diff --git a/pt100/pt100.tex b/pt100/pt100.tex index f7c9daf..a080e92 100644 --- a/pt100/pt100.tex +++ b/pt100/pt100.tex @@ -24,7 +24,6 @@ from an FMEA persepective as a component itself, with a set of known failure mod \end{abstract} } { - \section{Overview} The PT100, or platinum wire \ohms{100} sensor is a widely used industrial temperature sensor that is @@ -43,8 +42,6 @@ the failure modes of the components, analysing the circuit using FMEA and producing a failure mode model for the circuit as a whole. Thus after the analysis the PT100 temperature sensing circuit, may be veiwed from an FMEA persepective as a component itself, with a set of known failure modes. - - } \begin{figure}[h] @@ -271,6 +268,7 @@ and are thus enclosed by one contour each. \label{fig:pt100_tc} \end{figure} +ating input Fault This circuit supplies two results, sense+ and sense- voltage readings. To establish the valid voltage ranges for these, and knowing our valid temperature range for this example ({0\oc} .. {300\oc}) we can calculate @@ -566,8 +564,143 @@ conditions. \clearpage \section{ PT100 Double Simultaneous \\ Fault Analysis} +In this section we examine the failure mode behaviour for all single +faults and double simultaneous faults. +This corresponds to the cardinality contstrained powerset of +the failure modes in the functional group. +All the single faults have already be proved in the last section. +For the next set of test cases, let us again hypothesise +the failure modes, and then examine each one in detail with +potential divider equation proofs. + +Table \ref{tab:ptfmea2} lists all the combinations of double +faults and then hypothesises how the functional~group will react +under those conditions. + +\begin{table}[ht] +\caption{PT100 FMEA Double Faults} % title of Table +\centering % used for centering table +\begin{tabular}{||l|l|c|c|l|l||} +\hline \hline + \textbf{TC} &\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{General} \\ + \textbf{number} &\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{Symtom Description} \\ +% R & wire & res + & res - & description +\hline +\hline + TC 7: & $R_1$ OPEN $R_2$ OPEN & Floating input Fault & Floating input Fault & Unknown value readings \\ \hline + TC 8: & $R_1$ OPEN $R_2$ SHORT & low & low & Both out of range \\ \hline +\hline + TC 9: & $R_1$ OPEN $R_3$ OPEN & high & low & Both out of Range \\ \hline + TC 10: & $R_1$ OPEN $R_3$ SHORT & low & low & Both out of range \\ \hline +\hline + + TC 11: & $R_1$ SHORT $R_2$ OPEN & high & high & Both out of range \\ \hline +TC 12: & $R_1$ SHORT $R_2$ SHORT & high & low & Both out of range \\ \hline +\hline + TC 13: & $R_1$ SHORT $R_3$ OPEN & high & low & Both out of Range \\ \hline +TC 14: & $R_1$ SHORT $R_3$ SHORT & high & high & Both out of range \\ \hline + +\hline + TC 15: & $R_2$ OPEN $R_3$ SHORT & high & Floating input Fault & sense+ out of range \\ \hline +TC 16: & $R_2$ OPEN $R_3$ SHORT & high & high & Both out of Range \\ \hline +TC 17: & $R_2$ SHORT $R_3$ OPEN & high & low & Both out of Range \\ \hline +TC 18: & $R_2$ SHORT $R_3$ SHORT & low & low & Both out of Range \\ \hline +\hline +\end{tabular} +\label{tab:ptfmea2} +\end{table} + +\subsection{Verifying complete coverage for a \\ cardinality constrained powerset of 2} + +It is important to check that we have covered all possible double fault combinations. +We can use the equation \ref{eqn:correctedccps2}, reproduced below to verify this. -DO THE DOUBLE -% typeset in {\Huge \LaTeX} \today + +\begin{equation} + |{\mathcal{P}_{cc}SU}| = {\sum^{k}_{1..cc} \frac{|{SU}|!}{k!(|{SU}| - k)!}} +- \sum^{p}_{2..cc}{{\sum^{j}_{j \in J} \frac{|FM({C_j})|!}{p!(|FM({C_j})| - p)!