Fault Level Coverage Research Articles

A generalized ternary decision diagram for reliability analysis on fault-tolerant systems in different coverage models

ABSTRACT For systems subject to imperfect fault coverage, ternary decision diagrams (TDDs) can be used for reliability analysis, as the component state becomes ternary, namely, operational, failed in a covered mode, and failed in an uncovered mode. There are different coverage models (CMs), including the traditional imperfect fault coverage model (IFCM) and its new extension irrelevance coverage model (ICM). The ICM extends the coverage to irrelevant components in addition to the fault components but is limited to monotonic systems so far. In addition, the TDDs for different CMs are developed based on different operation rules, and can only be used in specific CMs. To address these problems, this paper presents a generalized ternary decision diagram (GTDD). On one hand, the GTDD can handle non-monotonic systems in the ICM by extending the calculation of minimal irrelevance triggers to non-monotonic systems. On the other hand, the GTDD is designed as an all-in-one solution for the reliability analysis in various CMs, including perfect fault coverage model, element-level coverage model, fault-level coverage model, one-on-one-level coverage model, and ICM. Two case studies are presented to demonstrate the effectiveness of GTDD.

Fault‐level coverage analysis of multistate cloud‐RAID storage systems

In this paper, a multistate cloud‐RAID (redundant array of independent disks) storage system subject to fault‐level coverage (FLC) is modeled and analyzed. Most of the existing works on reliability analysis of cloud‐RAID systems have either assumed binary‐state for storage disks or failed to consider imperfect fault coverage, an inherent behavior of fault‐tolerant systems. This work advances the state of the art by proposing a combinatorial method based on multivalued decision diagrams for analyzing reliability of a multistate cloud‐RAID system with FLC. The FLC is one common type of imperfect fault coverage behaviors, where the system fault recovery capability is dependent on the number of disk faults happening within a certain recovery window. Effects of the functional dependence behavior between the RAID controller and disks are addressed. The method is illustrated through a detailed analysis of an example cloud‐RAID 5 storage system. Numerical results are provided to show the impact of different design parameters on system performance. These results also demonstrate that failure to consider FLC leads to inaccurate system state probabilities, further misleading system design activities based on these probabilities such as maintenance and optimization.

Balancing Reliability and Cost in Cloud-RAID Systems with Fault-Level Coverage

Based on redundancy techniques, cloud-RAIDs (Redundant Array of Independent Disks) offer an effective storage solution to achieve high data reliability. Their performance however can be greatly hindered by the fault-level coverage (FLC) behavior, where an uncovered disk fault may crash the entire system in spite of adequate redundancy remaining. Moreover, different choices of cloud disk providers lead to designs with different overall reliability and cost. Thus, in this paper we formulate and solve optimization problems, which determine the combination of cloud disks (from different providers) maximizing the cloud-RAID system reliability or minimizing the total cost. The cloud-RAID reliability is analyzed using a combinatorial and analytical modeling method while considering effects of the FLC behavior. Multiple case studies are performed to demonstrate the considered optimization problems and proposed solution methodology.

Aggregated combinatorial reliability model for non-repairable parallel phased-mission systems

Phased-mission systems (PMSs) are common in many real-world applications. A PMS has to accomplish a mission with multiple phases with varied requirements on system operation and demand. Reliability evaluation of PMSs is more challenging than single-phased systems due to dynamics in system configuration (or structure function) and component behavior, as well as inherent inter-phase dependence. Though many efforts have been dedicated to the PMS reliability analysis, it is still difficult to evaluate the reliability of a large-scale PMS with many phases. In this paper, we make original contributions by proposing a new combinatorial model, named aggregated binary decision diagram (ABDD) for reliability analysis of non-repairable parallel PMSs subject to dynamic demand requirements. The proposed approach constructs a single ABDD model considering failure combinations in all phases simultaneously, enabling efficient analysis of PMSs with many phases. The approach is also extended to address the effects of fault level coverage. Examples of PMSs with different scales are analyzed to demonstrate application and efficiency of the proposed ABDD-based approach.

Reliability analysis of imperfect coverage systems with a shared warm standby

Redundancy technique is commonly applied to satisfy the reliability requirements of fault-tolerant systems. Warm standby, a compromise between hot standby and cold standby in term of power consumption and recovery time, has attracted wide attention over the past several decades. However, the existing reliability analysis methods for warm standby system with imperfect coverage are difficult to deal with some cases, such as non-exponential time-to-failure distributions for the system components and the systems with shared standbys. In this paper, a new approach based on step function and impulse function is proposed to overcome the limitations of the existing approaches. The reliability of a system including shared standbys is deduced considering two kinds of imperfect fault coverage models, which contain Element Level Coverage (ELC) and Fault Level Coverage (FLC). The proposed approach can applicable to any type of time-to-failure distributions for the system components subject to imperfect fault coverage. A case study is presented to illustrate the applications and advantages.

