fmmd concept fleshing out

fmmd_concept/fmmd_concept.tex

@@ -52,21 +52,25 @@ paper
 {
 chapter
 }
-presents a bottom up modular methodology, a extension and refinement of FMEA, where instead of looking
+presents a bottom up modular methodology, a extension and refinement to the FMEA, where instead of looking
 at individual component failure modes and deciding on their impact on the SYSTEM 
-it uses the component failure modes, to build modules or derived components.
+it uses the component failure modes, to build modules or derived components,
+using incremental steps to build a hierarchical model.
+%
 This methodology has been named Failure Mode Modular De-composition (FMMD)
 because it de-composes a SYSTEM into a hierarchy of modules or {\dc}s.
+%
 It does this by working from the bottom up, taking small groups
 of components, {\fgs}, and then analysing how they can fail.
 This analysis is performed using FMEA from a micro rather than a macro perspective.
-Thus instead of looked at a component failure modes, and determining how
-it {\em might} cause  a failure at SYSTEM level, we are looking at how
-it will affect the {\fg}.
+Thus instead of looking at a component failure modes, and determining how
+they {\em may} cause  a failure at SYSTEM level, we are looking at how
+they {\em will} affect the {\fg}.
 When we know the failure modes of a {\fg} we can treat it as a `black box'
 or {\dc}. With {\dc}s we can build {\fgs} 
 at higher levels of analysis, until we have a complete
 hierarchy representing the failure behaviour of the SYSTEM.
+%
 Because all the failure modes of all the components
 are held in a computer program, we can determine if the model is complete
 (i.e. all component failure modes have been included in the model).
@@ -78,21 +82,22 @@ are held in a computer program, we can determine if the model is complete
 
 \paragraph{Ideal Static failure mode methodology}
 An ideal Static failure mode methodology would build a failure mode model
-from which the the other four could be derived.
+from which the traditional four models could be derived.
 It would address the short-comings in the other methodologies, and
 would have a user friendly interface, with a visual (rather than mathematical/formal) syntax with icons
 to represent the results of analysis phases.
-
-There are four static analysis failure mode methodologies in common use.
-Each has its advantages and drawbacks, and each is suited for 
-a different phase in the product life cycle.
-These four methodologies are discussed briefly below.
+%
+%There are four static analysis failure mode methodologies in common use.
+%Each has its advantages and drawbacks, and each is suited for 
+%a different phase in the product life cycle.
+The four methodologies in current use are discussed briefly below.
 
 \subsection { FTA }
 
 This, like all top~down methodologies introduces the very serious problem
-of missing component failure modes, or modelling at
-a too high level of failure mode abstraction.
+of missing component failure modes \cite{faa}[Ch.9]
+%, or modelling at
+%a too high level of failure mode abstraction.
 FTA was invented for use on the minuteman nuclear defence missile
 systems in the early 1960's and was not designed as a rigorous
 fault/failure mode methodology. It is more like a structure to
@@ -263,6 +268,54 @@ to smaller and smaller functional modules \cite{maikowski}.
 
 \section{Proposed Methodology \\ Failure Mode Modular De-Composition (FMMD)}
 
+\paragraph{New methodology Must be bottom-up}
+In order to ensure that all component failure modes have been covered
+the methodology will have to work from the bottom-up
+and start with the component failure modes.
+%
+\paragraph{How to build a SYSTEM failure behaviour model}
+The next problem is how to we build a failure mode model
+that converges to a finite set of SYSTEM level failure modes.
+%
+\paragraph{incremental stages and {\fg}s}
+We can use incremental stages to build the hierarchy.
+we can take small {\fg}s of components, where the {\fg}
+is a small set of components that perform a simple
+task.
+This should be small enough to be able to consider all the failure
+modes of its components.
+We can consider these failure modes from the perspective
+of the {\fg}. In other words, for each component failure mode in the {\fg},
+we create a `test case' and decide how each failure affects the functional group.
+%
+With the results from the test cases we will now have the ways in which the 
+{\fg} can fail.
+%
+We can now treat the {\fg} as a component, or rather a {\dc}.
+We can refine this further, by grouping the common symptoms, or results that
+are the same failure w.r.t. the {\fg}.
+%
+We can now create a {\dc} and assign these common symptoms
+as its failure modes.
+%
+This {\dc} can be used to build higher level
+{\fg}s, and naturally a hierarchy is being formed, which is 
+a failure mode behaviour model.
+\paragraph{Directed Acyclic Graph}. This will naturally form a DAG
+meaning that for all SYSTEM failure modes, we will be able to trace
+back through the DAG to possible component failure mode causes.
+If statistical models exist for the component failure modes
+these failure causation trees (or minimal cut sets \cite{nucfta})
+can be used to calculate Mean Time to Failure (MTTF) or Probability of Failure on demand (PFD) figures.
+%
+Because common symptoms are being collected, as we build the tree up-ward
+the number of failure modes decreases (or exceptionally stays the same) at each level.
+%
+This decreasing of the number of failure modes is bourne out {\irl}.
+Of the thousands of component failure modes in a typical product
+there are generally only a handful of SYSTEM level failure modes. 
+%
+
 \subsection{Outline of the FMMD process}
 
 FMMD builds {\fg}s of components from the bottom-up. 
@@ -272,7 +325,7 @@ We can perform a failure mode effects analysis on each of the component failure
 modes within the {\fg}. We can thus ensure that all component failure modes 
 are covered. We can then treat the {\fg} as a `black box' or component in its own right.
 We can now look at how the {\fg} can fail. Many of the component failure modes will
-cause the same failure symptoms in the {fg} fialure behaviour.
+cause the same failure symptoms in the {fg} failure behaviour.
 We can collect these failures as common symptoms.
 When we have out set of symptoms, we can now create
 a {\dc}. The {\dc} will have as its set of failures
@@ -301,7 +354,8 @@ or even in other projects where the same {\dc} is used.
 for its results}
 Because the failure mode mode of a SYSTEM is a hierarchy of {\fg}s and derived components
 SYSTEM level failure modes are traceable back down the tree to
-component level failure modes. This proivides causation minimal cut sets \cite{sccs}
+component level failure modes. This proivides causation trees \cite{sccs} or, minimal cut sets
+\footnote{Here minimal cut sets represent combinations of component failure modes that can result in s SYSTEM level failure.} 
 for all SYSTEM failure modes.
 
 \subsubsection{ It should be capable of producing reliability and danger evaluation statistics.}

style.tex

@@ -74,6 +74,7 @@
 \newcommand{\dcs}{\em derived~components}
 \newcommand{\bc}{\em base~component}
 \newcommand{\bcs}{\em base~components}
+\newcommand{\irl}{in real life}
 \newcommand{\enc}{\ensuremath{\stackrel{enc}{\longrightarrow}}}
 \newcommand{\pin}{\ensuremath{\stackrel{pi}{\longleftrightarrow}}}
 %\newcommand{\pic}{\em pure~intersection~chain}