repair cannot remove the damage incurred before the ith failure. It can only reduce the additional age <~~math~~>{{x~~}_{~~i}}</~~math~~> to <~~math~~>q{{x~~}_{~~i}}</~~math~~> . The Type II model assumes that at the <~~math~~>i</~~math~~> th repair, the virtual age has been accumulated to <~~math~~>{{v~~}_{~~i-1}}+{{x~~}_{~~i}}</~~math~~> . The <~~math~~>i</~~math~~> th repair will remove the cumulative damage from both current and previous failures by reducing the virtual age to <~~math~~>q({{v~~}_{~~i-1}}+{{x~~}_{~~i}})</~~math~~> .		where <span class="texhtml">''v''<sub>''i''</sub></span> is the virtual age of the system right after <span class="texhtml">''i''</span> th repair. The Type I model assumes that the <span class="texhtml">''i''</span> th repair cannot remove the damage incurred before the ith failure. It can only reduce the additional age <span class="texhtml">''x''<sub>''i''</sub></span> to <span class="texhtml">''q''''x'''''<b><sub>''i''</sub></b></span> . The Type II model assumes that at the <span class="texhtml">''i''</span> th repair, the virtual age has been accumulated to <span class="texhtml">''v''<sub>''i'' − 1</sub> + ''x''<sub>''i''</sub></span> . The <span class="texhtml">''i''</span> th repair will remove the cumulative damage from both current and previous failures by reducing the virtual age to <span class="texhtml">''q''(''v''<sub>''i'' − 1</sub> + ''x''<sub>''i''</sub>)</span> .

	The power law function is used to model the rate of recurrence, which is:		The power law function is used to model the rate of recurrence, which is:

	::<~~math~~>~~\lambda~~ (t)=~~\lambda \beta {{~~t~~}^{\beta -~~1}}</~~math~~>		::<span class="texhtml">λ(''t'') = λβ''t''<sup>β − 1</sup></span>

	The conditional <~~math~~>~~pdf~~</~~math~~> is:		The conditional <span class="texhtml">''p''''d''''f''</span> is:

	::<math>f({{t}_{i}}\|{{t}_{i-1}})=\lambda \beta {{({{x}_{i}}+{{v}_{i-1}})}^{\beta -1}}{{e}^{-\lambda \left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i-1}^{\beta } \right]}}</math>		::<math>f({{t}_{i}}\|{{t}_{i-1}})=\lambda \beta {{({{x}_{i}}+{{v}_{i-1}})}^{\beta -1}}{{e}^{-\lambda \left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i-1}^{\beta } \right]}}</math>

	MLE method is used to estimate model parameters. The log likelihood function is [28]:		MLE method is used to estimate the model parameters. The log likelihood function is [[[Appendix: Weibull References\|28]]]:

	::<math>\begin{align}		::<math>\begin{align}
Line 25:		Line 28:
	\end{align}</math>		\end{align}</math>

	where <~~math~~>n</~~math~~> is the total number of events during the entire observation period. <~~math~~>T</~~math~~> is the stop time of the observation. <~~math~~>T={{t~~}_{~~n}}</~~math~~> if the observation stops right after the last event.		where <span class="texhtml">''n''</span> is the total number of events during the entire observation period. <span class="texhtml">''T''</span> is the stop time of the observation. <span class="texhtml">''T'' = ''t''<sub>''n''</sub></span> if the observation stops right after the last event.

Harry Guo: /* The GRP Model */

2012-02-22T18:33:11Z

The GRP Model

← Older revision		Revision as of 18:33, 22 February 2012
Line 1:		Line 1:
	===The GRP Model===		===The GRP Model===
	In this model, the concept of virtual age is introduced. Denote by <math>{{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}</math> the successive failure times and let <math>{{x}_{1}},{{x}_{2}},\cdots ,{{x}_{n}}</math> represent the time between failures ( <math>{{t}_{i}}=\sum_{j=1}^{i}{{x}_{j}})</math> . Assume that after each event, actions are taken to improve the system performance. Let <math>q</math> be the action effectiveness factor. There are two GRP models.		In this model, the concept of virtual age is introduced. Denote by <math>{{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}</math> the successive failure times and let <math>{{x}_{1}},{{x}_{2}},\cdots ,{{x}_{n}}</math> represent the time between failures ( <math>{{t}_{i}}=\sum_{j=1}^{i}{{x}_{j}})</math> . Assume that after each event, actions are taken to improve the system performance. Let <math>q</math> be the action effectiveness factor. There are two GRP models.


