11 Failure Analysis

Failure analysis displays causality in the system by showing the impact of faults through response simulations, propagation tables and failure reporting. MADE processes all the possible functional connections and functional failures in a model by using an n x n matrix (also known as a Functional Concept Map – FCM). This matrix represents every causal connection between input and output flow properties in the system model.

11.1 Connection Viewer

The connection viewer displays the source (input) and target (output) flow properties in each model item, including numerical (crisp) values of the causal strength, probability, progression rate (failure mechanism), and causal strength polarity.

To open the Connection viewer:

• Select the MADE module
• Select Windows → Open View → Connection Viewer from the main menu

(Other views listed in the same menu: Project Explorer, Properties, Failure Concepts, Hazard Concepts, Image, Library, Outline, Palette, Problems, Component List, Test Points, Connection Viewer, Critical Items, Criticality Viewer, Current Diagnostic Analysis, Technical Budget Analysis, Equation Set, Failure Step Table, Fault Code Viewer, Report History.)

Table 7: Description of Connection viewer columns

Column	Description
Untitled Column (1)	Displays the input flow property or failure concept of the selected model item (if a failure diagram is present).
Source	Describes the type of flow property or failure concept.
Component (1)	Displays the selected model item.
Gate	Displays the response filter for the causal connection between input and output flow properties (Block positive or negative), the gate type between failure causes and mechanisms (AND/OR gates), or remains blank if no gate types or response filters are applied.
Untitled Column (2)	Displays the output flow property or subsequent failure concept (if a failure diagram is present) of the selected model item.
Target	Describes the type of flow property or failure concept.
Component (2)	Displays the succeeding model item connected to the output flow property of the target model item.
Causal Strength	Displays the crisp value from 1.0 to 10.0 of each causal connection.
Probability	Displays the crisp value from 0.01 to 10.0 of each failure connection between failure concepts.
Progression Rate	Displays the crisp value from 1.0 to 10.0 of each failure connection from a failure mechanism to a fault.
Polarity	Displays the polarity (positive/negative) of each causal connection between input and output flow properties.

Example Connection Viewer rows (for "Diesel Engine", all OR-gated, Polarity Positive unless noted): Control Mechanical - linear Li[near velocity] → Governor: Regulate Liquid Dynamic press[ure] → Injector Pump (10.00 / 10.00); Convert Continuous Amplitud[e] → Diesel Engine: Control Mechanical - linear Lin[ear velocity] → Governor (10.00/10.00); Convert Electrical Voltage → Diesel Engine: Regulate Liquid Dynamic press[ure] → Injector Pump (5.00/10.00, distinct row); Convert Liquid Static pressure → Diesel Engine: Increase Liquid Flow rate → Lift Pump (10.00/10.00); Convert Mechanical - rotation[al] → Engine: Convert Mechanical - rotation[al] → Diesel Engine (blank causal strength, polarity Positive only); Convert Mechanical - rotation[al] → Engine: Couple Mechanical - rotational... → Coupling 1 (10.00/10.00); Couple Mechanical - rotationa[l] → Coupling 1: Increase Liquid Flow rate → Lift Pump (5.00/10.00); Increase Liquid Flow rate → Lift Pump: Refine Liquid Flow rate → Primary Fuel [Filter] (10.00/10.00); Refine Gas Mass flow rate → Air Filter: Refine Liquid... → Convert Mechanical - rotationa[l] → Engine (10.00/10.00); Refine Liquid Flow rate → Primary Fuel[ Filter]: Refine Liquid Flow rate → Secondary F[uel Filter] (10.00/10.00); Refine Liquid Flow rate → Secondary F[uel Filter]: Regulate Liquid Dynamic pres[sure] → Injector Pump (10.00/10.00); Regulate Liquid Dynamic pres[sure] → Injector Pump: Convert Mechanical - rotationa[l] → Engine (10.00/10.00).

To view the functional or causal connections of a specific component, click on the component in the project explorer or system diagram and the contents of the connection viewer table will automatically refresh to display them.

11.2 Step Table Viewer

The MADE step table viewer allows users to perturb (simulate) one or more failures in the system model, then uses a step table to determine how the effects of those failures are propagated throughout the system. This viewer is a useful way for tracing the results of a system response for an injected failure. Further information about the calculations used is available under the Step Table topics in the MADE Help topics.

To open the step table viewer:

• Select View → Open View → Failure Step Table

To run a failure analysis for a single FFM:

• Select (Right-click) an item (subsystem or component)
• Select Failure Injection → [Functional Flow] → [Failure Response]
• Select the step icons in the icon menu or Step Table Viewer to propagate the failure

Example: perturbing the fuel flow rate in a Lift Pump — right-click menu path Failure Injection → Liquid Flow rate → Up/Down/Perturb by Value, selecting Down.

Once a failure has been injected, the Propagation Table – FCM viewer will appear. Once the user selects the step icons (e.g. Run) the Step Table viewer will also appear. The step table will be initially empty. Selecting the Run icon will show the final state vector for the system, which is determined at the end of the iterations of analysis.

