User:David J. Groebel/MySandbox - Revision history

David J. Groebel: /* Actual Failure Intensity Function */

2017-01-31T02:05:02Z

Actual Failure Intensity Function

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	===Actual Failure Intensity Function===		===Actual Failure Intensity Function===
	'''Test Phase 1'''		'''Test Phase 1'''

	The actual failure intensity function for test phase 1 is given by:		The actual failure intensity function for test phase 1 is given by:

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	'''Test Phase i'''		'''Test Phase i'''

	For any test phase <math>i\,\!</math>, the actual idealized curve failure intensity is given by:		For any test phase <math>i\,\!</math>, the actual idealized curve failure intensity is given by:

David J. Groebel: /* Example */

2017-01-31T01:34:13Z

Example

← Older revision		Revision as of 01:34, 31 January 2017
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	<ol>		<ol>
	<li>The growth potential MTrBF and failure intensity.</li>		<li>The growth potential MTrBF and failure intensity.</li>
	<li>The initial failure intensity.</li>		<li>The initial failure intensity and reliability.</li>
	<li>The growth potential reliability.</li>		<li>The growth potential reliability.</li>
	<li>The type A and type B initial failure intensity.</li>		<li>The type A and type B initial failure intensity.</li>
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	= & \frac{0.0556}{\left( 1-0.85\cdot 0.97 \right)} \\		= & \frac{0.0556}{\left( 1-0.85\cdot 0.97 \right)} \\
	= & 0.2480		= & 0.2480
			\end{align}\,\!</math>

			The initial reliability is then:

			:<math>\begin{align}
			R_{I}=&1-f_{I} \\
			=& 1-0.2480 \\
			=& 0.7520
	\end{align}\,\!</math>		\end{align}\,\!</math>

David J. Groebel: /* Example */

2017-01-31T01:32:04Z

Example

← Older revision		Revision as of 01:32, 31 January 2017
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	==Example==		==Example==
	A missile system will be going through a reliability growth development program. The goal for the system is to reach a reliability requirement of 0.9 at the end of the program. This corresponds to a goal MTrBF, <math>{{R}_{I}}\,\!</math>, of 10 trials. The new missile system is similar to an existing missile system, but this will not be an upgrade. Therefore, to help design the reliability growth plan for the new system, parameters from the existing version will be used.		A missile system will be going through a reliability growth development program. The goal for the system is to reach a reliability requirement of 0.9 at the end of the program. This corresponds to a goal MTrBF, <math>{{R}_{G}}\,\!</math>, of 10 trials. The new missile system is similar to an existing missile system, but this will not be an upgrade. Therefore, to help design the reliability growth plan for the new system, parameters from the existing version will be used.

	The previous missile system met its reliability goal of <math>{{R}_{G}=0.95}\,\!</math> which corresponds to a MTrBF = 20. There were over 600 trials of this missile system during developmental testing. This large number of trials were used for testing, but also for training. In addition, given the complexity of the technology that was utilized, additional trials were needed. The system also had an initial reliability of <math>{{R}_{I}=0.84}\,\!</math>. Additional parameters associated with the previous system are given below:		The previous missile system met its reliability goal of <math>{{R}_{G}=0.95}\,\!</math> which corresponds to a MTrBF = 20. There were over 600 trials of this missile system during developmental testing. This large number of trials were used for testing, but also for training. In addition, given the complexity of the technology that was utilized, additional trials were needed. The system also had an initial reliability of <math>{{R}_{I}=0.84}\,\!</math>. Additional parameters associated with the previous system are given below:

David J. Groebel: /* Example */

2017-01-31T01:31:37Z

Example

← Older revision		Revision as of 01:31, 31 January 2017
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	A missile system will be going through a reliability growth development program. The goal for the system is to reach a reliability requirement of 0.9 at the end of the program. This corresponds to a goal MTrBF, <math>{{R}_{I}}\,\!</math>, of 10 trials. The new missile system is similar to an existing missile system, but this will not be an upgrade. Therefore, to help design the reliability growth plan for the new system, parameters from the existing version will be used.		A missile system will be going through a reliability growth development program. The goal for the system is to reach a reliability requirement of 0.9 at the end of the program. This corresponds to a goal MTrBF, <math>{{R}_{I}}\,\!</math>, of 10 trials. The new missile system is similar to an existing missile system, but this will not be an upgrade. Therefore, to help design the reliability growth plan for the new system, parameters from the existing version will be used.

