This paper addresses two important useful extensions of binary reliability techniques to multi-state reliability techniques, namely: (a) the problem of complementation or inversion of the function of system success to that of system failure (or equivalently, of deriving the logic...
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Research Article10.9734/jerr/2021/v20i817354
This paper utilizes a modern regular and modular eight-variable Karnaugh map in a systematic investigation of cause-effect relationships modeled by partially-defined Boolean functions (PDBF) (known also as incompletely specified switching functions). First, we present a Karnaugh-...
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Research Article10.9734/jerr/2021/v20i717348
This paper (the second of two sibling papers) continues the tutorial exposition presented in the first part of indicators derived from the ubiquitous two-by-two contingency table (confusion matrix). The indicators considered herein are those given in the context of clinical testi...
We use a regular and modular eight-variable Karnaugh map to reveal some technical details of Boolean minimization usually employed in solving problems of Qualitative Comparative Analysis (QCA). We utilize as a large running example a prominent eight-variable political-science pro...
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Research Article10.9734/ajess/2021/v17i230418
Qualitative Comparative Analysis (QCA) is an emergent methodology of diverse applications in many disciplines. However, its premises and techniques are continuously subject to discussion, debate, and (even) dispute. We use a regular and modular Karnaugh map to explore a prominent...
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Research Article10.9734/ajrcos/2021/v8i230199
This paper deals with an emergent variant of the classical problem of computing the probability of the union of n events, or equivalently the expectation of the disjunction (ORing) of n indicator variables for these events, i.e., the probability of this disjunction being equal to...
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Research Article10.9734/ajrcos/2021/v8i130191
This paper deals with the reliability of a multi-state delivery network (MSDN) with multiple suppliers, transfer stations and markets (depicted as vertices), connected by branches of multi-state capacities, delivering a certain commodity or service between their end vertices. We...
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Research Article10.9734/jamcs/2021/v36i230337
This paper is a preliminary step towards the assessment of an alarming widespread belief that victims of the novel coronavirus SARS-CoV-2 include the quality and accuracy of scientific publications about it. Our initial results suggest that this belief cannot be readily ignored,...
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Research Article10.9734/ijpr/2021/v6i230158
The synchronous Boolean network model is a simple and powerful tool in describing, analyzing and simulating cellular biological networks. This paper seeks a complete understanding of the dynamics of such a model by utilizing conventional matrix methods, rather than scalar methods...
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Research Article10.9734/jamcs/2020/v35i630293
In order to assess the performance indexes of some practical systems having fixed channel capacities, such as telecommunication networks, power transmission systems or commodity pipeline systems, we propose various types of techniques for analyzing a capacitated network. These in...
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Research Article10.9734/jamcs/2020/v35i630288
This paper examines two simple (albeit useful) methods used to evaluate the reliability of two-terminal multistate flow networks. These two methods involve two Karnaugh map versions, namely the Variable-Entered Karnaugh Map (VEKM) and the Multi-Valued Karnaugh Map (MVKM). These t...
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Research Article10.9734/jerr/2020/v13i317104
An -bit comparator is a celebrated combinational circuit that compares two -bit inputs and and produces three orthonormal outputs: G (indicating that is strictly greater than ), E (indicating that and are equal or equivalent), and L (indicating that is strictly less than )....
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Research Article10.9734/jamcs/2019/v32i330146
The JK flip flop is a flexible type of bistable elements that has extensive uses in digital electronics and control circuits. It is usually described by its characteristic equation or next-state table (used for analysis purposes) and its excitation table (used for synthesis purpo...
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Research Article10.9734/jerr/2019/v4i316903
A multi-state k-out-of-n: G system is a multi-state system whose multi-valued success is greater than or equal to a certain value j (lying between 1 (the lowest non-zero output level) and M (the highest output level)) whenever at least km components are in state m or above for al...
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Research Article10.9734/jamcs/2019/v31i230107
Multi-State systems are systems whose outputs are multi-valued (due to multiple levels of capacity or performance) and (possibly) whose inputs are also multi-valued (due to multiple performance levels or multiple modes of failure). These systems are a generalization of binary or...
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Research Article10.9734/jerr/2018/v3i316877
With the advent of digital computers, several prominent problems of digital circuit design emerged. A particular class of these problems, (called Type-2 problems) can be divided into two subclasses depending on whether an honest translator is possible or a sneaky translator is wa...
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Research Article10.9734/CJAST/2018/43728
This paper studies a prominent class of recursively-defined combinatorial functions, namely, the binomial and multinomial coefficients and probabilities. The paper reviews the basic notions and mathematical definitions of these four functions. Subsequently, it characterizes each...
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Research Article10.9734/JAMCS/2018/42137
Diagnostic testing concerning categorical or dichotomized variables is ubiquitous in many fields including, in particular, the field of clinical or epidemiological testing. Typically, results are aggregated in two-by-two contingency-table format, from which a surprisingly huge nu...
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Research Article10.9734/JAMCS/2018/39367
In standard problems of digital circuit design, a switching function (two-valued Boolean function) is specified declaratively as a (usually incomplete) asserted relation R(X,Z), or equivalently as an equation R(X,Z) = 1, where X and Z are inputs and outputs, respectively. To obta...
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Research Article10.9734/JAMCS/2018/39285
Any system of ‘big’ Boolean equations can be reduced to a single Boolean equation {g(Z) = 1} . We propose a novel method for producing a general parametric solution for such a Boolean equation without attempting to minimize the number of parameters used, but instead using indepen...
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Research Article10.9734/BJMCS/2017/33884
A prominent reliability model is that of the partially-redundant (k-out-of-n) system. We use algebraic as well as signal-flow-graph methods to explore and expose the AR algorithm for computing k-out-of-n reliability. We demonstrate that the AR algorithm is, in fact, both a recurs...
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Research Article10.9734/BJMCS/2017/33642
This paper handles a prominent problem of project management, namely that of project scheduling under uncertainty. The paper models this problem as a vector-weighted voting system and expresses the indicator variable for the successful (on-time) completion of project activities a...
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Research Article10.9734/BJMCS/2017/33161
This paper is a tutorial exposition on how to translate concepts of voting systems to the Boolean domain, and consequently on how to use Boolean tools in the computation of a prominent index of voting powers, viz., the Banzhaf voting index. We discuss Boolean representations for...
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Research Article10.9734/BJMCS/2017/31191
A double-threshold system (DTS) is a system that is successful if and only if the weighted arithmetic sum of its successes/failures equals or exceeds a certain threshold T1 and is smaller than or equal to a certain threshold T2. Generally a DTS is neither symmetric nor coherent....
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Research Article10.9734/BJMCS/2016/30264
This paper presents a review of flow network concepts, including definition of some graph-theoretic basics and a discussion of network flow properties. It also provides an overview of some crucial algorithms used to solve the maximum-flow problem such as the Ford and Fulkerson al...
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Research Article10.9734/ajrcos/2021/v7i330179
We provide a novel method for validating any purported set of the four most prominent indicators of diagnostic testing (Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value), by observing that these indicators constitute three rather than four indepe...
Checking a symbolic reliability expression for a flow network is useful for detecting faults in hand derivations and for debugging computer programs. This checking can be achieved in a systematic way, though it may be a formidable task. Three exhaustive tests are given when a rel...
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Research Article10.9734/jerr/2020/v18i217203
Although corona discharge is notorious for its detrimental effects, it is also used in many beneficial practical applications. Despite the existence of a variety of sophisticated theoretical and experimental methods for investigating corona discharge, we explore yet a much simple...
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Research Article10.9734/jerr/2020/v15i317146