To view the entire response to the perturbation:

• Select the Run icon from the icon menu (icon menu shows: Run/Run-Step/Step-Backward/Reset/Clear/Table-view icons, with tooltip "Run (Step to Equilibrium)")

This will generate a response in the system until a steady state or equilibrium is achieved. Since this takes multiple iterations, the user can instead view the step-by-step response to trace the response progression.

To view each step of the analysis:

• Select the Step Forward icon to advance the Step table iterations by one step (tooltip: "Step Forward one Step")
• Select the Step Backward icon to revert the Step table iteration by one step (tooltip: "Step Backward one step")

Each time the user Steps Forward One Step, a column will be populated with perturbation results for the current step or iteration. The system response at each step is highlighted in the system model above the step table. Initial changes from nominal behavior are highlighted in green cells. If a response does not occur for a step or occurs at a sub-component level, it is obscured from the current system level editor.

To reset the step table:

• Select the Reset Step Table icon — removes all current iterations in the Step Table for the user to repeat the current failure analysis.

To clear the step table:

• Select the Clear Step Table icon — resets the Step Table viewer if the user no longer requires the current perturbation results or desires to analyze a different set of step table results.

Example Step Table (Diesel Engine, perturbation "Increase Liquid Flow rate (Lift Pump)"), columns i, 1, 2, 3, 4, 5, 6, with representative rows: Air Filter Gas Mass flow rate all 0.0; Coupling 1 Mechanical-rotational Angular velocity reaching -0.44 at step 5 and -0.472 at step 6; Engine Mechanical-rotational Torque reaching -0.472 at steps 4 and 5; Injector Pump Liquid Dynamic pressure reaching -0.512 at steps 4-5; Lift Pump Liquid Flow rate reaching -0.762 from step 1 onward.

11.3 Functional Response Simulations

Another useful way to check the analysis results is to view a plot of the functional response of components to an activated failure mode. The example below continues from the previous Lift Pump perturbation to examine the consequent response in the Primary Fuel Filter if the Lift Pump experiences a flow rate drop.

To open the response simulation for the filter component:

• Select (Right-click) the Primary Fuel Filter in the system model
• Select Response Simulation > Liquid Flow Rate

A Functional Response Simulation viewer will appear. Plots for selected flow properties for specific components show the increase or decrease for each step in the system. Example: the functional response simulation graph for Primary Fuel Filter Liquid Flow rate shows a "FAILURE ACTIVATION" marker, dropping and stabilizing near -0.883 from step 2 onward.

To observe the response of a further downstream component (e.g. Engine):

• Check the checkbox for e.g. Engine > Mechanical – Rotational Torque in the response tree

The response of the engine occurs at 5 steps (iterations) of the FCM analysis, and the overall response is low (below nominal). The reason for the response is due to the initial drop from the Lift Pump. Plotting both the Primary Fuel Filter Liquid Flow rate and the Engine Mechanical-rotational Torque response together shows two lines converging to a low steady-state value (approximately -0.883 / near -1.0 respectively) after the failure injection in the fuel tank/lift pump chain.

11.4 View Propagation Table

The propagation table displays the initial (transient) and final (steady-state) responses of each flow property to the injected failure mode. The transient response of a flow property is taken as the first change to the flow property during the analysis. The steady-state response of a flow property is its final value after successive iterations yield two identical system state vectors.

To view the propagation table:

• Right-click the system model editor
• Select Diagram → Propagate All from the right-click menu
• Alternatively, select the Propagate All icon from the Icon Menu
• A Propagate All dialog will appear for the user to select flows to propagate

The Propagate All dialog has: Propagation Method (FCM / Bond radio buttons, default FCM); Response Types (Steady State / Transient State / Both radio buttons, default Steady State); a Propagation Summary tree (FCM > Energy > Mechanical-linear Linear velocity, Mechanical-rotational Angular velocity, Mechanical-rotational Torque; Material > Gas Mass flow rate, Liquid Dynamic pressure, Liquid Flow rate); and a right-hand Propagation Focus panel with a matching checked tree and Select all/Deselect all buttons. Buttons: Propagate, Cancel.

After selecting Propagate in the dialog, MADE automatically injects multiple failures and analyses the system response to every possible failure in the system, as determined by the failure paths mapped out in the item failure diagrams. The propagation table is interpreted as follows:

• Each row represents a failure mode and its effects on other model items
• Component column shows the model item display name and item type
• Flow Property column displays the associated flow properties to the model item
• Failure Response column details the failure mode response
• Subsequent columns display item responses in response to the failure in each row

Example Propagation Table header shows: "Coverage: 33% | Response State: Steady State | Threshold Type: Trivalent Sigmoid | Generated: 11:52:04am". Rows include Air Filter (Mass flow rate (Gas), Failure = High, with cascading High/Low responses across Coupling 1, Engine, Governor, Injector Pump, Lift Pump, Primary Fuel Filter, Secondary Fuel Filter columns); Coupling 1 (Angular velocity, Failure = Low); Engine (Torque, Failure = Low); Governor (Linear velocity, Failure = Low); Injector Pump (Dynamic pressure, Failure = Low); Lift Pump (Flow rate, Failure = Low); Primary Fuel Filter (Flow rate, Failure = Low); Secondary Fuel Filter (Flow rate, Failure = Low).