Modeling the reliability of threshold weighted voting systems

In many applications, ranging from target detection to safety monitoring systems, we are interested in determining whether or not to accept a hypothesis based on the information available. In this paper we model the reliability of threshold weighted voting systems (WVS) with multi-failure-modes, where a general recursive reliability function of the WVS is presented. We also develop approximation formulas for calculating the reliability of WVS based on a large number of units. We also develop reliability functions of time-dependent threshold weighted voting systems, where each unit is a function of time. Finally, the optimal stopping time that minimizes the total cost of the systems subject to a reliability constraint is discussed.     

Holistic reliability analysis of weighted voting systems from a multi-state perspective

The computation of the reliability of weighted voting systems is an important problem in reliability theory due to its potential application in security, target identification, safety and monitoring areas. Voting systems are used in a wide variety of applications where an acceptance or rejection decision has to be made about a binary proposition presented to the system. For these systems, it is of interest to obtain the probability so that based on the vote of decision-making units, the system aggregates these votes into the right decision when presented with such a proposition. This paper presents a holistic work on weighted voting system reliability by presenting modeling, computation, estimation and optimization techniques. The modeling part takes advantage of the structure of weighted voting systems to present a model of its reliability as a multi-state system. Next, based on the multi-state view of the system, an exact computational approach based on multi-state minimal cut and path vectors is introduced. The paper then acknowledges the computational complexity of the problem and provides a Monte Carlo simulation approach that estimates system reliability accurately and in an efficient computational time. Finally, an optimization heuristic that generates quasi-optimal solutions is presented that is able to solve the problem of maximizing the reliability of a weighted voting system based on a specified number of decision-making units with known reliability characteristics.     

Analyzing the behavior and reliability of voting systems comprising tri-state units using enumerated simulation

Voting is a common technique used in combining results from peer experts, for multiple purposes, and in a variety of domains. In distributed decision making systems, voting mechanisms are used to obtain a decision by incorporating the opinion of multiple units. Voting systems have many applications in fault tolerant systems, mutual exclusion in distributed systems, and replicated databases. We are specifically interested in voting systems as used in decision-making applications.In this paper, we describe a synthetic experimental procedure to study the behavior of a variety of voting system configurations using a simulator to: analyze the state of each expert, apply a voting mechanism, and analyze the voting results. We introduce an enumerated-simulation approach and compare it to existing mathematical approaches. The paper studies the following behaviors of a voting system: (1) the reliability of the voting system, R; (2) the probability of reaching a consensus, P_c; (3) certainty index, T; and (4) the confidence index, C. The configuration parameters controlling the analysis are: (1) the number of participating experts, N, (2) the possible output states of an expert, and (3) the probability distribution of each expert states. We illustrate the application of this approach to a voting system that consists of N units, each has three states: correct (success), wrong (failed), and abstain (did not produce an output). The final output of the decision-making (voting) system is correct if a consensus is reached on a correct unit output, abstain if all units abstain from voting, and wrong otherwise. We will show that using the proposed approach, we can easily conduct studies to unleash several behaviors of a decision-making system with tri-state experts.     

Asymmetric weighted voting systems

The weighted voting system (WVS) studied consists of n units, each of which provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual weight. System output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction τ of the cumulative weight of all non-abstaining units. Otherwise, system output is 0. The system input is either 0 or 1. Every unit is characterized by the probability of making decisions 0 and 1 and by probability of abstaining for each input. The system fails if the system output is not equal to its input.In this paper, an asymmetric WVS is suggested in which each voting unit has two weights. The first weight is applied when the unit's decision is 0 and the second weight is applied when the unit's decision is 1. The asymmetry of unit weights allows the WVS designer to take advantage of the knowledge of statistical asymmetry of voting units (asymmetric probabilities of making correct decisions with respect to the input). The paper presents an algorithm for asymmetric WVS reliability evaluation. This algorithm is based on using a universal generating function technique.For a system consisting of voting units with given reliability characteristics, one can maximize the entire system reliability by choosing proper unit weights and threshold value. An algorithm is suggested which finds the optimal unit weights and the threshold. A genetic algorithm is used as the optimization tool. An example is presented in which the superiority of asymmetric WVS over regular symmetric one is demonstrated.     

