Importance measures for multi-phase missions

Phased missions consist of consecutive operational phases where the system logic and failure parameters can change between phases. A component can have different roles in different phases and the reliability function may have discontinuities at phase boundaries. An earlier method required NOT-gates and negations of events when calculating importance measures for such missions with non-repairable components. This paper suggests an exact method that uses standard fault tree techniques and Boolean algebra without any NOT-gates or negations. The criticalities and other importance measures can be obtained for events and components relevant to a single phase or to a transition between phases or over the whole mission. The method and importance measures are extended to phased missions with repairable components. Quantification of the reliability, the availability, the failure intensity and the total number of failures are described. New importance indicators defined for repairable systems measure component contributions to the total integrated unavailability, to the mission failure intensity and to the total number of mission failures.     

Cause–consequence analysis of non-repairable phased missions

Many systems can be modelled as a mission made up of a sequence of discrete phases. Each phase has a different requirement for successful completion and mission failure will result if any phase is unsuccessful. Fault tree analysis and Markov techniques have been used previously to model this type of system for non-repairable and repairable systems, respectively. Cause–consequence analysis is an alternative assessment technique capable of modelling all system outcomes on one logic diagram. The structure of the diagram has been shown to have advantageous features in both its representation of the system failure logic and its subsequent quantification, which could be applied to phased mission analysis.This paper outlines the use of the cause–consequence diagram method for systems undergoing non-repairable phased missions. Methods for construction of the cause–consequence diagram are first considered. The disjoint nature of the resulting diagram structure can be utilised in the later quantification process. The similarity with the Binary Decision Diagram method enables the use of efficient and accurate solution routines.     

Birnbaum and criticality measures of component contribution to the failure of phased missions

This paper develops measures, which identify the contribution to system failure when the system operates a phased mission. The measures developed are the equivalent of Birnbaum's measure of importance and the criticality measure of importance in a conventional analysis. It is assumed that during the mission the system components cannot be repaired. In the determination of the importance measures, the contribution to phase failure is considered in two aspects: failure during the phase (in-phase importance) and failure on transition to a phase (transition importance). Component importance measures indicate the contribution to phase and overall mission unreliability.     

Maintenance free operating period – an alternative measure to MTBF and failure rate for specifying reliability?

The paper analyses the concept of maintenance free operating period (MFOP), the reliability requirement driven by the Ministry of Defence (UK) for the next generation of future aircraft to be included in the fleet. Since the traditional reliability requirement MTBF (mean operating time between failure) has several drawbacks, the immediate reaction would be to analyse the credibility of the new measure MFOP against MTBF. The paper discusses various issues associated with MFOP. Two mathematical models are developed to predict the maintenance free operating period survivability (MFOPS), one using mission reliability approach and the other using alternating renewal theory. The paper also analyses cost implications of MFOP to the customer and to the producer.     

Component testing of a series system in a random mission

Components of a series system are tested in order to assure desired levels of system reliability during the mission. The components are nonidentical but they all fail exponentially with failure rates that depend on the mission performed. There is a given set of missions that the device can be assigned randomly with respect to a given probability distribution. This directly implies that the failure rates of the components depend on the specific mission that the device performs. The objective is to find an optimal component test plan. We will show that, with some extra effort, this rather complicated but realistic model can be handled using available results in semi-infinite linear programming and d.c. (difference of convex functions) programming.     

Mission Reliability Assessment of Space TT&C System by Discrete Event System Simulation

Based on the analysis of system characteristics and mission process, space tracking, telemetry and command (TT&C) system can be viewed as a phased‐mission system (PMS). A general methodology using discrete event system simulation is proposed to quantitatively assess mission reliability of space TT&C system, because the traditional method is difficult to solve such complex problem. By dividing the time sequence of TT&C mission profile into several phases, the fault tree model of PMS is built to represent the system logical structure in each phase. In order to efficiently build simulation models, unified modeling language static class diagram is used to describe simulation model architecture. Extensible markup language is adopted to represent the mission reliability model in standard format for simulation input. By randomly generating the failure and repair events of the system components, the changes of the system state are simulated. The logic structure function of fault tree and observation data of the system state change jointly determines the mission reliability. A case study is given to illustrate the approach and validate its effectiveness. Copyright © 2013 John Wiley & Sons, Ltd.     

