diff --git a/submission_thesis/CH5_Examples/copy.tex b/submission_thesis/CH5_Examples/copy.tex index 841feec..b2f8b0e 100644 --- a/submission_thesis/CH5_Examples/copy.tex +++ b/submission_thesis/CH5_Examples/copy.tex @@ -1709,7 +1709,7 @@ $$ fm (DL2AL) = \{ LOW, HIGH, LOW\_{SLEW} \} $$ % This is a single component as a {\fg}, and we can state % $$ fm (DCM) = \{ HIGH, LOW, NOOP \} $$ -The digital element of the {\sd}, is the one bit memory, or D type flip flop. This +The digital element of the {\sd}, is a `one~bit~memory', or D type flip flop. This buffers the feedback result and provides the output bit stream. We create a {\fg} from the CLOCK and IC4 to model this digital buffer. @@ -1866,7 +1866,7 @@ We now show the final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}. The \sd example, shows that FMMD can be applied to mixed digital and analogue circuitry. -\clearpage +%\clearpage \section{Pt100 Analysis: FMMD and Double Failure Mode Analysis} \label{sec:Pt100} { diff --git a/submission_thesis/CH6_Evaluation/copy.tex b/submission_thesis/CH6_Evaluation/copy.tex index 965698e..a91e051 100644 --- a/submission_thesis/CH6_Evaluation/copy.tex +++ b/submission_thesis/CH6_Evaluation/copy.tex @@ -126,7 +126,7 @@ with additional indexing when appropriate. \paragraph{Defining a function that returns failure modes given a component.} The function $fm$ has a component as its domain and the components failure modes, $fms$, as its range. % (see equation~\ref{eqn:fm}). Where $\mathcal{F}$ is the set of all failures, -$$ fm: \mathcal{C} \rightarrow \mathcal{F}$$. +$$ fm: \mathcal{C} \rightarrow \mathcal{F}.$$ We can represent the number of potential failure modes of a component $c$, to be $ | fm(c) | .$ \paragraph{Indexing components with the group $G$.} @@ -146,7 +146,7 @@ Where $\mathcal{G}$ represents the set of all {\fgs}, and $ \mathbb{Z}^{+} $, $C % %and, where n is the number of components in the system/{\fg}, and $|fm(c_i)|$ is the number of failure modes -in component ${c_i}$, is given by +in component ${c_i}$, comparison complexity, $CC$ is given by \begin{equation} \label{eqn:CC} @@ -369,14 +369,15 @@ $$ %\clearpage \subsection{Complexity Comparison applied to previous FMMD Examples} -All the FMMD examples in chapters \ref{sec:chap5} and \ref{sec:chap6} showed a marked reduction in comparison -complexity compared to the RFMEA worst case figures. +All the FMMD examples in chapters \ref{sec:chap5} +and \ref{sec:chap6} showed a marked reduction in comparison +complexity compared to the RFMEA worst case figures. +To calculate RFMEA Comparison complexity equation~\ref{eqn:CC} is used. % - % Complexity comparison vs. RFMEA for the first three examples are presented in table~\ref{tbl:firstcc}. - +% %\usepackage{multirow} \begin{table} \label{tbl:firstcc} @@ -550,33 +551,39 @@ by more than a factor of ten. \multicolumn{3}{ |c| }{{\sd} FMMD Hierarchy: section~\ref{sec:sigmadelta}} \\ \hline %\multirow{3}{*} {Inverting Amplifier Two stage FMMD Hierarchy: section~\ref{sec:invamp}} & & \\ \hline -1 & & 4 & 2 \\ -1 & INVAMP & 16 & 3 \\ -0 & NIBUFF & 0 & 4 \\ -% -% final one has 8 components 3* NIBUFF + 1 * INVAMP + 4 * PHS45 -% (8-1) * ( (3*4) + (1*16) + (4 * 4) ) -2 & {\sd} & 308 & 2 \\ -% NIBUFF PHS45 -% 8 components so LEVEL 2 (8-1) \times ( (3*4) + (4*2) + 3 ) + LEVEL 0 16 for the INVAMP -2 & Total for {\sd}: & 328 (FMMD) & \\ -% R&C OPAMPS -% 14 components so 13 \times ( (10*2) (4*4) ) -0 & Total for {\sd}: & 468 (RFMEA) & \\ - \hline +1 & SUMJINT & 30 & 4 \\ +0 & HISB & 0 & 4 \\ +2 & BISJ & 8 & 2 \\ \hline + +1 & DIGBUF & 2 & 4 \\ +1 & PD & 4 & 2 \\ +2 & DL2AL & 6 & 3 \\ +3 & FFB & 5 & 2 \\ \hline +% +2 & {\sd} & 4 & 2 \\ \hline +% +% +2 & Total for {\sd}: & 55 (FMMD) & \\ +% R&C OPAMPS +% 14 components so (10-1) * +0 & Total for {\sd}: & 225 (RFMEA) & \\ + + \hline \hline \end{tabular} -\caption{Complexity Comparison figures for the Bubba Oscillator FMMD example (see section~\ref{sec:bubba}).} +\caption{Complexity Comparison figures for the {\sd} FMMD example (see section~\ref{sec:sigmadelta}).} \end{table} - +% +The complexity figures for this mixed analogue to digital circuit are not adversely affected by the digital to +analogue level interfacing circuitry. This is where the modular approach aids understanding and analysis. +When following this circuit through in a traditional way, we have to follow signal paths that +are level shifted, adding to the complication of analysing it for failures. % \subsection{Exponential squared to Exponential} % % can I say that ? - - - +% \section{Unitary State Component Failure Mode sets} \label{sec:unitarystate} \paragraph{Design Decision/Constraint} diff --git a/submission_thesis/appendixes/detailed_analysis.tex b/submission_thesis/appendixes/detailed_analysis.tex index aeaac9b..38d397f 100644 --- a/submission_thesis/appendixes/detailed_analysis.tex +++ b/submission_thesis/appendixes/detailed_analysis.tex @@ -204,10 +204,10 @@ $$ FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline % FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $270\_phaseshift$ \\ \hline - FS3: $INVAMP$ $L_{up}$ & & output high & & $NO_{signal}$ \\ - FS4: $INVAMP$ $L_{dn}$ & & output low & & $NO_{signal}$ \\ - FS5: $INVAMP$ $N_{oop}$ & & output low & & $NO_{signal}$ \\ - FS6: $INVAMP$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline + FS3: $INVAMP$ $L_{up}$ & & output high & & $NO_{signal}$ \\ + FS4: $INVAMP$ $L_{dn}$ & & output low & & $NO_{signal}$ \\ + FS5: $INVAMP$ $N_{oop}$ & & output low & & $NO_{signal}$ \\ + FS6: $INVAMP$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline \hline