Optimal unit grouping in weighted voting systems

The voting system studied consists of n units that each provide a binary decision (0 or 1) or abstain from voting. Each unit has its own individual weight. System output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction τ of the cumulative weight of all non-abstaining units. Otherwise system output is 0.For a system consisting of voting units with given reliability characteristics one can maximize the entire system reliability by choosing proper unit weights and threshold values τ. In this paper it is shown that additional system reliability improvement can be achieved by grouping units in voting subsystems and tallying the weighted votes of these subsystems (groups) to make a final decision. An algorithm is suggested which finds the optimal element grouping as well as unit weights within each group, weights of the groups and corresponding system thresholds. The approach is based on using a universal generating function technique for evaluating system reliability. A genetic algorithm is used as the optimization tool. Examples are presented.     

Analysis and optimization of weighted voting systems consisting of voting units with limited availability

The voting system studied consists of n voting units each either providing a binary decision (0 or 1) or abstaining from voting. The system output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction τ of the cumulative weight of all non-abstaining units. Otherwise, the system output is 0.In this paper, we study the effect of limited availability of the voting units on the entire voting system reliability. Two different types of systems are considered. In the system of type 1, the absence of unit output (unit unavailability) is interpreted by the system as abstention from voting. In the system of type 2, the unavailable state of the voting unit and its abstention from voting can be distinguished and the system parameters can be adjusted to optimize its performance for each combination of available units.There are two ways to improve reliability of weighted voting system consisting of units with the given output probability distribution: optimization of system parameters (weights of units and threshold factor value) and units availability enhancement (for example, by choosing proper maintenance policy). This paper shows a method of incorporating information about units' availability into a procedure for determining the optimal system parameters. It also presents a method for determining indices that measure importance of voting units availability for both types of systems. These indices indicate voting units for which efforts of availability enhancement are the most beneficial from the entire system reliability improvement point of view.The approach is based on using a universal generating function technique and optimization procedure presented in [5]. Examples are presented.     

On the notion of 'software independence' in voting systems

This paper defines and explores the notion of 'software independence' in voting systems: 'A voting system is software independent if an (undetected) change or error in its software cannot cause an undetectable change or error in an election outcome'. For example, optical scan and some cryptographically based voting systems are software independent. Variations and implications of this definition are explored. It is proposed that software-independent voting systems should be preferred, and software-dependent voting systems should be avoided.An initial version of this paper was prepared for use by the Technical Guidelines Development Committee in their development of the Voluntary Voting System Guidelines, which will specify the requirements that the USA voting systems must meet to receive certification.     

Strength and reliability of piping systems

Analytical and numerical methods have been developed for the solution of stress-strain and limit state problems of piping systems (in the case of the presence of flaws in them as well). The fracture strength of pipe steels during long-term service has been studied. A methodology and a software have been developed for the assessment of stress-strain state to extend the life of active pipelines. The developments made are used to increase the reliability of Ukrainian piping systems.     

Setting up reliability goals for systems

The quality of life of people of any country depends to a very large extent on the quality and reliability of products and services like transport, communications, power, broadcasting, telecasting, etc. Psychological and physical discomforts are felt by people only when things fail thereby reducing or removing the service. Everybody feels that ‘immortal’ services should be available, but services are created by man and are mortal like him. However, there is a need to have a reliability goal whereby one can guarantee the continuity of a service for a certain lengtht of time/distance with a known risk of failure. Reliability of services is dependent on the reliability of systems comprising them and the management. In this paper the author has tried to focus attention on the need to have reliability goals as distinct from availability goals. The paper gives the basis for setting up reliability goals for a system as well as its subsystems. The allocation of reliability goals for the subsystems is based on the operating experience with similar systems or on the basis of the knowledge of the system or both. Two typical cases of a nuclear power station and a particle accelerator are considered and reliability goals for both system and subsystems are arrived at. The author concludes by stating that reliability goals in respect of simple items produced in large quantities and used anywhere in the world are a necessity. This is so because cost of maintenance is bound to be large with such items.     

On structural reliability of parallel systems

The distribution of strength of a bundle of perfectly brittle components in parallel with equal load sharing is studied. An early asymptotic result for stochastically independent components which is due to Daniels is generalized for components whose bearing capacities depend on a second uncertain variable in a multiplicative manner. In particular, if the componental strengths are log-normally distributed and equicorrelated it is shown that system strength is asymptotically ormal. Some applications and their validity to structural design are discussed.     