Reliability modeling and optimization of K/N phased mission system with backup missions and global redundancy strategy

The mission success probability (MSP) is a critical indicator for phased mission systems (PMSs). In the modern aerospace industry, redundancy techniques, including component/phase redundancy, are commonly seen to increase the MSP of the whole system. These component/phase redundancies make the reliability analysis more complex. Meanwhile, one or more components are required for normal working for different subsystems, called the K/N structure. In this article, a Markov-process method is proposed for PMS with K/N subsystems and different redundancy strategies. Then, a universal system optimization model is proposed to optimize system structure and redundancy strategies for all subsystems at the same time. Then, an improved genetic algorithm (GA) is used to resolve the optimization problem. At last, a propulsion system is used as an engineering case, showing the proposed binary decision diagram-based method.     

Using reliability analysis to support decision making in phased mission systems

Because of the environments in which they will operate, future autonomous systems must be capable of reconfiguring quickly and safely following faults or environmental changes. Past research has shown how, by considering autonomous systems to perform phased missions, reliability analysis can support decision making by allowing comparison of the probability of success of different missions following reconfiguration. Binary decision diagrams (BDDs) offer fast, accurate reliability analysis that could contribute to real‐time decision making. However, phased mission analysis using existing BDD models is too slow to contribute to the instant decisions needed in time‐critical situations. This paper investigates 2 aspects of BDD models that affect analysis speed: variable ordering and quantification efficiency. Variable ordering affects BDD size, which directly affects analysis speed. Here, a new ordering scheme is proposed for use in the context of a decision‐making process. Variables are ordered before a mission, and reordering is unnecessary no matter how the mission configuration changes. Three BDD models are proposed to address the efficiency and accuracy of existing models. The advantages of the developed ordering scheme and BDD models are demonstrated in the context of their application within a reliability analysis methodology used to support decision making in an unmanned aerial vehicle.     

A multi-failure additive dependability model for transit system effectiveness analysis

Dependability has been recognized in the transportation reliability literature as an effective measure of transit system service quality. Dependability models link system dependability with reliability and maintainability characteristics of subsystems, incorporating special operating characteristics and recovery policy from failure of each particular transit system. In this paper a new transit system dependability model is proposed, which considers the possibility that a passenger may be delayed by the occurrence of more than one failure in a trip. The mathematical difficulties associated with the algebra of random variables are overcome by using the Monte Carlo method. The results of the proposed model are compared with those relative to different modelling approaches in the literature, by applying the model to a common test scenario.     

Evaluation of full and degraded mission reliability and mission dependability for intermittently operated, multi-functional systems

Availability is one of the metrics often used in the evaluation of system effectiveness. Its use as an effectiveness metric is often dictated by the nature of the system under consideration. While some systems operate continuously, many others operate on an intermittent basis where each operational period may often involve a different set of missions. This is the most likely scenario for complex multi-functional systems, where each specific system mission may require the availability of a different combination of system elements. Similarly, for these systems, not only is it important to know whether a mission can be initiated, it is just as important to know whether the system is capable of completing such a mission. Thus, for these systems, additional measures become relevant to provide a more holistic assessment of system effectiveness. This paper presents techniques for the evaluation of both full and degraded mission reliability and mission dependability for coherent, intermittently operated multi-functional systems. These metrics complement previously developed availability and degraded availability measures of multi-functional systems, in the comprehensive assessment of system effectiveness.     

Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break. A list of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme.     

A hierarchical combinatorial reliability model for smart home systems

As an application of the Internet of Things, smart home systems have received significant attentions in recent years due to their precedent advantages, eg, in ensuring efficient electricity transmission and integration with renewable energy. This paper proposes a hierarchical and combinatorial methodology for modeling and evaluating reliability of a smart home system. Particularly, the proposed methodology encompasses a multi‐valued decision diagram‐based method for addressing phased‐mission, standby sparing, and functional dependence behaviors in the physical layer; and a combinatorial procedure based on the total probability theorem for addressing probabilistic competing failure behavior with random propagation time in the communication layer. The methods are applicable to arbitrary types of time‐to‐failure and time‐to‐propagation distributions for system components. A detailed case study of an example smart home system is performed to demonstrate applications of the proposed method and effects of different component parameters on the system reliability.     