}} } + \label{eqn:correctedccps2} +\end{equation} + + +$|FM(C_j)|$ is always 2 here, as all the components are resistors and have two failure modes. + +% +% Factorial of zero is one ! You can only arrange an empty set one way ! + +Populating this equation with $|SU| = 6$ and $|FM(C_j)|$ is always 2 here as all the components are resistors and have two failure modes. + +\begin{equation} + |{\mathcal{P}_{2}SU}| = {\sum^{k}_{1..2} \frac{6!}{k!(6 - k)!}} +- \sum^{p}_{2..2}{{\sum^{j}_{1..3} \frac{2!}{p!(2 - p)!}} } + \label{eqn:correctedccps2} +\end{equation} + +$|{\mathcal{P}_{2}SU}|$ is the number of valid combinations of faults to check +under the conditions of unitary state failure modes for the components (a resistor cannot fail by being shorted and open at the same time). + +Expanding the sumations + + +$$ NoOfTestCasesToCheck = \frac{6!}{1!(6-1)!} + \frac{6!}{2!(6-2)!} - \Big( \frac{2!}{2!(2 - 2)!} + \frac{2!}{2!(2 - 2)!} + \frac{2!}{2!(2 - 2)!} \Big) $$ + +$$ NoOfTestCasesToCheck = 6 + 15 - ( 1 + 1 + 1 ) = 18 $$ + +As the test case are all different and are of the correct cardinalities (6 single faults and (15-3) double) +we can be confident that we have looked at all combinations up to two, of the possible faults +in the pt100 circuit. The next task is to investigate +these test cases in more detail to prove the failure mode hypothese set out in table \ref{tab:ptfmea2}. + + +\subsection{Proof of Double Faults Hypothese } + +\subsubsection{ TC 7 : Voltages $R_1$ OPEN $R_2$ OPEN } + +This double fault mode produces an interesting symptom. +Both sense lines are floating. +We cannot know what the {\adctw} readings on them will be. +In practise these would probably float to low values +but for the purpose of a safety critical analysis +all we can say is the values are `floating' and `unknown'. +This is an interesting case, because it is, at this stage an undetectable +fault that must be handled. + + +\subsubsection{ TC 8 : Voltages $R_1$ OPEN $R_2$ SHORT } + +This cuts the supply from Vcc. Both sense lines will be at zero. +Thus both values will be out of range. + + +\subsubsection{ TC 9 : Voltages $R_1$ OPEN $R_3$ OPEN } + +Sense- will be floating. +Sense+ will be tied to Vcc and will thus be out of range. + +\subsubsection{ TC 10 : Voltages $R_1$ OPEN $R_3$ SHORT } + +This shorts ground to the +both of the sense lines. +Both values thuis out of range. + +\subsubsection{ TC 11 : Voltages $R_1$ SHORT $R_2$ OPEN } + +This shorts both sense lines to Vcc. +Both values will be out of range. + + +\subsubsection{ TC 12 : Voltages $R_1$ SHORT $R_2$ SHORT } + +This shorts the sense+ to Vcc and the sense- to ground. +Both values will be out of range. + + + + + + + + +typeset in {\Huge \LaTeX} \today diff --git a/standards/standards.tex b/standards/standards.tex index 783735b..5e4c9f2 100644 --- a/standards/standards.tex +++ b/standards/standards.tex @@ -4,29 +4,37 @@ \ifthenelse {\boolean{paper}} { \begin{abstract} -This chapter describes the legal frameworks and standards organisations +This paper describes the legal frameworks and standards organisations that exist in Europe and North America. Some specific standards (that the author has experience with directly) are reviewed. \end{abstract} } -{} - +{ +This chapter describes the legal frameworks and standards organisations +that exist in Europe and North America. +Some specific standards (that the author has experience with directly) +are reviewed. +} \section{Introduction} \subsection{Product Life Cycle} -i + difffernent areas EN61508 REQ to SPEC to DESIGN EN298 -DESIGN TO PRODUCT +DESIGN TO +TESTING (EMC PRODUCT FM PRODUCT VERIFICATION MONITORING + +NEW A PRODUCT LIFE CYCLE IMAGE WITH AN EULER DIAGRMA FOR THE DIFFERENT STANDARDS + Different agencies - approval is testing of new product and verification to standard - manufacturing overwatch / supervision word on tip of tounge -