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Chapter 9 Markov 203 CHAPTER 9 Markov Markov Analysis is a technique used to obtain numerical measures related to the reliability and availability of a system or part of a system. Markov Analysis is performed when dependencies between the failure of multiple components as well as dependencies between component failures and failure rates cannot be easily represented using a combination of fault trees and standard time-to-failure and time-to-repair distributions. Specific examples of application areas are standby redundancy configurations as well as common cause failures. This chapter: 1. Introduces Markov system 2. Describes ToolKit’s Markov features 3. Outlines an example Markov System 4. Describes the Markov Editor Screen, Toolbars and Shortcut Keys
204 <strong>ITEM</strong> ToolKit Getting Started Guide 1. Introduction Why Use a Markov Analysis? Markov models allow for a detailed representation of failure and repair processes, particularly when dependencies are involved, and therefore result in more realistic assessments of system reliability measures than simple time-to failure and time-to-repair models. Markov Analysis is well suited to handle rare events, unlike simulation-based analyses, and therefore allows such events to be analyzed within a reasonable amount of time. When is Markov Model Used? Markov Analysis is a technique used to obtain numerical measures related to the reliability and availability of a system or part of a system. Markov Analysis is performed when dependencies between the failure of multiple components as well as dependencies between component failures and failure rates cannot be easily represented using a combination of fault trees and standard time-to-failure and time-to-repair distributions. Specific examples of application areas are standby redundancy configurations as well as common cause failures. Markov Construction A Markov Analysis consists of three major steps: 1. Specification of the states the system can be in 2. Specification of the rates at which transitions between states take place 3. Computation of the solutions to the model Steps 1 and 2 take place in the graphical Markov model editor. In this editor, drawing circles and arrows between the circles, respectively, can create states and transitions between them. The construction of larger Markov models is facilitated by the editor's ability to hierarchically construct Markov models, i.e. break down a higher-level state into lower-level states on a separate 'page', similar to the use of transfer gates in Fault Tree modeling. Both continuous and discrete transitions can be introduced into the model. Continuous transitions are those representing events that can take place at any time within a given time interval, whereas discrete transitions take place at a specified point in time. For this purpose, individual transitions belong to a transition group, consisting of all the transitions applicable to a given time interval, or taking place at a given point in time. Between intervals, the rate at which given transitions take place may be changed, providing a powerful scheme for phased-mission Markov Models. Another strong feature of ToolKit’s Markov Module is its capability to define state groups. State groups are groups of states within the model for which the user wants to obtain combined statistics, such as total time spent in any of the states, or number of transitions in or our out of the group. One group that is defined by default is the 'Unavailable' group. Any time spent in a state that is marked by the user as belonging to this group is considered to be system downtime, which is taken into account when computing reliability and availability measures. Once the definition of the model is complete, the user indicates which statistics should be computed, beyond the reliability measures that are computed by default. Available measures include state probabilities, time spent in a given state or state group, as well as transition rate and number of transitions in and out of a given state or state group. After computation of the solution, Step 3, these results can be observed in the various tabular and graphical formats.
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ITEM TOOLKIT ® TUTORIAL GETTING ST
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Contents Contents i CONTENTS ......