	Type I:		Type I:

Harry Guo: /* The GRP Model */

2012-02-22T18:32:59Z

The GRP Model

← Older revision		Revision as of 18:32, 22 February 2012
Line 1:		Line 1:
	===The GRP Model===		===The GRP Model===
	In this model, the concept of virtual age is introduced. Denote by <math>{{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}</math> the successive failure times and let <math>{{x}_{1}},{{x}_{2}},\cdots ,{{x}_{n}}</math> represent the time between failures ( <math>{{t}_{i}}=\sum_{j=1}^{i}{{x}_{j}})</math> . Assume that after each event, actions are taken to improve the system performance. Let <math>q</math> be the action effectiveness factor. There are two GRP models.		In this model, the concept of virtual age is introduced. Denote by <math>{{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}</math> the successive failure times and let <math>{{x}_{1}},{{x}_{2}},\cdots ,{{x}_{n}}</math> represent the time between failures ( <math>{{t}_{i}}=\sum_{j=1}^{i}{{x}_{j}})</math> . Assume that after each event, actions are taken to improve the system performance. Let <math>q</math> be the action effectiveness factor. There are two GRP models.


	Type I:		Type I:

Harry Guo at 18:31, 22 February 2012

2012-02-22T18:31:49Z

← Older revision		Revision as of 18:31, 22 February 2012
Line 22:		Line 22:
	::<math>\begin{align}		::<math>\begin{align}
	& \ln (L)= n(\ln \lambda +\ln \beta )-\lambda \left[ {{\left( T-{{t}_{n}}+{{v}_{n}} \right)}^{\beta }}-v_{n}^{\beta } \right] \\		& \ln (L)= n(\ln \lambda +\ln \beta )-\lambda \left[ {{\left( T-{{t}_{n}}+{{v}_{n}} \right)}^{\beta }}-v_{n}^{\beta } \right] \\
	& & -\lambda \underset{i=1}{\overset{n}{\mathop \sum }}\,\left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i}^{\beta } \right]+(\beta -1)\underset{i=1}{\overset{n}{\mathop \sum }}\,\ln ({{x}_{i}}+{{v}_{i-1}})		& -\lambda \underset{i=1}{\overset{n}{\mathop \sum }}\,\left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i}^{\beta } \right]+(\beta -1)\underset{i=1}{\overset{n}{\mathop \sum }}\,\ln ({{x}_{i}}+{{v}_{i-1}})
	\end{align}</math>		\end{align}</math>

	where <math>n</math> is the total number of events during the entire observation period. <math>T</math> is the stop time of the observation. <math>T={{t}_{n}}</math> if the observation stops right after the last event.		where <math>n</math> is the total number of events during the entire observation period. <math>T</math> is the stop time of the observation. <math>T={{t}_{n}}</math> if the observation stops right after the last event.

Harry Guo: /* The GRP Model */

2012-02-22T18:31:19Z

The GRP Model

← Older revision		Revision as of 18:31, 22 February 2012
Line 21:		Line 21:

	::<math>\begin{align}		::<math>\begin{align}
	& \ln (L)= & n(\ln \lambda +\ln \beta )-\lambda \left[ {{\left( T-{{t}_{n}}+{{v}_{n}} \right)}^{\beta }}-v_{n}^{\beta } \right] \\		& \ln (L)= n(\ln \lambda +\ln \beta )-\lambda \left[ {{\left( T-{{t}_{n}}+{{v}_{n}} \right)}^{\beta }}-v_{n}^{\beta } \right] \\
	& & -\lambda \underset{i=1}{\overset{n}{\mathop \sum }}\,\left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i}^{\beta } \right]+(\beta -1)\underset{i=1}{\overset{n}{\mathop \sum }}\,\ln ({{x}_{i}}+{{v}_{i-1}})		& & -\lambda \underset{i=1}{\overset{n}{\mathop \sum }}\,\left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i}^{\beta } \right]+(\beta -1)\underset{i=1}{\overset{n}{\mathop \sum }}\,\ln ({{x}_{i}}+{{v}_{i-1}})
	\end{align}</math>		\end{align}</math>

	where <math>n</math> is the total number of events during the entire observation period. <math>T</math> is the stop time of the observation. <math>T={{t}_{n}}</math> if the observation stops right after the last event.		where <math>n</math> is the total number of events during the entire observation period. <math>T</math> is the stop time of the observation. <math>T={{t}_{n}}</math> if the observation stops right after the last event.

