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@ -350,7 +350,7 @@ Electrical resistors can fail by going OPEN or SHORTED.
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For a given resistor R we can apply the
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For a given resistor R we can apply the
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function $fm$ to find its set of failure modes thus $ fm(R) = \{R_{SHORTED}, R_{OPEN}\} $.
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function $fm$ to find its set of failure modes thus $ fm(R) = \{R_{SHORTED}, R_{OPEN}\} $.
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A resistor cannot fail with both conditions open and short active at the same time! The conditions
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A resistor cannot fail with the conditions open and short active at the same time! The conditions
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OPEN and SHORT are thus mutually exclusive.
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OPEN and SHORT are thus mutually exclusive.
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Because of this, the failure mode set $F=fm(R)$ is `unitary~state'.
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Because of this, the failure mode set $F=fm(R)$ is `unitary~state'.
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@ -120,12 +120,12 @@ This is a bottom up methodology, which takes component failure modes
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and traces them to the SYSTEM level failures. The components
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and traces them to the SYSTEM level failures. The components
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have reliability data and this can be used to predict the
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have reliability data and this can be used to predict the
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failure statistics in the design stage \cite{mil1992}.
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failure statistics in the design stage \cite{mil1992}.
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It can do this using probability \footnote{for a given component failure mode there will be a $\Beta$ value, the
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It can do this using probability \footnote{for a given component failure mode there will be a $\beta$ value, the
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probability that the component failure mode will cause a given SYSTEM failure}.
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probability that the component failure mode will cause a given SYSTEM failure}.
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%
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%
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This lacks precision, or in other words, determinability prediction accuracy \cite{fafmea},
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This lacks precision, or in other words, determinability prediction accuracy \cite{fafmea},
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as often the component failure mode can't be proven to cause a SYSTEM level failure, but
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as often the component failure mode can't be proven to cause a SYSTEM level failure, but
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assigned a probability $\Beta$ fator by the design engineer.
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assigned a probability $\beta$ fator by the design engineer.
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%Also, it can miss combinations of failure modes that will cause SYSTEM level errors.
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%Also, it can miss combinations of failure modes that will cause SYSTEM level errors.
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%
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%
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The results, as with FMEA are an $RPN$ number determing the significance of the SYSTEM fault.
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The results, as with FMEA are an $RPN$ number determing the significance of the SYSTEM fault.
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@ -145,7 +145,7 @@ The results, as with FMEA are an $RPN$ number determing the significance of the
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This is a process that takes all the components in a system,
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This is a process that takes all the components in a system,
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and from the failure modes of those components
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and from the failure modes of those components
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tnote{for a given component failure mode there will be a $\Beta$ value, the
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tnote{for a given component failure mode there will be a $\beta$ value, the
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probability that the component failure mode will cause a given SYSTEM failure}.
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probability that the component failure mode will cause a given SYSTEM failure}.
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calculates a risk factor for each.
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calculates a risk factor for each.
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