	The previous missile system met its reliability goal of <math>{{R}_{G}}\,\!</math> ~~= 0.95~~ which corresponds to a MTrBF = 20. There were over 600 trials of this missile system during developmental testing. This large number of trials were used for testing, but also for training. In addition, given the complexity of the technology that was utilized, additional trials were needed. The system also had an initial reliability of <math>{{R}_{I}}\,\!</math> ~~= 0.84~~. Additional parameters associated with the previous system are given below:		The previous missile system met its reliability goal of <math>{{R}_{G}=0.95}\,\!</math> which corresponds to a MTrBF = 20. There were over 600 trials of this missile system during developmental testing. This large number of trials were used for testing, but also for training. In addition, given the complexity of the technology that was utilized, additional trials were needed. The system also had an initial reliability of <math>{{R}_{I}=0.84}\,\!</math>. Additional parameters associated with the previous system are given below:

	*Average Effectiveness Factor is <math>EF=0.85\,\!</math>		*Average Effectiveness Factor is <math>EF=0.85\,\!</math>

David J. Groebel: /* Example */

2017-01-31T01:30:36Z

Example

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	*Growth Potential Design Margin is <math>GPDM=1.8\,\!</math>		*Growth Potential Design Margin is <math>GPDM=1.8\,\!</math>

	For the new program, a <math>msr=0.97\!</math> will be used, along with an average <math>EF=0.8\,\!</math>.		For the new program, a <math>msr=0.97\!</math> will be used, along with an average <math>EF=0.8\,\!</math>. For initial planning purposes, the average fix delay will be assumed to be equal to zero. Therefore, the nominal idealized curve will equal the actual idealized curve.

	Determine the following:		Determine the following:
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	</li>		</li>
	</ol>		</ol>




	~~This then corresponds to a growth potential reliability of <math>{{R}_{GP}}=0.9444\,\!</math>.~~

	For the purposes of an initial reliability growth plan, we will be assuming that the average fix delay is equal to zero with the understanding that this is a best case scenario. Using the Discrete Reliability Growth Plan in RGA, the plan for the new missile system is shown next.

David J. Groebel: /* Example */

2017-01-31T01:29:15Z

Example

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	:<math>\begin{align}		:<math>\begin{align}
	{{f}_{NI}}({{t}_{0}})= & {{f}_{A}}+(1-d){{f}_{B}}+d\left[ \lambda {{t}^{\beta }}-\lambda {{({{t}_{0}}-1)}^{\beta }} \right]={{f}_{I}} \\		{{f}_{NI}}({{t}_{0}})= {{f}_{A}}+(1-d){{f}_{B}}+d\left[ \lambda {{t}^{\beta }}-\lambda {{({{t}_{0}}-1)}^{\beta }} \right]= & {{f}_{I}} \\
	= & 0.2480		= & 0.2480
	\end{align}\,\!</math>		\end{align}\,\!</math>

David J. Groebel: /* Example */

2017-01-31T01:28:19Z

Example

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	:<math>\begin{align}		:<math>\begin{align}
	{{f}_{NI}}({{t}_{0}})={{f}_{A}}+(1-d){{f}_{B}}+d\left[ \lambda {{t}^{\beta }}-\lambda {{({{t}_{0}}-1)}^{\beta }} \right]={{f}_{I}} \\		{{f}_{NI}}({{t}_{0}})= & {{f}_{A}}+(1-d){{f}_{B}}+d\left[ \lambda {{t}^{\beta }}-\lambda {{({{t}_{0}}-1)}^{\beta }} \right]={{f}_{I}} \\
	= & 0.2480		= & 0.2480
	\end{align}\,\!</math>		\end{align}\,\!</math>

David J. Groebel: /* Example */

2017-01-31T01:27:58Z

Example

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	:<math>\begin{align}		:<math>\begin{align}
	MTrB{{F}_{B}}=\sum\limits_{k=1}^{\infty }{k\centerdot {{g}_{k}}}\centerdot \left[ \prod\limits_{j=1}^{k-1}{{{P}_{j}}} \right] \\		MTrB{{F}_{B}}= & \sum\limits_{k=1}^{\infty }{k\centerdot {{g}_{k}}}\centerdot \left[ \prod\limits_{j=1}^{k-1}{{{P}_{j}}} \right] \\
	= & 4.0322		= & 4.0322
	\end{align}\,\!</math>		\end{align}\,\!</math>

David J. Groebel: /* Example */

2017-01-31T01:26:10Z

Example

← Older revision		Revision as of 01:26, 31 January 2017
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	{{MTrBF}_{GP}}= & \frac{1}{{{f}_{I}}} \\		{{MTrBF}_{GP}}= & \frac{1}{{{f}_{I}}} \\
	= & \frac{1}{0.2480} \\		= & \frac{1}{0.2480} \\
	= & 0.~~0556~~		= & 4.032
			\end{align}\,\!</math>

	<math>\lambda \,\!</math> is estimated such that:		<math>\lambda \,\!</math> is estimated such that:

David J. Groebel: /* Example */

2017-01-31T01:24:47Z

Example

← Older revision		Revision as of 01:24, 31 January 2017
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	:<math>\begin{align}		:<math>\begin{align}
	{{MTrBF}_{I}}= & \frac{1}{{{f}_{I}}} \\		{{MTrBF}_{GP}}= & \frac{1}{{{f}_{I}}} \\
	= & \frac{1}{0.2480} \\		= & \frac{1}{0.2480} \\
	= 4.~~0322~~		= & 0.0556
	~~\end{align}\,\!</math>~~

	<math>\lambda \,\!</math> is estimated such that:		<math>\lambda \,\!</math> is estimated such that: