Reliability Phase Diagrams (RPDs) - Revision history

Cruz Daniel at 14:21, 30 April 2021

2021-04-30T14:21:35Z

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	In this figure, the taxiing, take-off, cruising and landing blocks represent the operational phases and the final block is a maintenance phase. Each of the operational phases in this diagram has two paths leading from it: a success path and a failure path. This graphically illustrates the consequences in each case. For instance, if the first taxiing phase is successful, the airplane will proceed to the take-off phase; if it is unsuccessful, the airplane will be sent for maintenance. The failure paths for the take-off, cruising and landing phases point to stop blocks, which indicate that the simulation of the mission ends. For the final taxiing phase, both the success and failure paths lead to the maintenance path; the node block allows you to model this type of shared outcome.		In this figure, the taxiing, take-off, cruising and landing blocks represent the operational phases and the final block is a maintenance phase. Each of the operational phases in this diagram has two paths leading from it: a success path and a failure path. This graphically illustrates the consequences in each case. For instance, if the first taxiing phase is successful, the airplane will proceed to the take-off phase; if it is unsuccessful, the airplane will be sent for maintenance. The failure paths for the take-off, cruising and landing phases point to stop blocks, which indicate that the simulation of the mission ends. For the final taxiing phase, both the success and failure paths lead to the maintenance path; the node block allows you to model this type of shared outcome.

	The execution of a phase diagram from its first phase to its last phase is referred to as one cycle. For example, for the airplane mentioned above, a single mission from the initial taxiing through the post-flight maintenance is one cycle. If the simulation end time exceeds the total duration of one cycle of a phase diagram, the simulation continues and the phase diagram is executed multiple times until the simulation end time is reached. Execution of a phase diagram multiple times during a simulation is referred to as cycling. During cycling, the age of components accumulated in the last phase of the previous cycle is carried over to the first phase of the next cycle~~. The principle of cumulative damage is used to transfer the age across phases for each component (block)~~. In summary, cycling is used to model the continuous operation of a system involving repetition of the same phases in the same sequence (e.g., an airplane making multiple flights).		The execution of a phase diagram from its first phase to its last phase is referred to as one cycle. For example, for the airplane mentioned above, a single mission from the initial taxiing through the post-flight maintenance is one cycle. If the simulation end time exceeds the total duration of one cycle of a phase diagram, the simulation continues and the phase diagram is executed multiple times until the simulation end time is reached. Execution of a phase diagram multiple times during a simulation is referred to as cycling. During cycling, the age of components accumulated in the last phase of the previous cycle is carried over to the first phase of the next cycle. In summary, cycling is used to model the continuous operation of a system involving repetition of the same phases in the same sequence (e.g., an airplane making multiple flights).

	The sections that follow describe the types of phase blocks and other blocks that can be used in a phase diagram, as well as how those blocks can be connected. A more detailed example is then presented, followed by a discussion of the rules and assumptions that apply in phase diagram simulation. Finally, throughput in phase diagrams is discussed.		The sections that follow describe the types of phase blocks and other blocks that can be used in a phase diagram, as well as how those blocks can be connected. A more detailed example is then presented, followed by a discussion of the rules and assumptions that apply in phase diagram simulation. Finally, throughput in phase diagrams is discussed.

Richard House: /* Stop Blocks */

2015-12-11T20:02:31Z

Stop Blocks

← Older revision		Revision as of 20:02, 11 December 2015
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	Stop blocks indicate that the simulation of the mission ends. A new simulation may then begin, if applicable. This is useful in situations where maintenance is not possible upon failure.		Stop blocks indicate that the simulation of the mission ends. A new simulation may then begin, if applicable. This is useful in situations where maintenance is not possible upon failure.

	[[Image:Phase stop block.png\|center\|~~350px~~]]		[[Image:Phase stop block.png\|center\|450px\|link=]]

	Stop blocks can have unlimited incoming connections. No outgoing connections can be defined for stop blocks.		Stop blocks can have unlimited incoming connections. No outgoing connections can be defined for stop blocks.

