Phased-mission Systems Research Articles

Improved MDD Algorithm for Mission Reliability Estimation of an Escort Formation

An escort formation is a phased mission system of systems (PMSoS), which is composed of multiple ships with different functions. The configuration of the formation and success criteria for a mission may vary in different phases. Reliability estimation for PMSoS is complicated due to the strong phase dependence of multiple systems. This paper proposes an improved multiple-valued decision diagram (MDD) algorithm to perform reliability estimation of a nonrepairable escort formation. First, a phased fault tree is established to describe the failure mode of an escort formation throughout a mission, which is simplified according to the common failure basic mission (module) (CFBM). Bottom events are sorted based on the CFBM, and the case method is adopted to generate an MDD from the simplified fault tree model. On this basis, the MDD method is adopted to estimate mission reliability. The performance of the improved MDD method is compared with that of a binary decision diagram (BDD) method and a general MDD method. The results show that the improved MDD method can offer lower computational complexity as well as a simpler model construction over the BDD method and general MDD method. A case study of an escort formation PMSoS is analyzed to illustrate the proposed MDD method, and the sensitivity and composite importance measure (CIM) of each system are evaluated.

An extended object-oriented petri net model for mission reliability evaluation of phased-mission system with time redundancy

Phased-mission system (PMS) has been widely used as mission reliability model of many engineering mission-critical systems. In practical, PMS can have time redundancy both inner phase and between phases, i.e. the success of one phase may only require the system to keep operational for a given time interval instead of working throughout the phase. Besides, mission task failed in one phase can be re-executed in a later phase with change of its configurations.Based on the extended object-oriented Petri net (EOOPN), this paper proposes a general modeling procedure for mission reliability evaluation of PMS, which is capable of considering the time redundancy both inner phase and between phases in relatively intuitive way. The proposed approach is performed in system, phase and component levels. The system level depicts all possible executable paths of PMS via the token transition between different EOOPN subnets, including the re-execution arrangement of failed mission tasks. The phase level details the model structure of each EOOPN subnet, which addresses the system state change process and the minimal operational time requirement of a phase. The component level describes components state change during the mission. A discrete-event simulation is applied to the constructed EOOPNs for system mission reliability evaluation, and an example system under different time redundancy assumptions is analyzed to illustrate the effectiveness of this approach.

Mission success probability optimization for phased-mission systems with repairable component modules

Mission success probability (MSP) is an important measurement to evaluate the performance of phased-mission systems (PMSs). The PMSs consist of some subsystems in series, and each subsystem is made of some k-out-of-n structures with repairable component modules. Adjusting the reliability and maintainability of components can improve the MSP of repairable PMSs. Therefore, the objective of MSP optimization for PMSs with repairable component modules is to maximize the MSP considering the cost constraints on the adjustment process. The improved optimization algorithm combines the importance measure-based local search method with the ant colony optimization (ACO) algorithm, which is called the importance measure-based ACO (IMACO) algorithm, for solving the MSP optimization. Three numerical experiments are implemented to illustrate the parameter selection and the performance of IMACO algorithm. Comparing with ACO algorithm, the results show that the IMACO algorithm is more effective when the number of component modules is small, while the running time becomes shorter with the increase of the component modules. According to the numerical example of heavy-lift systems with multi-rotor unmanned aerial vehicles (UAVs), the improvement priority of components is analyzed, and the reliability variables of the indispensable components with more missions should be improved at first.

A New Study on Reliability Importance Analysis of Phased Mission Systems

Reliability importance which serves to quantify the influence of each component (or each type of components) in each phase on the reliability of a phased mission system (PMS) plays an important role in security assessment and risk management. In this paper, we present a new and efficient method for reliability importance analysis of PMSs using the theory of survival signature. A new kind of survival signature is applied to assess the reliability of PMS with multiple types of components. A closed-form formula is derived to predict reliability importance of the PMS with respect to each type of components in each phase. The Birnbaum importance model is further extended to calculate the reliability importance of the PMS with respect to each component in each phase. Finally, two numerical examples are used to demonstrate the validity and effectiveness of the proposed approaches.

Efficient reliability analysis of dynamic k-out-of-n heterogeneous phased-mission systems

In this paper, an efficient analytical modeling method is proposed for reliability analysis of k-out-of-n phased-mission systems (PMSs). A PMS is a system involving multiple, consecutive and non-overlapping phases of tasks during its mission, which abounds in complex technological systems such as aerospace systems, nuclear power plants, and high-performance computing systems. Due to dynamics in the system configuration and component behavior as well as statistical dependences across phases, exact reliability evaluation of a PMS is a time-consuming and complicated task. This paper proposes a new efficient multi-valued decision diagram (MDD) based method for the reliability analysis of a special class of non-repairable PMSs called k-out-of-n PMS where the same number of components n is involved in all the phases but the required number of working components k may vary from phase to phase. Particularly, a new MDD generation method is proposed for a fast construction of the PMS MDD model. The system components are not necessarily identical; they can be heterogeneous in their failure time distributions. Examples are provided to demonstrate the application and advantages of the proposed methodology.

