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An Efficient Approach for the Reliability Analysis of Phased-Mission Systems with Dependent Failures

We consider the reliability analysis of phased-mission systems with common-cause failures in this paper. Phased-mission systems (PMS) are systems supporting missions characterized by multiple, consecutive, and nonoverlapping phases of operation. System components may be subject to different stresses as well as different reliability requirements throughout the course of the mission. As a result, component behavior and relationships may need to be modeled differently from phase to phase when performing a system-level reliability analysis. This consideration poses unique challenges to existing analysis methods. The challenges increase when common-cause failures (CCF) are incorporated in the model. CCF are multiple dependent component failures within a system that are a direct result of a shared root cause, such as sabotage, flood, earthquake, power outage, or human errors. It has been shown by many reliability studies that CCF tend to increase a system's joint failure probabilities and thus contribute significantly to the overall unreliability of systems subject to CCF.We propose a separable phase-modular approach to the reliability analysis of phased-mission systems with dependent common-cause failures as one way to meet the above challenges in an efficient and elegant manner. Our methodology is twofold: first, we separate the effects of CCF from the PMS analysis using the total probability theorem and the common-cause event space developed based on the elementary common-causes; next, we apply an efficient phase-modular approach to analyze the reliability of the PMS. The phase-modular approach employs both combinatorial binary decision diagram and Markov-chain solution methods as appropriate. We provide an example of a reliability analysis of a PMS with both static and dynamic phases as well as CCF as an illustration of our proposed approach. The example is based on information extracted from a Mars orbiter project. The reliability model for this orbiter considers the various phases of Launch, Cruise, Mars Orbit Insertion, and Orbit. Some of the CCF for the orbiter in this mission include environmental effects, such as micrometeoroids, human operator errors, and software errors.

reliability analysis↗

A non-homogeneous Markov model for phased-mission reliability analysis

Three assumptions of Markov modeling for reliability of phased-mission systems that limit flexibility of representation are identified. The proposed generalization has the ability to represent state-dependent behavior, handle phases of random duration using globally time-dependent distributions of phase change time, and model globally time-dependent failure and repair rates. The approach is based on a single nonhomogeneous Markov model in which the concept of state transition is extended to include globally time-dependent phase changes. Phase change times are specified using nonoverlapping distributions with probability distribution functions that are zero outside assigned time intervals; the time intervals are ordered according to the phases. A comparison between a numerical solution of the model and simulation demonstrates that the numerical solution can be several times faster than simulation.

Smotherman, Mark↗

Phased-mission system analysis using Boolean algebraic methods

Most reliability analysis techniques and tools assume that a system is used for a mission consisting of a single phase. However, multiple phases are natural in many missions. The failure rates of components, system configuration, and success criteria may vary from phase to phase. In addition, the duration of a phase may be deterministic or random. Recently, several researchers have addressed the problem of reliability analysis of such systems using a variety of methods. A new technique for phased-mission system reliability analysis based on Boolean algebraic methods is described. Our technique is computationally efficient and is applicable to a large class of systems for which the failure criterion in each phase can be expressed as a fault tree (or an equivalent representation). Our technique avoids state space explosion that commonly plague Markov chain-based analysis. A phase algebra to account for the effects of variable configurations and success criteria from phase to phase was developed. Our technique yields exact (as opposed to approximate) results. The use of our technique was demonstrated by means of an example and present numerical results to show the effects of mission phases on the system reliability.

Somani, Arun K.↗

Simplified Phased-Mission System Analysis for Systems with Independent Component Repairs

Accurate analysis of reliability of system requires that it accounts for all major variations in system's operation. Most reliability analyses assume that the system configuration, success criteria, and component behavior remain the same. However, multiple phases are natural. We present a new computationally efficient technique for analysis of phased-mission systems where the operational states of a system can be described by combinations of components states (such as fault trees or assertions). Moreover, individual components may be repaired, if failed, as part of system operation but repairs are independent of the system state. For repairable systems Markov analysis techniques are used but they suffer from state space explosion. That limits the size of system that can be analyzed and it is expensive in computation. We avoid the state space explosion. The phase algebra is used to account for the effects of variable configurations, repairs, and success criteria from phase to phase. Our technique yields exact (as opposed to approximate) results. We demonstrate our technique by means of several examples and present numerical results to show the effects of phases and repairs on the system reliability/availability.

Somani, Arun K.↗

Markov reliability models for digital flight control systems

The reliability of digital flight control systems can often be accurately predicted using Markov chain models. The cost of numerical solution depends on a model's size and stiffness. Acyclic Markov models, a useful special case, are particularly amenable to efficient numerical solution. Even in the general case, instantaneous coverage approximation allows the reduction of some cyclic models to more readily solvable acyclic models. After considering the solution of single-phase models, the discussion is extended to phased-mission models. Phased-mission reliability models are classified based on the state restoration behavior that occurs between mission phases. As an economical approach for the solution of such models, the mean failure rate solution method is introduced. A numerical example is used to show the influence of fault-model parameters and interphase behavior on system unreliability.

Mcgough, John↗

Constellation Probabilistic Risk Assessment (PRA): Design Consideration for the Crew Exploration Vehicle

Managed by NASA's Office of Safety and Mission Assurance, a pilot probabilistic risk analysis (PRA) of the NASA Crew Exploration Vehicle (CEV) was performed in early 2006. The PRA methods used follow the general guidance provided in the NASA PRA Procedures Guide for NASA Managers and Practitioners'. Phased-mission based event trees and fault trees are used to model a lunar sortie mission of the CEV - involving the following phases: launch of a cargo vessel and a crew vessel; rendezvous of these two vessels in low Earth orbit; transit to th$: moon; lunar surface activities; ascension &om the lunar surface; and return to Earth. The analysis is based upon assumptions, preliminary system diagrams, and failure data that may involve large uncertainties or may lack formal validation. Furthermore, some of the data used were based upon expert judgment or extrapolated from similar components~systemsT. his paper includes a discussion of the system-level models and provides an overview of the analysis results used to identify insights into CEV risk drivers, and trade and sensitivity studies. Lastly, the PRA model was used to determine changes in risk as the system configurations or key parameters are modified.

Prassinos, Peter G.↗