Dynamic behavioural model for assessing impact of regeneration actions on system availability: Application to weapon systems

Mastering system availability all along the system life cycle is now a critical issue with regards to systems engineering. It is more true for military systems which operate in a battle context. Indeed as they must act in a hostile environment, they can become unavailable due to failures of or damage to the system. In both cases, system regeneration is required to restore its availability. Many approaches based on system modelling have been developed to assess availability. However, very few of them take battlefield damage into account and relevant methods for the model development are missing. In this paper, a modelling method for architecture of weapon system of systems that supports regeneration engineering is proposed. On the one hand, this method relies on a unified failure/damage approach to extend acknowledged availability models. It allows to integrate failures, damages, as well as the possibility of regeneration, into operational availability assessment. Architectures are modelled as a set of operational functions, supported by components that belong to platform (system). Modelling atoms (i.e. elementary units of modelling) for both the architecture components and functions are defined, based on state-space formalism. Monte Carlo method is used to estimate availability through simulation. Availability of the architecture is defined on the basis of the possible states of the required functions for a mission. The states of a function directly depend on the state of the corresponding components (i.e. the components that support the function). Aggregation rules define the state of the function knowing the states of each component. Aggregation is defined by means of combinatorial equations of the component states. The modelling approach is supported by means of stochastic activity network for the models simulation. Results are analysed in terms of graphs of availability for mission's days. Thus, given the simulation results, it is possible to plan combat missions based on criteria such as the number of platforms to be involved given functions required for the mission or the mean of regeneration to be deployed given the possible threats. Further, the simulation will help towards the design of improved architecture of system of systems which could focus on the factors affecting the availability.     

The Bayes linear approach to inference and decision-making for a reliability programme

In reliability modelling it is conventional to build sophisticated models of the probabilistic behaviour of the component lifetimes in a system in order to deduce information about the probabilistic behaviour of the system lifetime. Decision modelling of the reliability programme requires a priori, therefore, an even more sophisticated set of models in order to capture the evidence the decision maker believes may be obtained from different types of data acquisition.Bayes linear analysis is a methodology that uses expectation rather than probability as the fundamental expression of uncertainty. By working only with expected values, a simpler level of modelling is needed as compared to full probability models.In this paper we shall consider the Bayes linear approach to the estimation of a mean time to failure MTTF of a component. The model built will take account of the variance in our estimate of the MTTF, based on a variety of sources of information.     

Efficient reliability analysis of dynamic k-out-of-n phase-AND mission systems

Motivated by real-world applications of satellites and wireless sensor networks, this paper models and evaluates a dynamic k-out-of-n phase-AND mission system (k/n-PAMS). The mission task conducted by a k/n-PAMS involves multiple consecutive phases; the mission is successful as long as the task is successful in any of the phases. Due to factors, such as scheduled maintenance, location changes in task execution during different phases, and resource sharing with other tasks, the total number of available components n for the considered mission task and the required number of working components k may change from phase to phase. In addition, due to varying load and working environments, component failure time distributions are also phase dependent. This paper proposes an analytical modeling approach based on multivalued decision diagrams (MDDs) for assessing reliability of the considered k/n-PAMS. The approach encompasses a new and fast MDD model generation algorithm that considers behaviors of all the mission phases simultaneously based on node labeling. As demonstrated through empirical studies on k/n-PAMSs with different sizes (different numbers of phases and different numbers of system components), the proposed algorithm is more efficient than the traditional phase-by-phase model generation method.     

A reliability allocation method of mechanism considering system performance reliability

It is generally believed that the reliability of a mechanical system is determined by its composition. The system operates properly when all of its components do not fail. Based on this assumption, the reliability of the system can be represented by the reliability of its components. A problem arises when applying this hypothesis to a system containing motion mechanisms. There is a phenomenon in motion mechanism that the components do not happen structural failure (we call it “Type I failure”) and joint failure (we call it “Type II failure”), but the function of the mechanism cannot meet the requirements (we call it “Type III failure”). A reliability allocation method, which synthetically considers the composition and Type III failure modes of the motion mechanism, is proposed to solve this problem. A relative dispersion factor is introduced to describe the failure dependence of components and is proposed to calculate the complexity and criticality. A series system reliability allocation model considering three types of failure modes is established. Finally, using an airplane gear door lock mechanism as an example, a comparative analysis of the system reliability allocation results with and without considering Type III failure modes is made. The allocation results show the component reliability value without considering Type III failure modes is less than that when considering them, which will increase the system hazards. The result considering Type III failure modes is more reasonable than that from the traditional method.     

Selective maintenance scheduling under stochastic maintenance quality with multiple maintenance actions

Many systems are required to perform a series of missions with finite breaks between any two consecutive missions. To improve the probability of system successfully completing the next mission, maintenance action is carried out on components during the breaks. In this work, a selective maintenance model with stochastic maintenance quality for multi-component systems is investigated. At each scheduled break, a set of maintenance actions with different degrees of impact are available for each component. The impact of a maintenance action is assumed to be random and follow an identified probability distribution. The corresponding maintenance cost and time are modelled based on the expected impact of the maintenance action. The objective of selective maintenance scheduling is to find the cost-optimal maintenance action for each component at every scheduled break subject to reliability and duration constraints. A simulated annealing algorithm is used to solve the complicated optimisation problem where both multiple maintenance actions and stochastic quality model are taken into account. Two illustrative numerical examples and a real case study have been solved to demonstrate the performance of the proposed approach. A comparison with deterministic maintenance shows the importance of considering the proposed stochastic quality in selective maintenance scheduling.     