Redundancy versus protection for a non-reparable phased-mission system subject to external impacts

Systems that have multiple consecutive and non-overlapping phases of operations during their missions are referred to as phased-mission systems (PMSs). Previous research on modeling reliability of a PMS has mainly focused on internal failures. However, some real-world PMSs can also be subject to external impacts, which may contribute to the occurrences of system failures. This paper makes contributions by modeling a redundant PMS subject to both internal failures and external impacts with or without overarching protection. System reliability is modeled for cases where the demand levels are the same for all phases, and where they are not. The optimal resource allocation of redundancy and protection is further studied to maximize the system reliability. The expected system loss is also modeled and optimized for cases where the system can function partially when the demand is unsatisfied. Examples are presented to illustrate applications of the proposed models.

Reliability simulation and analysis of phased-mission system with multiple states

Basing on discrete event simulation, a reliability simulation algorithm of the phased-mission system with multiple states is put forth. Firstly, the concepts and main characters of phasedmission system are discussed, and an active and standby redundancy (AS) tree structure method to describe the system structure of each mission phase is brought forward. Secondly, the behavior of the phased-mission system with multiple states is discussed with the theory of state chart. Thirdly, basing on the discrete event simulation concept, a simulation algorithm to estimate reliability parameters of the phased-mission system with multiple states is explored. Finally, an example is introduced and analyzed, and the analysis result verifies the algorithms. The simulation algorithm is practical and versatile, for it can model complex behavior of phased-mission system flexibly, and more reliability parameters to understand system operation can be attained.

Mission success evaluation of repairable phased-mission systems with spare parts

Mission success is an important criterion to measure the performance of phased-mission systems, which is the ability of systems to finish the work successfully. Activating the spare parts takes little time, which can reduce the maintenance time while performing the mission. Moreover, adding the spare parts also can ensure the mission to complete with higher success probability. This paper puts forward an integrated modeling method to evaluate the mission success probability for repairable phased-mission systems with spare parts. Some illustrative examples are introduced to verify the flexibility and effectiveness of the proposed approach with different cases. Based on the state analysis of the component group, the risk ranking of component groups or mission phases is discussed to improve the mission success probability effectively. After analyzing the effect of spare parts on mission success probability, the optimal spare parts allocation method is proposed to obtain a cost-effective solution with the maximum mission success probability.

Reliability analysis of general phased mission systems with a new survival signature

It is often difficult for a phased mission system (PMS) to be highly reliable, because this entails achieving high reliability in every phase of operation. Consequently, reliability analysis of such systems is of critical importance. However, efficient and interpretable analysis of PMSs enabling general component lifetime distributions, arbitrary structures, and the possibility that components skip phases has been an open problem.In this paper, we show that the survival signature can be used for reliability analysis of PMSs with similar types of component in each phase, providing an alternative to the existing limited approaches in the literature. We then develop new methodology addressing the full range of challenges above. The new method retains the attractive survival signature property of separating the system structure from the component lifetime distributions, simplifying computation, insight into, and inference for system reliability.

Analyzing phased-mission industrial network systems with multiple ordered performance levels

ABSTRACTAn industrial network system consists of small, inexpensive nodes equipped with embedded processors and wireless communication, which enables flexible deployment in the industrial applications. Multiple phases are natural in many practical industrial network systems which further have multiple ordered performance levels. The networking needs of industrial devices and applications are distinct from the consumer world, especially in terms of reliability and security. The modeling and analysis of phased-mission industrial network systems remains a challenging task due to its inherent complexity. This paper proposes a new decision-diagram-based method, called multiple-terminal binary decision diagrams (MTBDD), for the analysis of phased-mission industrial network system with multiple ordered performance levels. Various performability measures are considered. Application and advantages of the proposed method are demonstrated through examples and case study. Empirical results show that our method can offer smaller model sizes and more efficient computation of reliability and performance measures as compared to the traditional separable approach.