Reliability analysis and optimal structure of series-parallel phased-mission systems subject to fault-level coverage

ABSTRACTMany practical systems have multiple consecutive and non-overlapping phases of operations during their mission and are generally referred to as phased-mission systems (PMSs). This article considers a general type of PMS consisting of subsystems connected in series, where each subsystem contains components with different capacities. The components within the same subsystem are divided into several disjoint work-sharing groups (WSGs). The capacity of each WSG is equal to the summation of the capacities of its working components, and the capacity of each subsystem is equal to the capacity of the WSG with the maximum capacity. The system capacity is bottlenecked by the capacity of the subsystem with the minimum capacity. The system survives the mission only if its capacity meets the predetermined mission demand in all phases. Such PMSs can be commonly found in the power transmission and telecommunication industries. A universal generating function–based method is first proposed for the reliability analysis of the capacitated series-parallel PMSs with the consideration of imperfect fault coverage. As different partitions of the WSGs inside a subsystem can lead to different system reliabilities, the optimal structure that maximizes the system reliability is investigated. Examples are presented to illustrate the proposed reliability evaluation method and optimization procedure.

Multi-Valued Decision Diagram Based Reliability Analysis of Demand-Based Warm Standby Systems with Imperfect Fault Coverage

In many real-world applications, warm standby redundancy is a commonly applied technique that can compromise recovery time and energy consumption in the fault-tolerant system design. It is considered as a generalization of cold standby and hot standby techniques and has attracted lots of research attentions. In this paper, a demand-based warm standby system subject to imperfect fault coverage is studied. The demand-based system consists of components with different capacities and fails if the cumulative capacity of working components is lower than the desired system demand. To adapt to different fault covering mechanisms, this paper considers two different kinds of fault coverage models, i.e. element level coverage and fault level coverage. A multi-valued decision diagram based approach is proposed to analyze the system reliability. The suggested method is combinatorial and has no limitation on the type of time-to-failure distributions for system components. An example is presented to illustrate the application and advantage of the proposed method.

Reliability of demand‐based warm standby systems subject to fault level coverage

AbstractFor mission‐critical or safety‐critical systems, redundancy techniques are often applied to satisfy the stringent reliability requirements of the system design. Warm standby sparing is a common redundancy technique, which compromises the high energy consumption of hot standby techniques and the long recovery time of cold standby techniques. This paper considers a more general model for warm standby systems, that is, the demand‐based warm standby system, where each component bears a nominal capacity and the system fails if the total capacity of the working components cannot meet the system demand. Moreover, fault level coverage is considered to model the imperfect coverage effect in the standby system. A multivalued decision diagram based approach is proposed to evaluate the reliability of the demand‐based warm standby system subject to the fault level coverage. Examples are given to illustrate the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

Reliability of demand-based phased-mission systems subject to fault level coverage

In many real-world applications, a mission may consist of several different tasks or phases that have to be accomplished in sequence. Such systems are referred to as phased-mission systems (PMS). In this paper we consider the demand-based PMS with parallel structure, where the system components function in parallel with different capacities in each phase of the mission and the mission is successful if and only if the total system capacity meets the predetermined mission demand in each phase. The reliability of the demand-based PMS (DB-PMS) with parallel structure subject to fault-level coverage (FLC) is first studied using a multi-valued decision diagram (MDD) based technique. The traditional MDD is modified to accommodate the FLC mechanism and new MDD construction and evaluation procedures are proposed for DB-PMS. To reduce the size of the MDD, an alternative construction procedure applying the branching truncation method and new reduction rules are further proposed. An upwards algorithm is put forward to evaluate the reliability of DB-PMS subject to FLC. The proposed approaches are illustrated through examples.

Binary decision diagram-based reliability evaluation of k-out-of-(n + k) warm standby systems subject to fault-level coverage

Warm standby sparing is a fault-tolerance technique that attempts to improve system reliability while compromising the system energy consumption and recovery time. However, when the imperfect fault coverage effect (an uncovered component fault can propagate and cause the whole system to fail) is considered, the reliability of a warm standby sparing can decrease with an increasing level of the redundancy. This article studies the reliability of a warm standby sparing subject to imperfect fault coverage, in particular, fault level coverage where the coverage probability of a component depends on the number of failed components in the system. The suggested approach is combinatorial and based on a generalized binary decision diagrams technique. The complexity for the binary decision diagram construction is analyzed, and several case studies are given to illustrate the application of the approach.