Production reliability in flexible manufacturing systems

A typical flexible manufacturing system, Westland Helicopters' sheet metal detail manufacturing complex, has been analysed for reliability. The techniques of fault tree analysis and event tree analysis are presented and their applicability to this study investigated. Event tree analysis has been found to be a more effective method for analysing manufacturing systems. The failure states of the system have been identified from the construction of an event tree which considers random hardware faults that influence production. Failure rate data have been used to quantify the critical production failure states in terms of machine failures. Estimates are made of the system's MTTF and percentage availability using typical MTTR figures. The probability that a selected production route fails to complete the manufacture of a set of parts is also evaluated. A dependency of systems reliability on the production demand has been discovered, and a possible method for modelling and assessing the reliability of systems capable of producing several products is proposed.     

Computer-aided reliability analysis of fault-tolerant systems

We present an overview of the major problems inherent in reliability modelling of fault-tolerant systems. The problems faced while modelling such systems include the need to consider a very large state space, non-exponential distributions, error analysis, the need to perform a combined evaluation of performance and reliability, and the need to include the details of fault/error handling behaviour. Some of the proposed solutions are discussed and current tools (harp, save, deep andsharpe) to facilitate evaluation of such systems are described. References are provided to many of the important techniques utilized in reliability, availability, and performance modelling of such systems. This research was supported in part by the Air Force Office of Scientific Research under grant AFOSR-84-0132, by the Army Research Office under contract DAAG29-84-0045 and by the National Aeronautics and Space Administration under grant NAG1-70.     

Age-related maintenance versus reliability centred maintenance: a case study on aero-engines

Reliability Centred Maintenance (RCM) is a procedure carried out as part of the logistic support analysis (LSA) process and is described in the US Department of Defence Military Standards (Mil Std 2173). RCM allows logisticians the opportunity to determine the best maintenance policy for each component within a system. However, the only data that are available to carryout RCM using Mil Std 2173 are of MTBF. This implies that all the necessary mathematical models need to be based on the exponential distribution. This is a serious drawback to the whole concept of RCM as the exponential distribution cannot be used to model items that fail due to wear, or any other mode that is related to their age. In this paper, a new approach to RCM is proposed using the concepts of soft life and hard life to optimise the total maintenance cost. For simplicity, only one mode of failure is considered for each component. However, the model can be readily applied to multiple failure modes. The proposed model is applied to find the optimal maintenance policies in the case of military aero-engines using Monte Carlo simulation. The case study shows a potential benefit from setting soft lives on relatively cheap components that can cause expensive, unplanned engine rejections.     

Reactive wetting in metal/metal systems: Dissolutive versus compound-forming systems

Reactive wetting in metal–metal systems involves complex interactions between the molten phase and the solid substrate. The simplest interaction involves only the dissolution of the substrate into the molten phase. The more complex interaction involves both dissolution of the substrate and compound formation at the solid–liquid boundary. The fundamental differences between these two types of reactive wetting are identified by studying the purely dissolutive system Bi–Sn and the compound-forming system Au–Sn. Experiments employ the traditional sessile drop technique as well as a novel two-dimensional drop transfer technique that enables real-time visualization of the solid–liquid interface evolution. Recent results from wetting of pure Sn on Au-coated Cu substrates are also presented and reveal a much richer wetting behavior than either Sn on Au or Sn on Cu binary systems.     

Mission reliability analysis of fault-tolerant multiple-phased systems

Fault-tolerant multiple-phased systems (FTMPS) are defined as systems whose critical components are independently replicated and whose operational life can be partitioned into a set of disjoint periods, called “phases”. Because of their deployment in critical applications, their mission reliability analysis is a task of primary relevance to validate the designs. This paper is focused on the reliability analysis of FTMPS with random phase durations, non-exponentially distributed repair activities and different repair policies. For self-repairable FTMPS with a component-level reconfiguration architecture, we derive several efficient formulations from the underlying structure characteristics for their intraphase behavior analysis. We also present a uniform solution framework of the mission reliability for FTMPS with generally distributed phase durations. Compared with existing methods based on deterministic and stochastic Petri nets or Markov regenerative stochastic Petri nets, our approach is more simple in concept and powerful in computation. Two examples of FTMPS are analyzed to illustrate the advantages of our approach.     

Estimation in coherent reliability systems through copulas

The problem of estimating the parameter of a common distribution of components' lifetimes from system's lifetime data is of interest and importance in reliability engineering. The present paper deals with this problem when the common component distribution is exponential with mean μ and the lifetimes of components have an exchangeable joint distribution which is constructed by the help of Archimedean copula. In particular we obtain moment estimator of μ for Clayton and Ali-Mikhail-Haq copulas. We illustrate the findings of the paper for a special class of coherent systems called consecutive k-within-m-out-of-n:F system. A simulation study is performed to investigate the properties of the moment estimator. The method presented in this paper can be applied to all coherent systems.