XML-based modeling method of phased-mission systems subject to probabilistic common cause failures

XML-based modeling method of phased-mission systems subject to probabilistic common cause failures

Nonlinear Damage Accumulation Rule for Solder Life Prediction Under Combined Temperature Profile With Varying Amplitude

Due to a mismatch of the coefficient of thermal expansion, electronic solder joints experience cyclic shear strain, which ultimately leads to fatigue failure. Traditional predictions of solder joint thermal fatigue life that use the experimental data or the physics-of-failure model often assume a regular profile. For complex temperature profiles, the linear accumulation rule is typically used to integrate the superposition effect. However, the linear rule was proved not applicable to most of the complex loading or temperature conditions. Based on the damage curve theory and the fatigue crack propagation theory, a novel nonlinear accumulation rule has been deduced for solder joint life predictions under irregular profiles, which were composed of two standard temperature cycles and may be experienced by phased-mission system. Four groups of experiments were conducted for ball grid array package solder joints with different dimensions and materials to determine parameters of the proposed nonlinear accumulation rule. The finite-element simulation method was used to extend this rule to more general cases for application. Compared to Miner’s linear accumulation rule, prediction of solder joint thermal fatigue life via the proposed nonlinear accumulation rule is closer to the accelerated life test results of real-world electronic solder joints under a combined temperature profile.

A Hierarchical Reduced Markov Model for Reliability Evaluation of Phased-Mission Systems

A Hierarchical Reduced Markov Model for Reliability Evaluation of Phased-Mission Systems

Path Sets Combination Method for Reliability Analysis of Phased-Mission Systems Based on Cumulative Exposure Model

The modeling of phased-mission systems is difficult and the solving process is complex because of the relevance of the phase tasks and the sharing of components existing in different phases or between phases. To solve the problem, based on the cumulative exposure model, the path sets combination method of phased-mission systems is proposed. Aiming at the problem of the cross-stage correlation of components and its different failure rate in each phase, the cumulative exposure model considering the historical damage of components is used to solve by obtaining the cumulative damage distribution of each component in each phase. Firstly, a phased-mission systems reliability model is build by mapping phased-mission system fault trees into a Bayesian network. By traversing the Bayesian network, the minimal path sets of each phase are obtained. Secondly, the disjoint formulas introduced by variable elimination method are used to do the disjoint operation of the minimal path sets of each phase and the conditional probability relations of the common components are used to reduce the minimal path sets scale. Finally, the minimum disjoint path sets of each phase are combined and summed according to the component conditional probability relation. The path sets combination method of phased-mission systems avoids the large conditional probability table, large storage and large computation problems caused by the excessive discrete states in the traditional Bayesian method and the problem that the PMS-BDD method has strict requirements for variable ordering and is difficult to solve the system reliability with multiple failure distribution types of components. In the end, a phased-mission systems reliability modeling and solving is carried out for a geosynchronous orbit satellite, and compared with the PMS-BDD method, which verifies the correctness of the method.

Reliability assessment of multi-state phased-mission systems by fusing observation data from multiple phases of operation

Abstract Multi-state phased-mission systems (MS-PMSs) are multi-state systems that intend to complete multiple, consecutive, and non-overlapping phases of operation with different functional requirements. Even though many computationally efficient tools have been developed to facilitate reliability modeling of MS-PMSs in the past few decades, reliability assessment of an MS-PMS by observation data is still a difficulty because of the state and phase dependencies. This paper devotes to addressing this challenge by putting forth a new method that can assess reliability of an MS-PMS by fusing observation data collected from multiple phases of operation. A dynamic Bayesian network (DBN) model is constructed to characterize the state dependence between an MS-PMS and its units as well as the phase dependence of each unit across consecutive phases. By putting observation data into the DBN model, the joint probability distributions of the nodes of the MS-PMS at any time slice can be updated, and with which the unknown parameters associated with the state transitions of all the units can be furtherly estimated by a tailored Expectation-Maximization (EM) algorithm. The reliability function of the MS-PMS can be, then, assessed by these estimates of all the units. Two illustrative examples, including a numerical case and a data collection robot are exemplified to demonstrate the effectiveness of the proposed method.

Selective maintenance optimization for random phased-mission systems subject to random common cause failures

In both industrial and military fields, there is such a kind of complicated system termed as phased-mission system, which executes missions composed of several different phases in sequence. The structure, failure behavior, and working conditions of such a system may change from phase to phase. The duration of each phase of such a system involved is random and follows a probability distribution, and the system may suffer some events resulting in simultaneous failures of different elements with different probabilities. In order to guarantee such a system completes the phased-mission successfully, a selective maintenance model for random phased-mission systems subject to random common cause failures is proposed to optimally identify a subset of maintenance activities to be performed on some elements of the system. Thereinto, a novel analytic model is developed to estimate the probability of the maintained random phased-mission system successfully completing the phased-mission, and we compare it with a well-known Monte Carlo Simulation approach. Finally, the proposed selective maintenance model has been successfully applied to an artillery weapon system. Comparative analysis is carried out to compare the proposed model with the traditional ones, including selective maintenance models for deterministic phased-mission systems and deterministic single-phase mission systems. The results show that ignoring some mission properties (e.g. randomness and multiple phases) in selective maintenance optimization will lead to (1) incorrect system and mission modeling, (2) incorrect computation of the probability of the random phased-mission system successfully completing a mission, and/or (3) nonoptimal selective maintenance options.

