evening edit

fmmd_design_aide/fmmd_design_aide.tex

@@ -16,33 +16,42 @@ of its failure mode behaviour.
 {
 \section{Introduction}
 This chapter 
-describes how the FMMD methodology can be used to refine
+describes how the FMMD methodology can be used to examine
 safety critical designs and identify undetectable faults.
 Used in this way, its is a design aide, giving the user
-the possibility to model a system from the perspective
+the possibility to refine/correct a {\dc} from the perspective
 of its failure mode behaviour.
 
 
+
 }
 
  
 \section{How FMMD Analysis can reveal design flaws in failure mode detection }
 
-A feature of FMMD analysis is symptom collection. Common symptoms are collected
-after analysis, and this means that the failure modes of the {\fg}
-are examined. The symptoms will be detectable (like a value of  of range)
+A feature of FMMD analysis is the collection of components
+into a {\fg}, which is then analysed  w.r.t. its failure mode behaviour.
+symptom collection. 
+From the failure mode behaviour of the {\fg} common symptoms are collected.
+These common symptoms are in effect the failure mode behaviour of
+the {\fg} viewed as a single entity, or a `black box' component.
+From the analysis of the {\fg} we can created a {\dc}, where the failure modes
+are the symptoms of the {\fg} we derived it from.
+The symptoms will be detectable (like a value of  of range)
 or undetectable (like a logic state or value being incorrect).
-The `undetectable' failure modes are the most worrying for thesafety critical designer.
-It is these that are, generally the ones that stand out as single 
-failure modes. For instance, out of range values, we know we can cope with; they
+The `undetectable' failure modes are the most worrying for the safety critical designer.
+%It is these that are, generally the ones that stand out as single 
+%failure modes. 
+For instance, out of range values, we know we can cope with; they
 are an obvious error condition that will be detected by any modules
-using the {\fg}.
-i
-\subsection{iterative design}
+using the {\dc}. An undetecable failure mode will introduce
+errors into a SYSTEM.
+
+\subsection{Iterative Design}
 
 By applying FMMD analysis to a {\fg} we can determine which failure
-modes are detectable, and which are undetectable.
-We can then either modifiy the circuit and iteratively
+modes of a {\dc} are detectable, and which are undetectable.
+We can then either modify the circuit and iteratively
 apply FMMD to the design again, or we could add another {\fg}
 that specifically tests for the undetectable conditions.
 
@@ -54,25 +63,79 @@ paper
 {
 chapter
 }
-describes a milli-volt amplifier, with an inbuilt safety\footnote{The `safety resistor also acts as a potential divider to provide a mill-volt offset}
+describes a milli-volt amplifier (see R18 in figure \ref{fig:mv1}), with an inbuilt safety\footnote{The `safety resistor' also acts 
+as a potential divider to provide a mill-volt offset. An offset is often required to allow for negative readings form the 
+milli-volt source being read}
 resistor. The circuit is analysed and it is found that all but one component failure modes
 are detectable.
 We then design a circuit to test for the `undetectable' failure mode
 and analyse this with FMMD.
 With both {\dcs} we then use them to form a {\fg} which we can call our `self testing milli-volt amplifier'.
-We then analsye the {\fg} and the resultant {\dc} failure modes descussed.
+We then analsye the {\fg} and the resultant {\dc} failure modes are discussed.
 \section{An example: A Millivolt Amplifier}
 
 \begin{figure}[h]
  \centering
  \includegraphics[width=200pt,bb=0 0 678 690,keepaspectratio=true]{./mv_opamp_circuit.png}
  % mv_opamp_circuit.png: 678x690 pixel, 72dpi, 23.92x24.34 cm, bb=0 0 678 690
- \caption{Milli-Volt Amplifier with Offset}
- \label{fig:mvamp}
+ \caption{Milli-Volt Amplifier with Safety/Offset Resistor}
+ \label{fig:mv1}
 \end{figure}
 
+\subsection{Brief Circuit Description}
+
+This circuit amplifies a milli-volt input by a gain of $\approx$ 184 ($\frac{150E3}{820}+1$).
+An offset is applied to the input by R18 and R22 forming a potential divider
+of $\frac{820}{2.2E6+820}$. Will 5V applied as Vcc this gives an input offset of 1.86mV.
+So the amplified offset is $\approx 342mV$. We can determine the output of the amplifier
+by subtracting this amount from the reading. We can also define an acceptable 
+range for the readings. This would depend on the milli-volt source, and also on the 
+detectability of the error volatges.
+
+EXPAND
+ 
 \section{FMMD Analysis}
 
+
+
+
+\begin{table}[h+]
+\caption{Milli Volt Amplifier //  Single Fault FMMD} % title of Table
+\centering % used for centering table
+\begin{tabular}{||l|c|c|l|l||}
+\hline \hline
+ \textbf{Test} & \textbf{Failure } & \textbf{Symptom } & \textbf{MTTF}   \\
+ \textbf{Case} &  \textbf{mode} & \textbf{       } & \textbf{per $10^9$ hours of operation}   \\
+%   R         &    wire        & res +         & res -    & description
+\hline
+\hline
+TC:1 $R18$ SHORT    &  Amp plus input high        &  Out of range       &  1.38  \\ \hline
+TC:2 $R18$  OPEN     &  No Offset Voltage         & Low reading     &  12.42\\ \hline
+ \hline
+TC:3 $R22$  SHORT    &  No offset voltage       & Low reading      & 1.38  \\ \hline
+TC:4 $R22$  OPEN     &  Amp plus high input       & Out of Range      & 1.38  \\ \hline
+\hline
+TC:5 $R26$ SHORT     &  No gain from amp         &  Out of Range   &  1.38  \\
+TC:6 $R26$ OPEN     &  Very high amp gain     & Out of Range     & 12.42 \\ \hline
+\hline
+TC:5 $R30$ SHORT     &  Very high amp gain         &  Out of range   &  1.38  \\
+TC:6 $R30$ OPEN     &  No gain from amp            &  Out of Range     & 12.42 \\ \hline
+\hline
+TC:7 $OP\_AMP$ LATCH UP     &   high amp output         &  Out of range   &  1.38  \\
+TC:8 $OP\_AMP$ LATCH DOWN     &  low amp output            &  Out of Range     & 12.42 \\ \hline
+
+\end{tabular}
+\label{tab:fmmdaide1}
+\end{table}
+
+The table \ref{tab:fmmdaide1} shows two possible causes for an undetectable
+error, that of a low reading due to the loss of the offset millivolt signal.
+Typically this type of circuit would be used to read a thermocouple
+and this erro symptom, "LOW READING" would mean our plant could 
+beleive that the temperature reading is lower than it actually is.
+To take an example from a K type thermocouple, the offset of 1.86mV
+from the potential divider represents about 46oC.
+
 \subsection{Undetected Failure Mode: Incorrect Reading}
 
 Although statistically, this failure is unlikely (get stats for R short FIT etc from pt100 doc)