Richard House: /* Node Blocks */

2015-12-11T20:02:12Z

Node Blocks

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	*If the operational phase stops upon failure of the block and the simulation moves to the next phase along the success path, you would use a node block to model this configuration, as shown next.		*If the operational phase stops upon failure of the block and the simulation moves to the next phase along the success path, you would use a node block to model this configuration, as shown next.

	[[Image:Phase node block.png\|center\|~~500px~~\|link=]]		[[Image:Phase node block.png\|center\|450px\|link=]]

	*If the operational phase continues for the specified duration despite failure and the simulation then moves to the next phase along the success path, you would simply not create a failure path.		*If the operational phase continues for the specified duration despite failure and the simulation then moves to the next phase along the success path, you would simply not create a failure path.

Richard House: /* Node Blocks */

2015-12-11T20:01:02Z

Node Blocks

← Older revision		Revision as of 20:01, 11 December 2015
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	*If the operational phase stops upon failure of the block and the simulation moves to the next phase along the success path, you would use a node block to model this configuration, as shown next.		*If the operational phase stops upon failure of the block and the simulation moves to the next phase along the success path, you would use a node block to model this configuration, as shown next.

	[[Image:Phase node block.png\|center\|~~350px~~]]		[[Image:Phase node block.png\|center\|500px\|link=]]

	*If the operational phase continues for the specified duration despite failure and the simulation then moves to the next phase along the success path, you would simply not create a failure path.		*If the operational phase continues for the specified duration despite failure and the simulation then moves to the next phase along the success path, you would simply not create a failure path.

Richard House: /* Maintenance Phases */

2015-12-11T19:49:27Z

Maintenance Phases

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	A maintenance phase represents the portion of a system's mission time where the system is down and maintenance actions are performed on some or all of its components. For representation ease a maintenance phase is defined by (linked to) a maintenance template. This template can be thought of as a list, or a collection, of the specific components (blocks) that are designated to undergo inspection, repair or replacement actions during the maintenance phase, along with their maintenance priority order. In other words, if blocks A, B and C are to undergo maintenance during a specific phase, they are placed in a maintenance template in a priority sequence. Depending on the resources available, the actions are prioritized as resources permit. That is, if three repair crews were available along with three spare parts, actions on A, B and C would be carried out simultaneously. However, if only one crew was available, the actions would be carried out based on the priority order defined in the template. Given that all aspects of maintenance can be probabilistically defined, the duration of a maintenance phase, unlike an operational phase, is not fixed and the phase lasts as long as it takes to complete all actions specified in the phase. To illustrate this, consider a race car that competes in two races, and even though corrective repair actions can be done during each race as needed, the race car then undergoes a major overhaul (i.e., series of maintenance actions). For this example assume the major sub-systems of the car undergoing these maintenance tasks are the engine, the transmission, the suspension system and the tires. The operation of the race car can then be represented as a phase diagram consisting of two operational phases, representing the two races, and one maintenance phase representing the maintenance activities. The figure below shows such a phase diagram along with the maintenance template.<br><br>		A maintenance phase represents the portion of a system's mission time where the system is down and maintenance actions are performed on some or all of its components. For representation ease a maintenance phase is defined by (linked to) a maintenance template. This template can be thought of as a list, or a collection, of the specific components (blocks) that are designated to undergo inspection, repair or replacement actions during the maintenance phase, along with their maintenance priority order. In other words, if blocks A, B and C are to undergo maintenance during a specific phase, they are placed in a maintenance template in a priority sequence. Depending on the resources available, the actions are prioritized as resources permit. That is, if three repair crews were available along with three spare parts, actions on A, B and C would be carried out simultaneously. However, if only one crew was available, the actions would be carried out based on the priority order defined in the template. Given that all aspects of maintenance can be probabilistically defined, the duration of a maintenance phase, unlike an operational phase, is not fixed and the phase lasts as long as it takes to complete all actions specified in the phase. To illustrate this, consider a race car that competes in two races, and even though corrective repair actions can be done during each race as needed, the race car then undergoes a major overhaul (i.e., series of maintenance actions). For this example assume the major sub-systems of the car undergoing these maintenance tasks are the engine, the transmission, the suspension system and the tires. The operation of the race car can then be represented as a phase diagram consisting of two operational phases, representing the two races, and one maintenance phase representing the maintenance activities. The figure below shows such a phase diagram along with the maintenance template.<br><br>
	[[Image:11_2.png\|center\|300px\|Phase diagram illustrating the three-phase mission of the race car along with the maintenance template]] <br>		[[Image:11_2.png\|center\|300px\|Phase diagram illustrating the three-phase mission of the race car along with the maintenance template\|link=]] <br>

