Deterministic reliability-modeling of dynamic redundancy

Temporal logic, an extension of the traditional Boolean logic, is applied to deterministic reliability modeling and probabilistic analysis of systems with dynamic redundancy. Temporal logic is introduced, and the temporal structure function is defined. The expressions of temporal logic for active and passive redundancy are explained, followed by a discussion of switches. The concept of the temporal structure function is illustrated by important classes of dynamic systems. It is shown how temporal specifications of structural reliability facilitate subsequent probabilistic analysis and make the reliability analysis of complex dynamic systems feasible     

More realistic reliability analysis by conditional distributions

It is shown how the distribution and expectation of component life changes under various stresses. Subsequently the modified life distributions of components serve as input to reliability analysis of systems. In case the modification is caused by handing over the workload of failing components to functioning ones the new results are compared with those assuming statistically independent components.     

Bounds on Reliability of a Noncoherent System Using its Length & Width

A new kind of bounds on the reliability of s-noncoherent systems increases the variety of methods for probabilistic analysis of s-noncoherent systems. To compute the bounds, only a) the length and width of the system, and b) component reliabilities must be known. The weak and strong points of the bounds are illustrated by examples. The first example demonstrates the manifold applicability of s-noncoherent systems and compares the new bounds with those of Chu & Apostolakis.     

Verbesserte Einzelschrittverfahren

Based on the theory ofL-weak-regular splittings there will be described some Gauss-Seidel like iterative methods to solve systems of linear equationsAx=b with an M-MatrixA. Then we compare their rapidity of convergence, apply them especially to tridiagonal M-matrices and give some numerical examples.     

Improved Method of Inclusion-Exclusion Applied to k-out-of-n Systems

The method of inclusion-exclusion is represented in general form for reliability analysis. Applying it to the reliability of k-out-of-n system causes many cancelling terms. The method is improved to use only noncancelling terms in evaluating bounds on the reliability of k-out-of-n systems. These bounds are appreciably better, and converge to the exact system reliability in at most n ? k + 1 steps. In conclusion some numerical considerations suggest the quality of the bounds. Similar results for the reliability analysis of networks were derived by Satyanaraynna & Prabhakar.     

Synthesis and Number of all Series-Parallel Structures with n Components

A synthesis procedure and?as a by-product?the number of different redundant structures for series-parallel systems with n components is derived. The reliability graphs of these structures, especially their fault trees, are branched like true rooted trees in the sense of graph theory. The results might be useful for some reliability optimization procedures and other applications.     

Smaller sums of disjoint products by subproduct inversion

A new method is presented for calculating system reliability by sum of disjoint products. While the Abraham algorithm (1979) and its successors invert single variables, this new method applies inversion also to products of several variables. This results in shorter computation time and appreciably fewer disjoint products. Hence, the system reliability formula is considerably reduced in size. The Abraham algorithm, for instance, produces 71 disjoint products for network of 12 components and 24 minipaths, while this new method produces only 41 disjoint terms. This facilitates the numerical evaluation of the system reliability formula by reducing computation and rounding errors. Computer programs for both algorithms are included. They were written in Pascal and run on a microcomputer