Reliability Phase Diagrams (RPDs)

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:

Systems whose components exhibit different failure distributions depending on changes in the stress on the system.
Systems or processes requiring different equipment to function over a cycle, such as start-up, normal production, shut-down, scheduled maintenance, etc.
Systems whose RBD configuration changes at different times, such as the RBD of the engine configuration on a four-engine aircraft during taxi, take-off, cruising, and landing.
Systems with different types of machinery operating during day and night shifts and with different amounts of throughput during each shift.

To analyze such systems, each stage during the mission can be represented by a phase whose properties are inherited from an RBD corresponding to that phase's reliability configuration, along with any associated resources of the system during that time. A phase diagram is then a series of such phases drawn (connected) in a sequence signifying a chronological order.

To better illustrate this, consider the four-engine aircraft mentioned previously. Furthermore, assume that the taxi phase requires only one engine, the take-off phase requires all four engines, the cruising phase requires any three of the four engines and the landing phase requires any two of the four engines. To model this, each one of these cases would require a different k-out-of-n redundancy on the engines and thus a different RBD. Creating an RBD for each phase is trivial. However, what you need is a way to transition from one RBD to the next, in a specified sequence, while maintaining all the past history of each component during the transition.

Figure 11.1: Phase diagram illustrating the mission of a four-engine aircraft.

In other words, a new engine would transition to the next 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). (The age equal to the time is more correctly stated with an accumulated damage equal to the damage it accumulated during the taxi phase. For more discussion on this see the Age Transfer Across Phases Using Cumulative Damage section later on in this chapter.) To model this, an RBD for each phase would be used in the phase diagram, and each phase would be linked to the appropriate RBD. This is illustrated in Figure . In this figure each block represents an operational phase. This concept can be expanded further by also including phases for maintenance actions. (Maintenance tasks are allowed in an operational phase.) However, a maintenance phase may be used to represent the portion of a system's mission having only maintenance actions. The next section discusses these types of phases.

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