	==== Maintenance Phase Properties ==== <!-- THIS SECTION HEADER IS LINKED TO: Interval_Maintenance_Threshold_Example. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->		==== Maintenance Phase Properties ==== <!-- THIS SECTION HEADER IS LINKED TO: Interval_Maintenance_Threshold_Example. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->

Richard House at 19:48, 11 December 2015

2015-12-11T19:48:19Z

← Older revision		Revision as of 19:48, 11 December 2015
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	In other words, a new engine would transition to the take-off phase with an age equal to the time it was used during taxi, or an engine that failed while in flight would remain failed in the next phase (i.e., landing). To model this, a block for each phase would be used in the phase diagram, and each phase block would be linked to the appropriate RBD. This is illustrated in the figure below.		In other words, a new engine would transition to the take-off phase with an age equal to the time it was used during taxi, or an engine that failed while in flight would remain failed in the next phase (i.e., landing). To model this, a block for each phase would be used in the phase diagram, and each phase block would be linked to the appropriate RBD. This is illustrated in the figure below.

	[[Image:11.1.png\|center\|500px\|Phase diagram illustrating the mission of a four-engine aircraft]]		[[Image:11.1.png\|center\|500px\|Phase diagram illustrating the mission of a four-engine aircraft\|link=]]

	In this figure, the taxiing, take-off, cruising and landing blocks represent the operational phases and the final block is a maintenance phase. Each of the operational phases in this diagram has two paths leading from it: a success path and a failure path. This graphically illustrates the consequences in each case. For instance, if the first taxiing phase is successful, the airplane will proceed to the take-off phase; if it is unsuccessful, the airplane will be sent for maintenance. The failure paths for the take-off, cruising and landing phases point to stop blocks, which indicate that the simulation of the mission ends. For the final taxiing phase, both the success and failure paths lead to the maintenance path; the node block allows you to model this type of shared outcome.		In this figure, the taxiing, take-off, cruising and landing blocks represent the operational phases and the final block is a maintenance phase. Each of the operational phases in this diagram has two paths leading from it: a success path and a failure path. This graphically illustrates the consequences in each case. For instance, if the first taxiing phase is successful, the airplane will proceed to the take-off phase; if it is unsuccessful, the airplane will be sent for maintenance. The failure paths for the take-off, cruising and landing phases point to stop blocks, which indicate that the simulation of the mission ends. For the final taxiing phase, both the success and failure paths lead to the maintenance path; the node block allows you to model this type of shared outcome.

Lisa Hacker: /* Node Blocks and Stop Blocks */

2013-06-11T16:46:04Z

Node Blocks and Stop Blocks

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	= Node Blocks and Stop Blocks =		= Node Blocks and Stop Blocks =

	~~In BlockSim~~ 8, the two possible outcomes of an operational phase block are modeled using success and failure paths. Where previously a failure outcome was defined as part of the operational phase block's properties, it is now graphically represented within the diagram. Node blocks and stop blocks are provided ~~in version 8~~ to allow you to build configurations that are both accurate and readable.		Starting with Version 8, the two possible outcomes of an operational phase block are modeled using success and failure paths. Where previously a failure outcome was defined as part of the operational phase block's properties, it is now graphically represented within the diagram. Node blocks and stop blocks are provided to allow you to build configurations that are both accurate and readable.

