Klaus D. Heidtmann

Computing k-out-of-n System Reliability

A linear-time algorithm and its short computer program in BASIC for k-out-of-n:G system reliability computation is presented.

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. >

Arithmetic spectrum applied to fault detection for combinational networks

A method for the derivation of fault signatures for the detection of faults in single-output combinational networks is described. The approach uses the arithmetic spectrum instead of the Rademacher-Walsh spectrum. It is a form of data compression that serves to reduce the volume of the response data at test time. The price which is paid for the reduction in the storage requirements is that some of the knowledge of exact fault location is lost. The derived signatures are short and easily tested using very simple test equipment. The test circuitry could be included on the chip since the overhead involved is comparatively small. The test procedure requires a high-speed counter cycling at maximum speed through selected subsets of all input combinations. Hence, the network under test is exercised at speed, and a number of dynamic errors that are not testable by means of conventional test-set approaches will be detected. >

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.

Statistical Comparison of Two Sum-of-Disjoint-Product Algorithms for Reliability and Safety Evaluation

The evaluation of system reliability and safety is important for the design of new systems and the improvement or further development of existing systems. Especially the probability that a systems operates (safely) using the probabilities that its components operate is a vital system characteristic and its computation is a non-trivial task. The most often used method to solve this problem is to derive disjoint events from the description of the system structure and to sum up the probabilities of these disjoint events to quantify system reliability or safety. To compute disjoint products as logical representation of disjoint events Abrahams algorithm inverts single variables indicating the state of a component and therefor produces a huge number of disjoint products. To avoid this disadvantage Heidtmann developed a new method which inverts multiple variables at once and results in a much smaller number of disjoint products as confirmed by some examples. This paper quantifies this advantage by statistical methods and statistical characteristics for both algorithms presenting measurements of the number of produced disjoint products and the computation time of both algorithms for a large sample of randomly generated systems. These empirical values are used to investigate the efficiency of both algorithms by statistical means showing that the difference between both algorithm grows exponentially with system size and that Heidtmanns method is significantly superior. The results were obtained using our Java tool for system reliability and safety computation which is available in the WWW.

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. >

Fehlertolerante Videokommunikation über verlustbehaftete Paketvermittlungsnetze

Verlustbehaftete Paketvermittlungsnetze besitzen eine Reihe von Unzulanglichkeiten bei der Datenubertragung, deren Folgen fur die Videokommunikation gemas der H.26x- und MPEG-Normen wir aufzeigen. Dabei wird ein Modell entwickelt, das die Fehlerakkumulation reflektiert, die dadurch entsteht, das Bilder aus Grunden der Datenreduktion lediglich als Differenz zu anderen ahnlichen Bildern codiert werden. Dieses Modell dient als Grundlage fur ein neu entwickeltes Fehlertoleranzverfahren, bei dem intracodierte Bildinformationen in gemas dem Modell berechneten Abstanden uber mehrere Bilder verteilt gesendet werden. Neben diesem senderseitigen Verfahren werden mehrere vom Empfangerendsystem auszufuhrende Fehlertoleranzmasnahmen untersucht. In beiden Fallen werden die erzielten Qualitatsverbesserungen sowohl quantifiziert als auch fur eine subjektive Qualitatsbewertung illustriert.

More realistic reliability analysis by conditional distributions

Abstract 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.

Evaluation of Video Communication over Packet Switching Networks

Real-time video communication as a component of distributed multimedia systems for new evolving applications like video telefony and video-conferencing is strongly dependent on the quality of service provided by its communication support. Dependability attributes of the undelying communication system playing a predominant role with regard to the quality achievable from applications and users point of view. Especially video compression reduces data rates by removing the original redundancy of video sequencies but creates dependencies between data of different images enabling extensive error propagation. So real-time video communication becomes extremely sensitive to faulty transmitted, lost or too late arriving data. This dependability inherent for instance in most packet switching networks results in low video quality. In this paper we study video communication via best-effort networks, which present the actual communication infrastructure. First we illustrate the effect of transmission deficiencies on the visual quality of the received video. Then an analytical model of dependability is developed, which reflects the transmission of MPEG and H.261 coded video streams. We apply our model to compute appropriate or even optimal parameters for video encoders. Forward error control using error correcting codes provides the communication process with fault tolerance, which may improve the quality of video transmission by systematic redundancy. So we extend our model to determine the required level of redundancy. Finally we discuss further mechanisms of fault tolerance to achieve high video quality even in case of modest or even low quality of service delivered by communication systems.