BlockSim Analytical Examples: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
Line 1: Line 1:


=Example 15=
For this example, obtain the reliability equation of the system shown in Figure fig29.
==Solution to Example 15==
The system reliability equation is:
<br>
::<math>{{R}_{System}}={{R}_{Computer1}}\cdot {{R}_{Computer2}}</math>
<br>
:Now:
<br>
::<math>\begin{align}
{{R}_{Computer1}}= & ({{R}_{Power\,Supply}}\cdot {{R}_{Processor}}\cdot {{R}_{HardDrive}} \\
&\cdot(-{{R}_{Fan}}\cdot {{R}_{Fan}}+{{R}_{Fan}}+{{R}_{Fan}})) 
\end{align}</math>
<br>
Since the structures of the computer systems are the same,  <math>{{R}_{Computer1}}={{R}_{Computer2}}</math> , then substituting Eqn. (excomp2a) into Eqn. (excomp) yields:
<br>
::<math>\begin{align}
{{R}_{System}}= & ({{R}_{Power\,Supply}}\cdot {{R}_{Processor}}) \\
& \cdot {{R}_{HardDrive}}(-R_{Fan}^{2}+2{{R}_{Fan}}){{)}^{2}} 
\end{align}</math>
When using BlockSim to compute the equation, the software will return Eqn. (excomp) for the system and Eqn. (excomp2a) for the subdiagram.  Even though BlockSim will make these substitutions internally when performing calculations, it does show them in the System Reliability Equation window.
<br>
[[Image:chp4image27.png|thumb|center|400px|Illustration of subdiagrams.]]
<br>
[[Image:BS4.23.png|thumb|center|400px|]]
<br>
==Example 16==
In the diagram shown in Figure Fig32, electricity can flow in both directions.  Successful system operation requires at least one output (O1, O2 or O3) to be working.
<br>
<br>
Create a block diagram for this system.
===Solution to Example 16===
The bidirectionality of this system can be modeled using mirrored blocks.  The diagram is shown in Figure fig33a.
<br>
<br>
Blocks 5A, 7A and 1A are duplicates (or mirrored blocks) of 5, 7 and 1 respectively.
===Example 18===
Assume that a system has six failure modes: A, B, C, D, E and F.  Furthermore, assume that failure of the entire system will occur if:
<br>
:• Mode B, C or F occurs.<br>
:• Modes A and E, A and D or E and D occur.<br>
<br>
Draw the block diagram and obtain the reliability equation.
====Solution to Example 18====
The diagram is shown in Figure fig35
<br>
The reliability equation, as obtained from BlockSim is:
<br>
::<math>\begin{align}
{{R}_{System}}= & (-2{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{2/3}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
& +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{2/3}}\cdot {{R}_{F}} \\
& +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{2/3}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
& +{{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{2/3}}\cdot {{R}_{E}}\cdot {{R}_{F}}) 
\end{align}</math>
<br>
The BlockSim equation includes the node reliability term  <math>{{R}_{2/3}},</math>  which cannot fail, or  <math>{{R}_{2/3}}=1</math> .  This can be removed, yielding:
<br>
::<math>\begin{align}
{{R}_{System}}= & (-2{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
& +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{F}} \\
& +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
& +{{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{E}}\cdot {{R}_{F}}) 
\end{align}</math>
<br>

Revision as of 02:40, 16 August 2012

Retrieved from "https://www.reliawiki.com/index.php?title=BlockSim_Analytical_Examples&oldid=32195"