	=== Node Blocks ===		=== Node Blocks ===

Richard House at 16:36, 21 September 2012

2012-09-21T16:36:22Z

← Older revision		Revision as of 16:36, 21 September 2012
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	::<math>\begin{align}		::<math>\begin{align}
	y=ax+b		y=ax+b
	\end{align}</math>		\end{align}\,\!</math>

	:This model describes the change in throughput <math>y\,\!</math> as a linear function of time <math>x\,\!</math>. Throughput processed between any two points of time <math>{{x}}_{{1}}\,\!</math> and <math>{{x}}_{{2}}\,\!</math> is obtained by integration of the linear function as:		:This model describes the change in throughput <math>y\,\!</math> as a linear function of time <math>x\,\!</math>. Throughput processed between any two points of time <math>{{x}}_{{1}}\,\!</math> and <math>{{x}}_{{2}}\,\!</math> is obtained by integration of the linear function as:
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	= & \mathop{}_{{{x}_{1}}}^{{{x}_{2}}}(ax+b)dx \\		= & \mathop{}_{{{x}_{1}}}^{{{x}_{2}}}(ax+b)dx \\
	= & \frac{a}{2}(x_{2}^{2}-x_{1}^{2})+b({{x}_{2}}-{{x}_{1}})		= & \frac{a}{2}(x_{2}^{2}-x_{1}^{2})+b({{x}_{2}}-{{x}_{1}})
	\end{align}</math>		\end{align}\,\!</math>

	:2. Exponential model:		:2. Exponential model:
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	::<math>\begin{align}		::<math>\begin{align}
	y={be}^{ax}		y={be}^{ax}
	\end{align}</math>		\end{align}\,\!</math>

	:This model describes the change in throughput <math>y\,\!</math> as an exponential function of time <math>x\,\!</math>. Throughput processed in a period of time between any two points <math>{{x}}_{{1}}\,\!</math> and <math>{{x}}_{{2}}\,\!</math> is obtained as:		:This model describes the change in throughput <math>y\,\!</math> as an exponential function of time <math>x\,\!</math>. Throughput processed in a period of time between any two points <math>{{x}}_{{1}}\,\!</math> and <math>{{x}}_{{2}}\,\!</math> is obtained as:
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	= & \mathop{}_{{{x}_{1}}}^{{{x}_{2}}}b{{e}^{ax}}dx \\		= & \mathop{}_{{{x}_{1}}}^{{{x}_{2}}}b{{e}^{ax}}dx \\
	= & \text{ }\frac{b}{a}({{e}^{a{{x}_{2}}}}-{{e}^{a{{x}_{1}}}})		= & \text{ }\frac{b}{a}({{e}^{a{{x}_{2}}}}-{{e}^{a{{x}_{1}}}})
	\end{align}</math>		\end{align}\,\!</math>
	:3. Power model:		:3. Power model:

	::<math>\begin{align}		::<math>\begin{align}
	y={bx}^{a}		y={bx}^{a}
	\end{align}</math>		\end{align}\,\!</math>

	:This model describes the change in throughput <math>y\,\!</math> as a power function of time <math>x\,\!</math>. Throughput processed between two points of time <math>{{x}}_{{1}}\,\!</math> and <math>{{x}}_{{2}}\,\!</math> is obtained as:		:This model describes the change in throughput <math>y\,\!</math> as a power function of time <math>x\,\!</math>. Throughput processed between two points of time <math>{{x}}_{{1}}\,\!</math> and <math>{{x}}_{{2}}\,\!</math> is obtained as:
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	= & \mathop{}_{{{x}_{1}}}^{{{x}_{2}}}b{{x}^{a}}dx \\		= & \mathop{}_{{{x}_{1}}}^{{{x}_{2}}}b{{x}^{a}}dx \\
	= & \frac{b}{a+1}(x_{2}^{a+1}-x_{1}^{a+1})		= & \frac{b}{a+1}(x_{2}^{a+1}-x_{1}^{a+1})
	\end{align}</math>		\end{align}\,\!</math>

