K.B. Misra

Minimal pathset and minimal cutsets using search technique

Abstract Application of graph theory to reliability analysis was first made in 1970 [1] . Over the years, a large number of computer programmes have been developed to determine the spanning trees, the minimal paths and cutsets, which are essential for determining the reliability of the network. In recent years, there has been an interest [2–4] in developing small desk top calculators for specific purposes, which could be used by the designers of transportation systems, communication systems, etc. In this article the authors present an approach to design a microprocessor based equipment to determine minimal pathset and minimal cutset from the incidence matrix of the graph. The authors have presented a new design approach, based on search technique. The salient feature of the new approach is a novel tracing process in which the desired graph is traced by operating a set of constraints. The new design approach has already been used by the authors to develop a microprocessor based spanning tree generator [2, 3] .

On Bayesian estimation of system reliability

For a system with n s-independent components, the uncertainty regarding the reliability of components for a fixed point of time is expressed by a Bayesian probability distribution. Using the moments of these distributions, the exact moments of the system reliability distribution are derived, from which a discrete probability density function is obtained on the basis of the principle of maximum entropy. Taking this distribution as a prior distribution for system reliability, a posterior density function for the system reliability is constructed either using the data obtained from life tests conducted at a system level or from field data. For tracking the evolution of the reliability distribution over time, a modified Kalman filter technique, along with use of a Bayesian procedure, is proposed. This method is simple, elegant and easy to compute.

A least square estimation of three parameters of a Weibull distribution

Abstract The present paper applies a least square method to estimate parameters of a Weibull distribution, with the shape parameter lying in the range 0–3, where other methods like the maximum likelihood method are generally not applicable. Further, Fishers F-test is employed to find the goodness of fit of a straight line. Two approximate methods have also been developed for the remaining range of the shape parameter. Illustrations are provided wherever necessary.

Performance index to quantify reliability using fuzzy subset theory

The system performance is generally assessed through reliability. There are gaps in the quantification through probability. An alternate concept of performance index is proposed in the paper which is expected to permit the consideration of any number of graded states of a system or a subsystem states and laws to compute the performance index. The theory of fuzzy sets permits the mathematical models to be flexible and close to human thinking, assessment or interpretations. This helps considerably in decision making process as it brings human thinking very close to engineering system performance.

Improved implementation of search technique to find spanning trees

Abstract The authors have developed a set of algorithms to find the spanning trees, the minimal paths and minimal cutsets of a graph, starting from the incidence matrix of the graph [1,3]. All the above algorithms employ a unique tracing process based on search techniques. The above algorithms have a number of salient features. The arithmetic and logic operations are very simple, which makes it possible to design small desk top calculators capable of handling reasonably large and complex graphs. The major constraint of these equipments is the memory capacity vis a vis their capability of handling larger graphs. The authors designed a microprocessor based system [2] to find spanning trees. The end results were available in the form of code numbers of branches appearing in a spanning tree, which had to be noted down, every time a tree was generated. In the new system the end results are in a more compact form, i.e. the vectors (see definition), one vector for one tree. The user can easily note down the vectors and decode them later to obtain the branches of a tree. In the new system the user can reallocate the available working memory space to suit the problem. The memory requirement in the new approach is also less.

A procedure for solving general integer programming problems

Recently, Misra [Microelectron. Reliab. 31, 285–294 (1991)] introduced a procedure for solving a variety of reliability optimization problems. In the present paper, the authors demonstrate that this procedure can also be used for solving a general class of integer programming problems, which are usually encountered in many allocation problems. System reliability design is only one of the applications. The algorithm, while being simple, has been found to be an economical and exact solution to the integer programming problem. The algorithm solves a very wide variety of the problems which otherwise cannot be easily solved through any of the existing search methods. Several illustrations are provided to establish the superiority of the approach.

Moments of order statistics using the orthogonal inverse expansion method and its application in reliability

Moments of order statistics have widespread use in life-testing and reliability studies. The orthogonal inverse expansion method is a unique method which allows one to obtain moments and product moments of order statistics of any distribution. In the present paper, we demonstrate the application of the orthogonal inverse expansion method to compute moments of order statistics and the use of these moments in various reliability studies.

Quantitative analysis of software quality during the “design and implementation” phase

Abstract An approach for quantitative evaluation of software quality during the “design and implementation” phase of the software life cycle is presented. This evaluation starts by defining a set of software quality characteristics, viz. usability, efficiency and complexity. Each of these attributes is assessed through a set of software quality metrics, such as completeness, communicativeness, conciseness, accessibility and device efficiency. The software quality metric is then, in turn, evaluated through a checklist consisting of a detailed questionnaire. The multi-element component comparison and analysis (MECCA) method has been used for quantitative analysis. This analysis provides a quantitative measure, which reflects the figure of merit or degree of excellence of software quality during the design and implementation phase.

A new heuristic approach for redundancy optimization problem

The present paper describes a simple heuristic approach to solve redundancy optimization problem without much of computation to help reliability designers choose an appropriate configuration. The solution technique is simpler than all previous methods and offers optimal results with a high success rate.

Quadrilateral-star transformation—II. Algorithmic aspects

The evaluation of system probability of failure based on transformation approach basically needs the knowledge of two equally important aspects, viz. (i) transformation equations and (ii) systematic methodology for network reduction using transformations. The present paper discusses various features of the second aspects such as transformation selection criteria, subnetwork configurations and their identification scheme, network reduction process, algorithm etc.