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Weibull distribution is one of the most widely used model for failure data in reliability studies. In this paper a sequential estimation procedure for estimating the parameters of Weibull distribution is proposed, which is, in principle similar to Kalman filtering. The main advantage of this approach is that it shows the variation of parameters over a time as new failure data becomes available to the analyst for estimation. Also once an available data has been used, the method does not require that data for further processing as and when the new data becomes available for updating the estimates of parameters. Its use in Quality control asa control chart has been indicated and the procedure is illustrated with the help of examples.

A method of obtaining a minimized system reliability or unreliability expression using Demorgan's theorem is presented. Some formulae based on this theorem are provided, from which the minimized expression of system unreliability can be obtained by knowledge of pathsets. At the same time, this expression can also provide minimum cutsets of the system easily. On the other hand, one can obtain the minimum pathsets of a system without much difficulty, if the minimum cutsets are known.

It is well known that conventional reliability analysis using probabilities has been found to be inadequate to handle uncertainty of failure data and modelling. To overcome this problem, the concept of “fuzzy probability” has been used in the evaluation of reliability of a general non-series parallel network. Basically, only two operations, i.e. multiplication and complementation, need to be performed in assessing system reliability of a non-series parallel system. A procedure is developed to carry out these operations efficiently.

Several applications are proposed for an efficient, fast and exact technique for solving integer programming problems that normally arise in optimal reliability design problems. The computational experience of solving these problems is described and the algorithm is found to be superior to any of the earlier methods available to date in solving a wide variety of reliability design problems. The paper aims to demonstrate this capability of the algorithm; as the algorithm is based on functional evaluations only, it solves even very large system problems economically.

In many reliability design problems, the decision variables can only have integer values. The redundancy allocation is an example of one such problem; others include spare parts allocation, or repairmen allocation, which necessitate an integer programming formulation. In other words, integer programming plays an important role in system reliability optimization. In this paper, an algorithm is presented which provides an exact, simple and economical solution to any general class of integer programming problems and thereby offers reliability designers an efficient tool for system design. The algorithm can be used effectively to solve a wide variety of reliability design problems. The scope of use of this algorithm is also indicated and the procedure is illustrated by an example.

An efficient search technique is used to obtain the optimal configuration of a computer communication network. The method is based on an earlier paper and is easily programmable. An interactive computer code in FORTRAN 77 for the use on IBM-compatible PCs has also been developed. The approach has been illustrated by several examples.

The present paper provides an efficient approach to multiple criteria redundancy optimization problems, often encountered in reliability design of engineering systems. A search technique introduced earlier [10,11] in combination with the multicriteria optimization methods, based on min-max concept for finding Pareto optimal solution of multicriteria optimization problems, provides an efficient and excellent approach for solving redundancy optimization problems. The approach is illustrated through several numerical examples. Further, based on this approach, a very general computer code called ESMOP (Efficient Search Multi-Objective Programming) has also been developed. It is capable of considering any type of redundancy, constraint or individual cost function and thus offers to solve many reliability design problems.

The present paper provides a new mathematical formulation of a combined reliability and redundancy allocation involving multiple objective functions in the reliability design of a system employing mixed type of redundancy. The paper proposes an easily computerizable procedure for solving a variety of design problems. The proposed solution technique is a combination of the direct search technique [9,10] and a random search procedure for optimizing redundancy and reliability at the same time at each subsystem and uses multicriteria optimization procedure based on min-max approach [11,12] for obtaining Pareto optimal solutions. The procedure is illustrated through several examples. A general computer code, called ESMOP (Efficient Search Multi-Objective Programming), for the use on IBM compatible PCs has also been developed. The code takes into account all kinds of redundancies including multiple discrete choices for component reliabilities, and a wide variety of resource coefficients and constraint functions.

At a post-Chernobyl conference on Probabilistic Safety Assessment and Risk management (PSA '87) held in September 1987, the inadequacies of the current Probabilistic Risk Assessment (PSA) came into sharp focus. Highlighting the importance of improvements in the current PSA, Professor Rasmussen - a pioneer in the PSA methodology - made a strong plea for reduction of rather large uncertainties in the results of current PSA. Obviously, amongst the ways to achieve this, one of the approaches would be to encourage collection and use of accurate failure data. However as the state of affairs is, a better alternative would be to develop a methodology which could handle imprecision of data and uncertainties of models which are existence in the current PSA. Fuzzy Set Theory (FST) provides a natural framework to achieve the above goal and therefore the present paper is intended to emphasize and explore the possibility of the use of such a theory to develop a methodology which is computationally simple and easy to use in the quantitative assessment of failure probability of catastrophic events in PSA, particularly, in level-I studies. Some illustrative examples are provided to demonstrate the feasibility and effectiveness of such an approach. It is demonstrated that a general purpose computer code can be developed without much difficulty to recast the PRA studies to incorporate fuzzy probabilities.

The present study gives a computerizable exact method to obtain the optimal design of a repairable computer communication system, assuming that a given amount of resources is available for linking the centres. The method is based on the Lawler-Bell algorithm. The objective is to obtain a design that maximizes the global availability of the system. This paper also provides several heuristics for the same problem, when the system under consideration is very large.

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, Fisher's 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.

A geometric programming formulation of tolerance assignment problem in circuit is presented. The expressions for optimum component tolerances in circuit are derived. A method is also suggested for the tolerance assignment problem having multiple constraints. The advantage of the method is that it involves only hand calculations.