	All of the above models also have a user defined maximum throughput capacity value. Once this maximum throughput capacity value is reached, the throughput per unit time becomes constant and equal in value to the maximum throughput capacity specified by the user. In this situation, the variable throughput model would then act as a constant throughput model. The above models may at first glance seem limited, when in fact they do provide ample modeling flexibility. This flexibility is achieved by using these functions as building blocks for more complex functions. As an example, a step model can be easily created by using multiple phases, each with a constant throughput. A ramp model would use phases with linearly increasing functions in conjunction with constant phases, and so forth.		All of the above models also have a user defined maximum throughput capacity value. Once this maximum throughput capacity value is reached, the throughput per unit time becomes constant and equal in value to the maximum throughput capacity specified by the user. In this situation, the variable throughput model would then act as a constant throughput model. The above models may at first glance seem limited, when in fact they do provide ample modeling flexibility. This flexibility is achieved by using these functions as building blocks for more complex functions. As an example, a step model can be easily created by using multiple phases, each with a constant throughput. A ramp model would use phases with linearly increasing functions in conjunction with constant phases, and so forth.

Melinda Caroline at 01:06, 23 August 2012

2012-08-23T01:06:47Z

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	{{Template:bsbook\|10}}		{{Template:bsbook\|10}}
	The term ''phase diagram'' is used in many disciplines with different meanings. In physical chemistry, mineralogy and materials science, a phase diagram is a type of graph used to show the equilibrium conditions among the thermodynamically-distinct phases. In mathematics and physics, a phase diagram is used as a synonym for a phase space. In reliability engineering we introduce the term phase diagram, or more specifically Reliability Phase Diagram or RPD as an extension of the reliability block diagram (RBD) approach to graphically describe the sequence of different operational and/or maintenance phases experienced by a system. Whereas a reliability block diagram (RBD) is used to analyze the reliability of a system with a fixed configuration, a phase diagram can be used to represent/analyze a system whose reliability configuration and/or other properties change over time. In other words, during a mission the system may undergo changes in its reliability configuration (RBD), available resources or the failure, maintenance and/or throughput properties of its individual components. Examples of this include: <br>		The term ''phase diagram'' is used in many disciplines with different meanings. In physical chemistry, mineralogy and materials science, a phase diagram is a type of graph used to show the equilibrium conditions among the thermodynamically-distinct phases. In mathematics and physics, a phase diagram is used as a synonym for a phase space. In reliability engineering, we introduce the term phase diagram, or more specifically Reliability Phase Diagram or RPD, as an extension of the reliability block diagram (RBD) approach to graphically describe the sequence of different operational and/or maintenance phases experienced by a system. Whereas a reliability block diagram (RBD) is used to analyze the reliability of a system with a fixed configuration, a phase diagram can be used to represent/analyze a system whose reliability configuration and/or other properties change over time. In other words, during a mission the system may undergo changes in its reliability configuration (RBD), available resources or the failure, maintenance and/or throughput properties of its individual components. Examples of this include: <br>

	::#Systems whose components exhibit different failure distributions depending on changes in the stress on the system.		::#Systems whose components exhibit different failure distributions depending on changes in the stress on the system.

Melinda Caroline: /* Rules and Assumptions */

2012-08-23T01:05:38Z

Rules and Assumptions

← Older revision		Revision as of 01:05, 23 August 2012
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	{{:BlockSim Example: Aircraft Phases with Forced Landing}}		{{:BlockSim Example: Aircraft Phases with Forced Landing}}

	= Rules and Assumptions =		= Simulation Rules and Assumptions =

	=== When Transferring Interrupted Maintenance Tasks Across Phases ===		=== When Transferring Interrupted Maintenance Tasks Across Phases ===