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Contents 1. CREATING A BILL OF MATE
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Preface 1 Preface ITEM ToolKit is a
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Chapter 1 Introducing ITEM ToolKit
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Chapter 1 Introducing ITEM ToolKit
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2. Hardware and Software Requiremen
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Chapter 2 Installing ITEM ToolKit 9
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Activating the Software Chapter 2 I
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• When the InstallShield Wizard C
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Network TCP/IP Connections Setup Ch
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3. License Server Installation Chap
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Installing the License Manager Chap
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• When the InstallShield Wizard C
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• Selecting Unlock Online opens t
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Network File Share Connections Setu
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Network TCP/IP Connections Setup Ch
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4. Network Client Installation Chap
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Installing the Software Chapter 2 I
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Activating the Software Chapter 2 I
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5. View-Only Client Installation Ch
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Installing the Software Chapter 2 I
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• The Choose Network Destination
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Chapter 3 ToolKit Basics 83 CHAPTER
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Chapter 3 ToolKit Basics 85 The Sys
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Chapter 3 ToolKit Basics 87 The Gri
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Chapter 3 ToolKit Basics 89 The Cha
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3. The ToolKit Menus Chapter 3 Tool
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Add Menu Chapter 3 ToolKit Basics 9
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Analysis Menu Chapter 3 ToolKit Bas
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4. The ToolKit Toolbars Chapter 3 T
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Chapter 4 Project Basics 99 CHAPTER
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2. Opening a Project Chapter 4 Proj
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4. Editing Project and System Prope
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6. Closing a Project Chapter 4 Proj
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Chapter 5 Predictions 107 CHAPTER 5
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3. Creating a Prediction Project Ch
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Chapter 5 Predictions 111 F E The t
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Field Part Number Name Circuit Ref
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Chapter 5 Predictions 115 D B A C E
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Chapter 5 Predictions 117 Viewing R
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Chapter 5 Predictions 119 4. Derati
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2. Select the desired Derating stan
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Chapter 5 Predictions 123 Creating
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Chapter 5 Predictions 125 5. Predic
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The Project Toolbar The Project Too
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Chapter 5 Predictions 129 The NSWC
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Chapter 6 FMECA 131 CHAPTER 6 FMECA
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3. Creating a FMECA Project Chapter
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Chapter 6 FMECA 135 A B C 2. Select
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Chapter 6 FMECA 137 Field Mode - Re
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Chapter 6 FMECA 139 2. Place the bl
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Adding and Editing Components Chapt
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Chapter 6 FMECA 143 Field Descripti
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Defining FMECA Severity Chapter 6 F
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3. Click the Mode + button to add a
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Chapter 6 FMECA 149 D F G E H J 4.
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Chapter 6 FMECA 151 5. If no errors
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Page 164 and 165: Chapter 7 RBD 157 CHAPTER 7 RBD A r
Page 166 and 167: 3. Creating an RBD Project Creating
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Page 170 and 171: Chapter 7 RBD 163 What is a Node? N
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Page 174 and 175: When verifying RBD projects, ToolKi
Page 176 and 177: Understanding Analysis Results Chap
Page 178 and 179: The Default Toolbar Chapter 7 RBD 1
Page 180 and 181: Chapter 7 RBD 173 The Project Toolb
Page 182 and 183: Chapter 7 RBD 175 The Graph Toolbar
Page 184 and 185: Chapter 8 Fault Tree 177 CHAPTER 8
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Page 206 and 207: The Align Toolbar Chapter 8 Fault T
Page 208 and 209: Chapter 8 Fault Tree 201 The Canvas
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Page 228 and 229: The Canvas Toolbar The Canvas Toolb
Page 230 and 231: The Graph Toolbar Chapter 9 Markov
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Page 240 and 241: Viewing Results To view the project
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Page 246 and 247: Chapter 11 SpareCost 239 CHAPTER 11
Page 248 and 249: Powerful Customizable Reports ToolK
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Shortcut Keys: Chapter 11 SpareCost
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Chapter 12 Event Tree 255 CHAPTER 1
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Chapter 12 Event Tree 257 Once the
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Binary Decision Diagram (BDD): Chap
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5. Enter your project information b
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Chapter 12 Event Tree 263 11. Enter
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5. Click on Event List and the Proj
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2. Double Click on the Consequence
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1. Click on the Event Tree Tab to o
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Chapter 12 Event Tree 271 To Verify
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Chapter 12 Event Tree 273 Importanc
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Chapter 12 Event Tree 275 4. Event
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The Project Toolbar The Project Too
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Chapter 12 Event Tree 279 The Zoom
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Chapter 13 Reports 281 CHAPTER 13 W
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Chapter 13 Reports 283 Preview Tab
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Chapter 13 Reports 285 This is an e
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Chapter 13 Reports 287 Inserting a
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Chapter 13 Reports 289 The Field Wi
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Chapter 13 Reports 291 4. Problem S
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Chapter 14 Import/Export 293 CHAPTE
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Chapter 14 Import/Export 295 2. Imp
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Chapter 14 Import/Export 297 8. Cli
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Chapter 14 Import/Export 299 3. Exp
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Chapter 14 Import/Export 301 Select
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Chapter 15 Library Facilities 303 C
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Chapter 15 Library Facilities 305 2
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Chapter 15 Library Facilities 307 3
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Chapter 16 Grid View Customization
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Chapter 16 Grid View Customization
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ITEM Software (USA) 34 Executive Pa
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