Phase Analysis with Complex Diagrams
Reliability Phase Diagrams or RPDs, can be thought of as an extension of the Reliability Block Diagram
(RBD) approach. RPDs graphically describe the sequence of different operational and/or maintenance phases
experienced by a system. This means that, unlike an RBD which is limited to systems with fixed configurations,
RPDs can be used to represent complex systems that may
change over time. The change may be in the reliability configurations (i.e.
the RBD) and/or other properties, such as the availability of resources or throughput properties.
In this article, we will use BlockSim to
illustrate the use of reliability phase diagrams to study a complex system.
In complex systems, each stage during a mission can be represented by a phase block. The properties
of the phase block are inherited from an RBD corresponding to the system's reliability configuration in
that phase, along with any associated resources of the system during that time. A reliability phase
diagram is then a series of such phase blocks connected in
chronological
order. For more information on reliability phase diagrams, see [1].
Example
Consider a process where a robot manipulator is used. Because the system operates in a remote location
and stopping the operation is costly, individual components that fail but do not cause a system failure
are not repaired immediately. The failed components are repaired only during the scheduled yearly
maintenance of the entire operation. System failures, however, are given immediate attention, and these repairs are
costly, timeconsuming and incur additional warranty costs per hour of downtime. The robot manipulator
is warranted for 5 years. The goal of the analysis is to determine the warranty costs incurred by the
system. In order to accomplish this, three metrics are of interest: the expected number of failures
of the system, the system downtime associated with unplanned system failures and the expected number
of component replacements during the yearly maintenance.
The Reliability Phase Diagram
Representing the robot system with a single RBD would result in limitations. For example, a
corrective repair of a component that is due to a system failure needs to be handled differently
than a corrective repair performed during the yearly maintenance because they incur different
costs. Therefore, the following RPD will be used.
Figure 1 shows the properties of each phase.
Figure 1: Phase properties for the robot manipulator system RPD.
By using two phases to represent the system, we segregate the results obtained from different stages
(normal vs. yearly maintenance) as well as any input variations. The Normal Operation phase represents the system
while in operation. In this phase, blocks that fail but do not bring down the system are not repaired
upon failure but remain down until the scheduled yearly maintenance. However, the failure of a block that
causes a system failure will result in the repair of that block as well as a repair of all other failed
components. The Normal Operation phase inherits its properties from an RBD representing the system
(Figure 2). Meanwhile, the Scheduled Yearly Maintenance phase represents the portion of the mission time
when the system is brought down each year so that maintenance actions can be performed on some or all of
its components. In Blocksim, a maintenance phase block is defined by, and
linked to, a maintenance template. This template can be thought of as a list of the
specific components (blocks) that are designated to undergo inspection, repair or replacement actions
during the maintenance phase. The template and subtemplates for this
example are shown in Figure 3.
Note that BlockSim 7 recognizes that a component is present in more than one phase by
checking the name of the component. In order to keep the integrity of this name convention, the maintenance
template must follow the same structure as the original system RBD. In other words, if the robot
system is represented by one main diagram with five subdiagrams, the maintenance template must be
defined as one main template with five subtemplates.
Robot Manipulator Failure Modes 
Jam Subdiagram 


Brake Subdiagram 
Watchdog Subdiagram 


Comm Subdiagram 
Mechanical Failure Subdiagram 


Figure 2: Robot Manipulator System diagram and subdiagrams.
Robot Manipulator Template 
Jam Subtemplate 


Break Subtemplate 
Watchdog Subtemplate 


Comm Subtemplate 
Mechanical Failure Subtemplate 


Figure 3: Scheduled Yearly Maintenance template and subtemplates.
The Analysis
Table 1 gives the failure and repair inputs of the system.
Block Name 
Failure Distribution Normal Operation (in days) 
Repair Distribution Normal Operation (in days) 
Repair Distribution Yearly Maintenance (in days) 
JF 
WBL(Beta=4, Eta=6000) 
EXP(Mean=12) 
EXP(Mean=3) 
KRF 
WBL(Beta=2, Eta=7000) 
EXP(Mean=12) 
XP(Mean=4) 
COM 
EXP(Mean=5000) 
EXP(Mean=16) 
EXP(Mean=4) 
EStop 
EXP(Mean=4000) 
EXP(Mean=14) 
EXP(Mean=2) 
MSF 
WBL(Beta=3, Eta=10000) 
EXP(Mean=13) 
EXP(Mean=4) 
RCF 
EXP(Mean=5000) 
EXP(Mean=14) 
EXP(Mean=5) 
Primary Brake 
Cold Standby, Active distribution: WBL(Beta=2, Eta=1000) 
EXP(Mean=10) 
EXP(Mean=5) 
Secondary Brake 
Cold Standby, Active distribution: WBL(Beta=2, Eta=1000) 
EXP(Mean=10) 
EXP(Mean=5) 
Processor I 
Load sharing, WBLIPL: Beta=1.5, K=2.38E4, n=1.32) 
EXP(Mean=9) 
EXP(Mean=2) 
Processor II 
Load sharing, WBLIPL: (Beta=1.5, K=2.38E4, n=1.32) 
EXP(Mean=9) 
EXP(Mean=2) 
Sensor 
EXP(Mean=5000) 
EXP(Mean=9) 
EXP(Mean=2) 
Primary PN 
EXP(Mean=5000) 
EXP(Mean=12) 
EXP(Mean=3) 
Secondary PN 
EXP(Mean=5000) 
EXP(Mean=12) 
EXP(Mean=3) 
Third PN 
EXP(Mean=5000) 
EXP(Mean=12) 
EXP(Mean=3) 
Fourth PN 
EXP(Mean=5000) 
EXP(Mean=12) 
EXP(Mean=3) 
Other 
EXP(Mean=100000) 
EXP(Mean=15) 
EXP(Mean=3) 
Table 1: Failure and repair properties.
We can now run a simulation for the mission time of interest (5 years or 1825 days).
Figure 4: Simulation settings.
BlockSim 7 provides multiple results at the overall mission level, as well as at the
phase level. The results of interest are highlighted in Figures 5 and 6.
Figure 5: The expected number of failures and the component downtime associated
with system failures.
Figure 6: The expected number of component replacements during yearly maintenance.
Conclusion
This article presented an example of how to use reliability phase diagrams for modeling a
system with multiple levels of complexity, including subdiagrams and container constructs,
along with the use of a maintenance phase. We also demonstrated how RPD analysis can obtain
specific metrics of interest that can be used to perform a warranty analysis.
References
[1] ReliaSoft Corporation, System Analysis: Reliability, Availability
and Optimization Reference. ReliaSoft Publishing, 2007.
http://reliawiki.org/index.php/Reliability_Phase_Diagrams_(RPDs)
