morning edit

pt100/pt100.tex

@@ -34,7 +34,7 @@ from an FMEA persepective as a component itself, with a set of known failure mod
 
 \section{Overview of PT100 four wire circuit}
 
-The PT100 four wire circuit consists supplies a test current vis two wires
+The PT100 four wire circuit uses two wires to supply small electrical current,
 and returns two sense volages by the other two.
 By measuring volatges
 from sections of this circuit forming potential dividers, we can determine the 
@@ -356,12 +356,71 @@ The PT100 circuit can now be treated as a component in its own right, and has on
 
 %Interestingly we can calculate the failure statistics for this circuit now.
 %Mill 1991 gives resistor stats of ${10}^{11}$ times 6 (can we get special stats for pt100) ???
+\clearpage
+\subsection{Mean Time to Failure}
+
+Using the MIL1991\cite{mil1991} specifications for resistor and thermistor
+failure statistics we calculate the reliability of this circuit.
+MIL1991 gives MTTF for a wide range of common components.
+It does not specify how the components will fail (in this case OPEN or SHORT).
+RIAC does specify that resistors are expevcted to fail OPEN in 90\% of cases and SHORTED 
+in the other 10\%, so we can use this.
+
+A standard fixed film resistor, for use in a benign environment, non military spec at
+temperatures up to 60\oc is given a probability of 13.8 failures per billion ($10^9$)
+hours of operation. This figure is referred to as a FIT\footnote{FIT values are measured as failures per billion hours of operation, roughly 114,000 years}, Failure in time.
+
+A thermistor, bead type, non military spec is given a FIT of 3150.
+
+Using the RIAC finding we can draw up the following table \ref{tab:stat_single},
+showing the FIT values for all faults considered.
+
+
+
+\begin{table}[h+]
+\caption{PT100 FMEA Single Fault Statistics} % title of Table
+\centering % used for centering table
+\begin{tabular}{||l|c|c|l|l||}
+\hline \hline
+ \textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF}   \\
+ \textbf{Case} &  \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation}   \\
+%   R         &    wire        & res +         & res -    & description
+\hline
+\hline
+TC:1 $R_1$ SHORT    &  High Fault        &  -       &  12.42 \\ \hline
+TC:2 $R_1$  OPEN     &  Low Fault         & Low Fault     &  1.38 \\ \hline
+ \hline
+TC:3 $R_3$  SHORT    &  Low Fault          & High Fault      &   2835 \\ \hline
+TC:4 $R_3$  OPEN     &  High Fault         & Low  Fault    &   315 \\ \hline
+\hline
+TC:5 $R_2$ SHORT     &  -         &  Low Fault   &  12.42 \\  
+TC:6 $R_2$ OPEN     &  High Fault         & High Fault     &  1.38 \\ \hline
+\hline
+\end{tabular} 
+\label{tab:stat_single}
+\end{table}
+
+The FIT for the circuit as a whole is the sum of MTTF values for all the 
+test cases. The PT100 circuit here has a  FIT of 3177.6.
+
+A Probablistic tree can now be drawn, with a FIT value for the PT100
+circuit and FIT values for all the component fault modes that it was calculated from.
+
+
+\begin{figure}[h+]
+ \centering
+ \includegraphics[width=400pt,bb=0 0 856 327,keepaspectratio=true]{./stat_single.jpg}
+ % stat_single.jpg: 856x327 pixel, 72dpi, 30.20x11.54 cm, bb=0 0 856 327
+ \caption{Probablistic Fault Tree : PT100 Single Faults}
+ \label{fig:stat_single}
+\end{figure}
+
 
 The PT100 analysis presents a simple result for single faults. 
 The next analysis phase looks at how the circuit will behave under double simultaneous failure
 conditions.
 
-
+\clearpage
 \section{ PT100 Double Simultaneous Fault Analysis}
 
 % typeset in {\Huge \LaTeX} \today