Nicolette Young: Created page with '===The GRP Model=== In this model, the concept of virtual age is introduced. Denote by ${{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}$ the successive failure times and let …'

2012-01-04T23:30:11Z

Created page with '===The GRP Model=== In this model, the concept of virtual age is introduced. Denote by <math>{{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}</math> the successive failure times and let …'

New page

===The GRP Model===
In this model, the concept of virtual age is introduced. Denote by <math>{{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}</math> the successive failure times and let <math>{{x}_{1}},{{x}_{2}},\cdots ,{{x}_{n}}</math> represent the time between failures ( <math>{{t}_{i}}=\sum_{j=1}^{i}{{x}_{j}})</math> . Assume that after each event, actions are taken to improve the system performance. Let <math>q</math> be the action effectiveness factor. There are two GRP models.

Type I:
::<math>{{v}_{i}}={{v}_{i-1}}+q{{x}_{i}}=q{{t}_{i}}</math>

Type II:
::<math>{{v}_{i}}=q({{v}_{i-1}}+{{x}_{i}})={{q}^{i}}{{x}_{1}}+{{q}^{i-1}}{{x}_{2}}+\cdots +{{x}_{i}}</math>

where <math>{{v}_{i}}</math> is the virtual age of the system right after <math>i</math> th repair. The Type I model assumes that the <math>i</math> th repair cannot remove the damage incurred before the ith failure. It can only reduce the additional age <math>{{x}_{i}}</math> to <math>q{{x}_{i}}</math> . The Type II model assumes that at the <math>i</math> th repair, the virtual age has been accumulated to <math>{{v}_{i-1}}+{{x}_{i}}</math> . The <math>i</math> th repair will remove the cumulative damage from both current and previous failures by reducing the virtual age to <math>q({{v}_{i-1}}+{{x}_{i}})</math> .

The power law function is used to model the rate of recurrence, which is:

::<math>\lambda (t)=\lambda \beta {{t}^{\beta -1}}</math>

The conditional <math>pdf</math> is:

::<math>f({{t}_{i}}|{{t}_{i-1}})=\lambda \beta {{({{x}_{i}}+{{v}_{i-1}})}^{\beta -1}}{{e}^{-\lambda \left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i-1}^{\beta } \right]}}</math>

MLE method is used to estimate model parameters. The log likelihood function is [28]:

::<math>\begin{align}
& \ln (L)= & n(\ln \lambda +\ln \beta )-\lambda \left[ {{\left( T-{{t}_{n}}+{{v}_{n}} \right)}^{\beta }}-v_{n}^{\beta } \right] \\
& & -\lambda \underset{i=1}{\overset{n}{\mathop \sum }}\,\left[ {{\left( {{x}_{i}}+{{v}_{i-1}} \right)}^{\beta }}-v_{i}^{\beta } \right]+(\beta -1)\underset{i=1}{\overset{n}{\mathop \sum }}\,\ln ({{x}_{i}}+{{v}_{i-1}})
\end{align}</math>

where <math>n</math> is the total number of events during the entire observation period. <math>T</math> is the stop time of the observation. <math>T={{t}_{n}}</math> if the observation stops right after the last event.

Template:Grp model - Revision history

Kate Racaza: Redirected page to Recurrent Event Data Analysis

Kate Racaza at 17:25, 8 March 2012

Kate Racaza at 16:21, 8 March 2012

Kate Racaza at 16:21, 8 March 2012

Harry Guo: /* The GRP Model */

Harry Guo: /* The GRP Model */

Harry Guo at 18:31, 22 February 2012

Harry Guo: /* The GRP Model */

Nicolette Young: Created page with '===The GRP Model=== In this model, the concept of virtual age is introduced. Denote by {{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}} the successive failure times and let …'

Nicolette Young: Created page with '===The GRP Model=== In this model, the concept of virtual age is introduced. Denote by ${{t}_{1}},{{t}_{2}},\cdots ,{{t}_{n}}$ the successive failure times and let …'