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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.

Very few techniques exist for reliability evaluation of communication systems where links as well as nodes have certain probability of failure. This correspondence describes a technique by which the reliability expression for such a system can be conveniently derived. It is also shown that using the concept of this correspondence, it is possible to extend all the existing reliability-evaluation algorithms to communication systems with little effort.

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.

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.

This paper presents a method of maximizing reliability of a series system subject to multiple constraints. The use of both active series parallel and standby redundancy is considered to increase the reliability of the system. A flexible tree search method has been used in this paper which is found to be an efficient method of solution, as it requires only simple mathematical computations. A three stage system is used for illustration.

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 system design engineer often resorts to redundancies while maximizing the probability of success of a system designed to perform a certain job over a period, This will have to be done within the resources available. The problem of maximizing system reliability, subject to some linear constraints such as cost, weight or volume, is considered in this paper- The usual problem is transformed to a suitable form and the least square concept is used to develop a solution technique. This type of approach is found to be very simple and faster than earlier methods although the solution is an approximate one.

The reliability literature offers an abundance of methods for the optimal design of systems under some constraints. In most of the papers, the problem considered is: given reliabilities of each constituent component and their constraint-type data, optimize the system reliability. This amounts to the assignment of optimal redundancies to each stage of the system, with each component reliability specified. This is a partial optimization of the system reliability. At the design stage, a designer has many options, e.g., component reliability improvement and use of redundancy. A true optimal system design explores these alternatives explicitly. Our paper demonstrates the feasibility of arriving at an optimal system design using the latter concept. For simplicity, only a cost constraint is used, however, the approach is more general and can be extended to any number of constraints. A particular cost-reliability curve is used to illustrate the approach.

This paper provides a simple algorithm for the solution of the redundancy optimization problem in the presence of multiple linear constraints. Basicaily, the solution to an r-constraint problem is obtained successively from the solution of r-unconstrained problems. At each step, an active constraint is picked out, then the maximum gradient concept is used to find a closer point. The approach requires minimum effort and time for solution.

The redundancy optimization problem is formulated as an integer programming problem of zero-one type variables. The solution is obtained making use of an algorithm due to Lawler and Bell. Objective function and constraints can be any arbitrary functions. Three different variations of the optimization problem are considered. The formulation is easy and the solution is convenient on a digital computer. The size of the problem that can be solved is not restricted by the number of constraints.

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.

An algorithm is presented for evaluation of reliability of any redundant network. It uses the properties of digraphs and is especially suitable for the computer analysis of large complex networks. A method for deriving the reliability expression for any type of network is also described along with a Fortran computer program for the reliability evaluation of series-parallel networks.

A flow graph approach for reliability analysis is applied to redundancy with elements in the simple series-parallel networks and to the more general case with elements in non-series-parallel combinations. The reliability of networks for elements with open or short failures is analyzed with flow graphs. Typical examples are shown.

A mathematical model is formulated for optimizing the reliability of a system subject to given linear constraints; the system has several stages in series; each stage has parallel redundancy to improve the reliability. Part I shows a new way to transform the model of constrained optimization to a saddle point problem by using Lagrange multipliers. Conditions are derived for maximizing the reliability function; Newton's method is used to solve the resulting multidimensional nonlinear algebraic equations. Further modifications are provided to avoid inverting the large Jacobian matrices; therefore this method is practical for large systems. Part II shows how to transform the model of constrained optimization to a multistage decision process and uses the Maximum principle to arrive at the optimal decision. This approach is easy to apply, formulate, and program. The solution can be obtained without fear of nonconvergence (very often experienced with earlier methods) besides providing considerable saving in computer time. Design alternatives can be easily considered.

A new formulation for the problem of system reliability optimization when constrained by some linear constraints is presented in this paper. The formulation provided is easily adaptable to geometric programming form. The problem is further reduced to that of an optimization of an unconstrained objective function with variables one less than the number of constraints, when its dual is defined. It is amply demonstrated through this paper that the formulation and approach of this paper are simpler than earlier attempts described elsewhere. An example is also given.

An algorithm is developed to obtain a simplified reliability expression for a general network. All the success paths of the network are determined; then they are modified to be mutually disjoint. The reliability expression follows directly from the disjoint paths. The algorithm is easy and computationally economical. The reliability expression involves fewer terms and arithmetic operations than any of the existing methods. This is an advantage, considering the size of the system a reliability engineer normally handles and the frequency with which the expression is used for reliability studies.

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.

An algorithm for the heuristic solution of redundancy optimization problems is presented. There may be any number of constraints which need not be linear. For selecting the stage where redundancy is to be added, a heuristic criterion is introduced which takes into account the relative increment in reliability versus decrement in slacks. The algorithm is simple and requires minimum computation.