FIT calculations

fmmd_design_aide/fmmd_design_aide.tex

@@ -494,9 +494,69 @@ We can surmise the symptoms in a list.
 \item symptom: \textbf{no~test~effect} caused by the failure modes: no~test~effect, low~reading.
 \end{itemize}
 
+\section{MTTF Reliability statistics}
 
 
-\section{conclusions}
+%\clearpage
+\subsection{OP-AMP FIT Calculations}
+The DOD electronic reliability of components
+document  MIL-HDBK-217F\cite{mil1992}[5.1] gives formulae for calculating
+the 
+%$\frac{failures}{{10}^6}$ 
+${failures}/{{10}^6}$ % looks better
+hours for a wide range of generic components.
+These figures are based on components from the 1980's and MIL-HDBK-217F
+gives very conservative reliability figures when applied to
+modern components. The formula for a generic packaged micro~circuit
+is reproduced in equation \ref{microcircuitfit}. 
+The meanings of and values assigned to its co-efficients are described in table \ref{tab:opamp}.
+
+\begin{equation}
+ {\lambda}_p = (C_1{\pi}_T+C_2{\pi}_E){\pi}_Q{\pi}_L 
+ \label{microcircuitfit}
+\end{equation}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Low SIL assessment MAX3053
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ 
+\begin{table}[ht]
+\caption{OP AMP FIT assessment} % title of Table
+\centering % used for centering table
+\begin{tabular}{||c|c|l||}
+\hline \hline
+ \em{Parameter}      &  \em{Value}    &   \em{Comments} \\
+                     &                &      \\ \hline \hline
+ $C_1$     &  0.040    &   $300 \ge 1000$ 1001 BiCMOS transistors (1214) \\ \hline
+ ${\pi}_T$ &  1.4         & max temp of $60^o$ C\\ \hline
+ $C_2$     &  0.0026   &  number of functional pins(8) \\ \hline
+ ${\pi}_E$ &  2.0         & ground fixed environment (not benign)\\ \hline
+ ${\pi}_Q$ &  2.0         & Non-Mil spec component\\ \hline
+ ${\pi}_L$ &  1.0         & More than 2 years in production\\ \hline
+
+\hline \hline
+\end{tabular}
+\label{tab:opamp}
+\end{table} 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% END OF Low SIL assessment MAX3053
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Taking these parameters and applying equation \ref{microcircuitfit},
+$$ 0.04 \times1.4 \times0.0026 \times2.0 \times2.0 \times1.0 =  .0005824 $$
+we get a value of $0.0005824 \times {10}^6$ failures per hour.
+This is a worst case FIT\footnote{where FIT (Failure in Time) is defined as 
+failures per Billion (${10}^9$) hours of operation} of 1. 
+
+\subsection{Switching Transistor}
+
+The switching transistor will be operating at a low frequency
+and well within  50\% of it maximum voltage.
+MIL-HDBK-217F\cite{mil1992}[6-25]  gives an exmaple
+transistor in these environmental conditions, and assigns an FIT value of 11.
+
+\section{Conclusions}
 
 With the safety addition the undetectable failure mode of \textbf{low~reading}
 disappears.