It is well-known that the conventional fault tree analysis using probabilities has been found to be inadequate to handle the imprecision of input failure data and the uncertainties associated with the modelling particularly in relation to dependency of failures. Therefore, to overcome these problems, a Fuzzy Fault Tree Analysis (FFTA) based on possibility distributions associated with the basic events and a fuzzy algebra for combining these events, has been presented in this paper. The authors propose an algorithm based on a discretization procedure which permits consideration of any arbitrary possiblity distribution for the events and provides a higher precision than that could be obtained in a graphical approach, as is presented here. The method described in this paper can be used for any coherent system. Further, an approximate representation for conditional possibility distributions has also been provided which can be used in conjunction with AND and OR-gates of the fault tree to consider the dependency of failures.

This paper presents a simple heuristic technique to arrive at the optimal redundancy allocation. There is a drastic reduction in the number of steps because of the criterion evolved, which allows for the addition of one or more units, simultaneously, at more than one stage. Examples have been provided to demonstrate the effectiveness of the technique.

Reliability evaluation of complex systems is of interest to engineers of all disciplines. The techniques for reliability evaluation depend upon the logic diagram of the system. System reliability evaluation is straight forward in case of series-parallel systems; while this is not so in general nonseries parallel systems. In this paper, many different techniques for reliability evaluation of general systems have been presented. Merits and demerits of every method are discussed. An example is solved by all the methods to have a comparison of computational labour involved and the size of final derived reliability expression.

Once a system has been designed to meet its operational requirements, an analysis is usually carried out to redesign the system such that reliability goals are satisfied. The objective of this analysis is to work out a tradeoff between the design parameters based on system reliability effectiveness, and the availability of resources. Efforts have been made to systematize reliability design procedures, however much remains to be done in this area. Although each system is unique, a general design philosophy and methodology could be described that may be found useful for designing reliable systems. The paper describes state of art on optimum design of systems based on reliability effectiveness.

The present paper develops mathematical models for evaluating the exact reliability and mean time to failure of k-out-of-m: G systems with different unit failure probabilities. The ith unit is assumed to be characterized by a general hazard rate hi(t) = λitb. The models are based on the concepts of tie sets; they are fairly simple and can be used for any values of m and k. The algorithm developed for these models is suitable for adoption for a computer code.

Reliability of a network containing only link failures is well attempted in the reliability literature. In a communication network, node failure probability is sometimes as significant as link failure probability. The problem has been given little attention. The procedure evolved is tedious and the resulting reliability expression is quite lengthy. In this paper, the flow graph method of reliability evaluation has been extended to consider simultaneously the node as well as link failure. The method suggested is simple and leads to a simpler reliability expression. An example has been solved doing all the steps of the procedure clearly.

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.

An algorithm has been developed for enumerating all simple paths in a communication network for specified terminal pairs. The efficiency of the method increases with the number of terminal pairs for which path enumeration is required. The algorithm generates the paths in ascending order of cardinality. The method is applicable to the graphs having finite non zero failure probability nodes. A FORTRAN program for implementation of the algorithm has been developed and results are reported.

The tolerance analysis problem is formulated as a non-linear integer programming problem. A Beta type penalty function corresponding to discrete variables has been used in the formulation. The resultant problem is then solved with the help of modified Newton method. The advantage of this formulation lies in its requiring fewer variables than in any other formulation available in the literature. Also the discretized decision variables are obtained within a few iterations. The method described in this paper is thus simple and quick in solving the complex problem of tolerancing in electric networks.

A laboratory model of a reliability analyzer is described. The idea behind the development of such an analyzer is to provide an analogue model for determining all pathsets or cutsets of a system and thereby determining the system reliability when the system configuration is known along with the reliability of its constituent elements. Any system with unreliable branches and nodes can be simulated on the reliability analyzer using the logic gates. The analyzer provides tremendous flexibility in changing of the system configuration for reliability studies. The users require manually plugging in or out of a particular link to simulate addition or removal of a branch. The reliability parameters such as terminal reliability and global reliability in the case of a communication network can also be studied. Block diagram or fault tree approaches can be used to analyze a system on the analyzer described in this paper.

A simple and new method is provided for allocating redundancies to various stages of a system, to maximize the system reliability under some given constraints. The approach suggested does not require tedious and long computations. The approach may be helpful to system designers to arrive at the solution quickly with little algebraic manipulation. The feasibility of developing standard redundancy allocation charts in the case of simple forms of the constraints is indicated.

A method is presented for computing system reliability in terms of the reliabilities of constituent elements. The method is applicable to both series parallel as well as nonseries-parallel systems of any complexity. A technique of finding out all transmission paths of a general network is provided, which leads to the network reliability expression. A minimization technique is introduced to simplify this expression, which will have a lesser number of terms than obtained by any existing method. The reduced expression helps a design engineer to evaluate the system reliability speedily.

Reliability expression of a system derived by various methods of reliability evaluation varies considerably. Therefore, computational time needed for the numerical evaluation of reliability of a particular system shall depend upon the method applied. Also, the absolute error in the final result for reliability shall depend upon the complexity of reliability expression, and hence on the method applied. A quantitative study of these two important aspects is given in this paper.

A fast method for redundancy allocation for a series system is described in this paper. The approach makes use of some of the special features of the problem and thereby reduces it to the solution of a set of inequalities. Two illustrative problems—one with linear and the other with the non-linear constraints are given as examples. The type of constraints and the number of stages do not set a limitation on the choice of this approach as with the existing methods.