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FIT of 1 is 1 failure per 1.1 million years

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Robin 2010-03-25 22:11:15 +00:00
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pt100/pt100.tex
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@ -59,7 +59,7 @@ Note that the low reading goes down as temperature increases, and the higher rea
For this reason the low reading will be reffered to as {\em sense-} For this reason the low reading will be reffered to as {\em sense-}
and the higher as {\em sense+}. and the higher as {\em sense+}.
\subsection{Accuracy despite variable resistance in cables} \subsection{Accuracy despite variable \\ resistance in cables}
For electronic and accuracy reasons a four wire circuit is preffered For electronic and accuracy reasons a four wire circuit is preffered
because of resistance in the cables. Resistance from the supply because of resistance in the cables. Resistance from the supply
@ -69,7 +69,7 @@ is carried by the two `sense' lines the resistance back to the ADC
causes only a negligible voltage drop, and thus the four wire causes only a negligible voltage drop, and thus the four wire
configuration is more accurate. configuration is more accurate.
\subsection{Calculating Temperature from the sense line voltages} \subsection{Calculating Temperature from \\ the sense line voltages}
The current flowing though the The current flowing though the
whole circuit can be measured on the PCB by reading a third whole circuit can be measured on the PCB by reading a third
@ -100,7 +100,7 @@ Where this occurs a circuit re-design is probably the only sensible course of ac
\subsection{Single Fault FMEA Analysis of PT100 Four wire circuit} \subsection{Single Fault FMEA Analysis \\ of PT100 Four wire circuit}
\label{fmea} \label{fmea}
This circuit simply consists of three resistors. This circuit simply consists of three resistors.
@ -208,7 +208,7 @@ for any single error (short or opening of any resistor) this bounds check
will detect it. will detect it.
\section{Single Fault FMEA Analysis of PT100 Four wire circuit} \section{Single Fault FMEA Analysis \\ of PT100 Four wire circuit}
\subsection{Single Fault Modes as PLD} \subsection{Single Fault Modes as PLD}
@ -250,7 +250,7 @@ for the circuit shown in figure \ref{fig:vd}.
\subsection{Proof of Out of Range Values for Failures} \subsection{Proof of Out of Range \\ Values for Failures}
\label{pt110range} \label{pt110range}
Using the temperature ranges defined above we can compare the voltages Using the temperature ranges defined above we can compare the voltages
we would get from the resistor failures to prove that they are we would get from the resistor failures to prove that they are
@ -287,7 +287,7 @@ With pt100 at the high end of the temperature range 300\oc.
$$ highreading = 5V $$ $$ highreading = 5V $$
$$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$ $$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
Thus with $R_2$ shorted both readingare outside the Thus with $R_2$ shorted both readings are outside the
proscribed range in table \ref{ptbounds}. proscribed range in table \ref{ptbounds}.
\subsubsection{ TC : 4 Voltages $R_2$ OPEN } \subsubsection{ TC : 4 Voltages $R_2$ OPEN }
@ -368,7 +368,7 @@ in the other 10\%, so we can use this.
A standard fixed film resistor, for use in a benign environment, non military spec at 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 ($10^9$) 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. hours of operation. This figure is referred to as a FIT\footnote{FIT values are measured as the number of failures per billion hours of operation, (roughly 1.1 Million years). The smaller the FIT number the more reliable the fault~mode}, Failure in time.
A thermistor, bead type, non military spec is given a FIT of 3150. A thermistor, bead type, non military spec is given a FIT of 3150.
@ -378,7 +378,7 @@ showing the FIT values for all faults considered.
\begin{table}[h+] \begin{table}[h+]
\caption{PT100 FMEA Single Fault Statistics} % title of Table \caption{PT100 FMEA Single // Fault Statistics} % title of Table
\centering % used for centering table \centering % used for centering table
\begin{tabular}{||l|c|c|l|l||} \begin{tabular}{||l|c|c|l|l||}
\hline \hline \hline \hline
@ -401,7 +401,8 @@ TC:6 $R_2$ OPEN & High Fault & High Fault & 1.38 \\ \hline
\end{table} \end{table}
The FIT for the circuit as a whole is the sum of MTTF values for all the 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. test cases. The PT100 circuit here has a FIT of 3177.6. This is a MTTF of
about 360 years per circuit.
A Probablistic tree can now be drawn, with a FIT value for the PT100 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. circuit and FIT values for all the component fault modes that it was calculated from.
@ -425,7 +426,7 @@ The next analysis phase looks at how the circuit will behave under double simult
conditions. conditions.
\clearpage \clearpage
\section{ PT100 Double Simultaneous Fault Analysis} \section{ PT100 Double Simultaneous \\ Fault Analysis}
% typeset in {\Huge \LaTeX} \today % typeset in {\Huge \LaTeX} \today