From 7f47ceace99a182510e96da482eef089803c2c4e Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Mon, 21 Jan 2013 22:11:41 +0000 Subject: [PATCH] JMCPR --- submission_thesis/CH6_Evaluation/copy.tex | 40 ++++++++++++----------- 1 file changed, 21 insertions(+), 19 deletions(-) diff --git a/submission_thesis/CH6_Evaluation/copy.tex b/submission_thesis/CH6_Evaluation/copy.tex index c14b66d..47a6b93 100644 --- a/submission_thesis/CH6_Evaluation/copy.tex +++ b/submission_thesis/CH6_Evaluation/copy.tex @@ -6,7 +6,7 @@ % This chapter begins by defining a metric for the complexity of an FMEA analysis task. % -This concept is called `comparisson~complexity' and is a means to assess +This concept is called `comparison~complexity' and is a means to assess the performance of FMMD against current FMEA methodologies. % This metric is developed using set threory % formally @@ -54,8 +54,8 @@ We can view FMEA as a process, taking each component in the system and for each applying analysis with respect to the whole system. % This however entails a problem: which other components in the system must we -check against the %current failure mode. -each particular failure mode. +check, against %current failure mode. +each particular failure mode? % Often a component failing will have obvious effects on functionally adjacent components. Sometimes %though, perhaps in the case of de-coupling capacitors in a digital ciruit, @@ -115,7 +115,7 @@ $ | G | $. %, %within an FMMD hierarchy is given in section~\ref{sec:indexsub}). \paragraph{Defining Components} -We define the set of all components as $\mathcal{C}$. Individiual components are denoted as $c$ +We define the set of all components as $\mathcal{C}$. Individual components are denoted as $c$ with additional indexing when appropriate. \paragraph{Defining a function that returns failure modes given a component.} @@ -281,12 +281,15 @@ would look like figure~\ref{fig:three_tree}. \subsection{RFMEA FMMD Comparison Example} Using the diagram in figure~\ref{fig:three_tree}, we have three levels of analysis. +% Starting at the top, we have a {\fg} with three derived components, each of which has three failure modes. -Thus the number of checks to make in the top level is $3^0.3.2.3=18$. -On the level below that, we have three {\fgs} each with a -an identical number of checks, $3^1.3.2.3=56$.%{\fg} -On the level below that we have nine {\fgs}, $3^2.3.2.3=168$. +% +Thus the number of checks to make in the top level is $3^0\times3\times2\times3 = 18$. +On the level below that, we have three {\fgs} each with +an identical number of checks, $3^1 \times 3 \times 2 \times 3 = 56$.%{\fg} +% +On the level below that we have nine {\fgs}, $3^2 \times 3\times2\times3=168$. Adding these together gives $242$ checks to make to perform FMMD (i.e. RFMEA {\em{within the}} {\fgs}). @@ -497,10 +500,9 @@ Where this occurs a circuit re-design is probably the only sensible course of ac \paragraph{Single Fault FMEA Analysis of $Pt100$ Four wire circuit.} \label{fmea} -The Pt00 circuit consists of three resistors, two `current~supply' +The Pt100 circuit consists of three resistors, two `current~supply' wires and two `sensor' wires. -Resistors %according to the European Standard EN298:2003~\cite{en298}[App.A] -, are considered to fail by either going OPEN or SHORT (see section~\ref{sec:res_fms}). %circuit\footnote{EN298:2003~\cite{en298} also requires that components are downrated, +Resistors, are considered to fail by either going OPEN or SHORT (see section~\ref{sec:res_fms}). %circuit\footnote{EN298:2003~\cite{en298} also requires that components are downrated, %and so in the case of resistors the parameter change failure mode~\cite{fmd-91}[2-23] can be ommitted.}. %Should wires become disconnected these will have the same effect as %given resistors going open. @@ -646,15 +648,15 @@ The \ohms{2k2} loading resistors should have a good temperature co-effecient To calculate the resistance of the Pt100 element % (and thus derive its temperature), knowing $V_{R3}$ we now need the current flowing in the temperature sensor loop. % -Lets use, for the sake of example $R_2$ to measure the current. +Lets use, for the sake of example, $R_2$ to measure the current. % We can calculate the current $I$, by reading -the voltage over the known resistor $R_2$ and using ohms law\footnote{To calculate the resistance of the Pt100 we need the current flowing though it. -We can determine this via ohms law applied to $R_2$, $V=IR$, $I=\frac{V}{R_2}$, -and then using $I$, we can calculate $R_{3} = \frac{V_{3}}{I}$.} and then use ohms law again to calculate +the voltage over the known resistor $R_2$ and using Ohms law\footnote{To calculate the resistance of the Pt100 we need the current flowing though it. +We can determine this via Ohms law applied to $R_2$, $V=IR$, $I=\frac{V}{R_2}$, +and then using $I$, we can calculate $R_{3} = \frac{V_{3}}{I}$.} and then use Ohms law again to calculate the resistance of $R_3$. % -As ohms law is linear, the accuracy of the reading +As Ohms law is linear, the accuracy of the reading will be determined by the accuracy of $R_2$ and $R_{3}$. It is reasonable to take the mean square error of these accuracy figures~\cite{probstat}. @@ -785,7 +787,7 @@ resistors in this circuit has failed. \subsection{Derived Component : The Pt100 Circuit} The Pt100 circuit can now be treated as a component in its own right, and has one failure mode, {\textbf OUT\_OF\_RANGE}. This is a single, detectable failure mode. The observability of a -fault condition is very good with this circuit.This should not be a surprise, as the four wire $Pt100$ +fault condition is very good with this circuit. This should not be a surprise, as the four wire $Pt100$ has been developed for safety critical temperature measurement. % \ifthenelse{\boolean{pld}} @@ -1289,7 +1291,7 @@ condition in higher levels of the system. \subsubsection{Side Effects: A Problem for FMMD analysis} \label{sec:sideeffects} -A problem with modularising according to functionality is that we can have component failures that would +A problem with modularising according to functionality is that we can have component failures that would % poss split infinitive intuitively be associated with one {\fg} that may cause unintended side effects in other {\fgs}. For instance were we to have a component that on failing $SHORT$ could bring down @@ -1327,7 +1329,7 @@ Some logic chips are more susceptible to $INTERFERENCE$ than others. A logic chip with de-coupling capacitor failing, may operate correctly but interfere with other chips in the circuit. -There is no reason why the de-coupling capacitors could not be included {\em in the {\fg} they would intuitively be associated with as well}. +There is no reason why the de-coupling capacitors could not be included {\em in the {\fg} they would intuitively be associated with as well}.% poss split infinitive This allows for the general principle of a component failure affecting more than one {\fg} in a circuit. This allows functional groups to share components where necessary.