Efficient Reliability Assessment of Redundant Systems Subject to Imperfect Fault Coverage Using Binary Decision Diagrams

Systems requiring very high levels of reliability, such as aircraft controls or spacecraft, often use redundancy to achieve their requirements. This paper provides highly efficient techniques for computing the reliability of redundant systems involving simple k-out-of-n arrangements, and those involving complex structures which may include imbedded k-out-of-n structures. Techniques for modeling systems subject to imperfect fault coverage must be appropriate to the redundancy management architecture utilized by the system. Systems for which coverage can be associated with each of the redundant components, perhaps taking advantage of the component's built-in test capability, are modeled with what we term element level coverage (ELC); while systems which utilize majority voting for the selection from among redundant components are modeled with fault level coverage (FLC). In FLC, systems coverage is a function of the fault sequence, i.e., coverage will be greater for the initial faults which can utilize voting for redundant component selection, but will have a lower coverage value when the system must select from among the last two operational components. Occasionally, FLC systems can be adequately modeled using a simplified version of FLC in which it can be assumed that the initial fault coverage values are unity. This model is called one-on-level coverage (OLC). The FLC algorithms provided in this paper are of particular importance for the correct modeling of systems which utilize voting to select from among their redundant elements. While combinatorial, and recursive techniques for modeling ELC, FLC, and OLC have been previously reported, this paper presents new table-based algorithms, and binary decision diagram-based algorithms for these models which have superior computational complexity. The algorithms presented here provide the ability to analyse large, and complex systems very efficiently, in fact with a computational complexity comparable to the best available techniques for systems with perfect fault coverage.

Achievable Limits on the Reliability of $k$-out-of-$n$:G Systems Subject to Imperfect Fault Coverage

Systems which must be designed to achieve very low probabilities of failure often use redundancy to meet these requirements. However, redundant <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -out-of- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> :G systems which are subject to imperfect fault coverage have an optimum level of redundancy, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> . That is to say, additional redundancy in excess of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nopt</i> will result in an increase, not a decrease, in the probability of system failure. This characteristic severely limits the level of redundancy considered in the design of highly reliable systems to modest values of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> . Correct modeling of imperfect coverage is critical to the design of highly reliable systems. Two distinctly different <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -out-of- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> :G imperfect fault coverage reliability models are discussed in this paper: Element Level Coverage (ELC), and Fault Level Coverage (FLC). ELC is the appropriate model when each component can be assigned a given coverage level, while FLC is the appropriate model for systems using voting as the primary means of selection among redundant components. It is shown, over a wide range of realistic coverage values and relatively high component reliabilities, that the optimal redundancy level for ELC systems is 2 and 4 for FLC systems. It is also shown that the optimal probability of failure for FLC systems exceeds that of ELC systems by several orders of magnitude. New functions for computing the mean time to failure for i.i.d. <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -out-of- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> :G ELC, and FLC systems are also presented.

Multi-state systems with multi-fault coverage

The paper introduces a new model of fault level coverage for multi-state systems in which the effectiveness of recovery mechanisms depends on the coexistence of multiple faults in related elements. Examples of this effect can be found in computing systems, electrical power distribution networks, pipelines carrying dangerous materials, etc. For evaluating reliability and performance indices of multi-state systems with imperfect multi-fault coverage, a modification of the generalized reliability block diagram (RBD) method is suggested. This method, based on a universal generating function technique, allows performance distribution of complex multi-state series–parallel system with multi-fault coverage to be obtained using a straightforward recursive procedure. Illustrative examples are presented.

$k$-out-of-$n$:G System Reliability With Imperfect Fault Coverage

Systems requiring very high levels of reliability, such as aircraft controls or spacecraft, often use redundancy to achieve their requirements. Reliability models for such redundant systems have been widely treated in the literature. These models describe k-out-of-n:G systems, where n is the number of components in the system, and k is the minimum number of components that must work if the overall system is to work. Most of this literature treats the perfect fault coverage case, meaning that the system is perfectly capable of detecting, isolating, and accommodating failures of the redundant elements. However, the probability of accomplishing these tasks, termed fault coverage, is frequently less than unity. Correct modeling of imperfect coverage is critical to the design of highly reliable systems. Even very high values of coverage, only slightly less than unity, will have a major impact on the overall system reliability when compared to the ideal system with perfect coverage. The appropriate coverage modeling approach depends on the system design architecture, particularly the technique(s) used to select among the redundant elements. This paper demonstrates how coverage effects can be computed, using both combinatorial, and recursive techniques, for four different coverage models: perfect fault coverage (PFC), element level coverage (ELC), fault level coverage (FLC), and one-on-one level coverage (OLC). The designation of PFC, ELC, FLC, and OLC to distinguish types of coverage modeling is suggested in this paper.