A multi-objective discrete reliability optimization problem for dissimilar-unit standby systems

A new methodology for the reliability optimization of a k dissimilar-unit nonrepairable cold-standby redundant system is introduced in this paper. Each unit is composed of a number of independent components with generalized Erlang distributions of lifetimes arranged in a series–parallel configuration. We also propose an approximate technique to extend the model to the general types of nonconstant hazard functions. To evaluate the system reliability, we apply the shortest path technique in stochastic networks. The purchase cost of each component is assumed to be an increasing function of its expected lifetime. There are multiple component choices with different distribution parameters available for replacement with each component of the system. The objective of the reliability optimization problem is to select the best components, from the set of available components, to be placed in the standby system to minimize the initial purchase cost of the system, maximize the system mean time to failure, minimize the system variance of time to failure, and also maximize the system reliability at the mission time. The goal attainment method is used to solve a discrete time approximation of the original problem.      

Improving the Reliability in the Next Generation of US Army Platforms through Physics of Failure Analysis

Published studies and audits have documented that a significant number of U.S. Army systems are failing to demonstrate established reliability requirements. In order to address this issue, the Army developed a new reliability policy in December 2007 which encourages use of cost-effective reliability best practices. The intent of this policy is to improve reliability of Army systems and material, which in turn will have a significant positive impact on mission effectiveness, logistics effectiveness and life-cycle costs. Under this policy, the Army strongly encourages the use of Physics of Failure (PoF) analysis on mechanical and electronics systems. At the US Army Materiel Systems Analysis Activity, PoF analyses are conducted to support contractors, program managers and engineers on systems in all stages of acquisition from design, to test and evaluation (T&E) and fielded systems. This article discusses using the PoF approach to improve reliability of military products. PoF is a science-based approach to reliability that uses modeling and simulation to eliminate failures early in the design process by addressing root-cause failure mechanisms in a computer-aided engineering environment. The PoF approach involves modeling the root causes of failure such as fatigue, fracture, wear, and corrosion. Computer-aided design tools have been developed to address various loads, stresses, failure mechanisms, and failure sites. This paper focuses on understanding the cause and effect of physical processes and mechanisms that cause degradation and failure of materials and components. A reliability assessment case study of circuit cards consisting of dense circuitry is discussed. System level dynamics models, component finite element models and fatigue-life models were used to reveal the underlying physics of the hardware in its mission environment. Outputs of these analyses included forces acting on the system, displacements of components, accelerations, stress levels, weak points in the design and probable component life. This information may be used during the design process to make design changes early in the acquisition process when changes are easier to make and are much more cost effective. Design decisions and corrective actions made early in the acquisition phase leads to improved efficiency and effectiveness of the T&E process. The intent is to make fixes prior to T&E which will reduce test time and cost, allow more information to be obtained from test and improve test focus. PoF analyses may be conducted for failures occurring during test to better understand the underlying physics of the problem and identify the root cause of failures which may lead to better fixes for problems discovered, reduced test-fix-test iterations and reduced decision risk. The same analyses and benefits mentioned above may be applied to systems which are exhibiting failures in the field.     

A new combinatorial model for deterministic competing failure analysis

Components in many engineering and industrial systems can experience propagated failures, which not only cause the failure of the component itself but also affect other components, causing extensive damage to the entire system. However, in systems with functional dependence behavior where failure of a trigger component may cause other components (referred to as dependent components) to become unusable or inaccessible, failure propagation originating from a dependent component could be isolated if the corresponding trigger component fails first. Thus, a time-domain competition exists between the failure propagation effect and the failure isolation effect, which poses a great challenge to the system reliability modeling and analysis. In this work, a new combinatorial model called competing binary decision diagram (CBDD) is proposed for the reliability analysis of systems subject to the competing failure behavior. In particular, special Boolean algebra rules and logic manipulation rules are developed for system CBDD model generation. The corresponding evaluation algorithm for the constructed CBDD model is also proposed. The proposed CBDD modeling method has no limitation on the type of component time-to-failure distributions. A memory system example and a network example are provided to demonstrate the application of the proposed model and algorithms. Correctness of the proposed method is verified using the Markov method.