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...
Open access
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-...
Open access
Research Article10.9734/jerr/2021/v20i717348
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
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
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...
Open access
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...
Open access
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...
Open access
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
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...
Open access
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...
Open access
Research Article10.9734/jerr/2020/v15i317146