Reliability assessment of phased-mission systems under random shocks

Phased-mission systems (PMSs) are widely used, especially in the aerospace industry. As in the outer space there are many kinds of cosmic rays, such as the Galactic Cosmic Rays (GCR), randomly hitting on these systems and causing significant impact on the electronics inside or outside the equipment, a reliability model for PMSs considering both finite and infinite random shocks is proposed in this paper. The modularization method is used to simplify the state space model for each phase and reduce the amount of system states, and the Markov regenerative process (MRGP) is used to describe the hybrid components’ lifetime distributions and the dynamic behaviors within the modules. Then, two kinds of scenarios, finite and infinite random shocks effect, are both integrated into the dynamic modules. For demonstration, a phased altitude and orbit control system (AOCS) subjected to infinite random shocks is illustrated to demonstrate the procedure of the proposed Monte Carlo simulation. Thirdly, the evaluated system reliability under infinite random shocks is compared with the same system without considering random shocks. At last, a sensitivity analysis is also provided for completion.

An efficient phased-mission reliability model considering dynamic k-out-of-n subsystem redundancy

ABSTRACTIn this article, an efficient method is proposed for exact reliability evaluation of a special class of Phased-Mission Systems (PMSs) containing multiple k-out-of-n subsystems, each of which has multiple identical and non-repairable components. A PMS performs missions involving multiple, consecutive, and non-overlapping phases of operations. In each phase, the system has to accomplish a specific task and may be subject to different stresses. Thus, the configuration of each subsystem can change from phase to phase, including its active and inactive status, redundancy type, and minimum required working components. If any one of the required (active) subsystems is failed in a phase, the system is considered to be failed in that phase. The proposed method for accurate reliability analysis of PMS considers statistical dependencies of component states across the phases, time-varying and phase-dependent failure rates, and associated cumulative damage effects. Based on conditional probabilities and an efficient recursive formula to compute these probabilities, the proposed method has both computational time and memory requirements linear to the system size. Medium-scale and large-scale systems are analyzed to demonstrate high efficiency of the proposed method.

Reliability allocation model and algorithm for phased mission systems with uncertain component parameters based on importance measure

This paper presents a model to deal with reliability allocation problem of phased mission systems (PMS), especially for PMS with uncertainty in components’ parameters due to inaccurate information and different phase environments. In practice, real value of the reliability of a component may become lower than its designed value due to such uncertainty, thus making the whole system fail to meet the required reliability level. Therefore, in this paper, we present a model that incorporates the component uncertainty in the system reliability allocation process and then propose a variance-based global importance hybrid heuristic algorithm for its solution. The variance-based global importance measure is used to evaluate the importance of a component to the mission reliability of PMS while the reliabilities of all components vary randomly. The main procedures of the proposed algorithm include: (1) generate feasible solutions by roulette wheel selection method based on a global importance index; (2) improve solutions by adjusting reliability parameter values of components according to their global importance; and (3) improve solutions by crossover and mutation operations of genetic algorithm (GA). To illustrate the effectiveness of the proposed model and algorithm, two examples of PMS are presented and the allocation solutions are validated through Monte–Carlo simulation method. Finally, we compare the proposed model with a general allocation model that does not consider component uncertainty, and additionally with a cost-based heuristic algorithm and a particle swarm optimization (PSO) algorithm. Our results show that component uncertainty has significant influence on the confidence level that an allocation solution satisfies the required system reliability. Hence, it is essential to consider component uncertainty in reliability allocation process. In comparison with the cost heuristic algorithm and the PSO algorithm, the proposed algorithm is more effective in reliability allocation of PMS with uncertainty in components’ parameters.

Reliability evaluation of unrepairable k-out-of-n: G systems with phased-mission requirements based on record values

In this paper, the reliability evaluation problem for k-out-of-n: G phased-mission systems with imperfect fault coverage is studied. The system is composed of n identical components, and the mission consists of multiple, consecutive, and non-overlapping phases. Each phase of the mission has a specified requirement of the minimal number of working components, and therefore the system forms a certain k-out-of-n: G system at the phase. The failure distributions of the components are affected by working circumstance of the mission phases, and the degradation accumulates with the phases for each component. The formulas for computing the state probabilities of the system at different phases and the overall mission reliability are derived with the consideration of imperfect fault coverage for the components. The explicit expression of mission reliability is presented for the phased-mission systems with the same components requirements for all phases. In numerical examples, not only the mission reliability of the system is calculated, but also the optimal number of components is obtained to maximize the reliability for a given phased mission system.