Many algorithms for computing the reliability of linear or circular consecutive-k-out-of-n:F systems appeared in this Transactions. The best complexity estimate obtained for solving this problem is O(k3log(n/k)) operations in the case of i.i.d. components. Using fast algorithms for computing a selected term of a linear recurrence with constant coefficients, we provide an algorithm having arithmetic complexity O(k log (k) log(log(k)) log(n)+komega) where 2<omega< 3 is the exponent of linear algebra. This algorithm holds generally for linear, and circular consecutive-k-out-of-n:F systems with independent but not necessarily identical components.

It is shown in detail that the steady-state availability of a series-system with no aging of components during the repair of another one can be interpreted as a conditional probability of the well-known s-independent case conditioned on allowing for at most one failed component at any time. Trivially, this conditional probability is larger than the standard probability, viz. the product of all components' probabilities. Yet it can be shown that also without this new interpretation of the formula for the availability of a series-system without aging during repairs it is exceptionally easy to prove the fact that by no aging during repairs, the availability of series-systems increases; a most plausible result.

One of the basic problems of dependability modeling is the adequate abstraction of real-world technological problems to the principle terms of reliability/safety scenarios. This concerns primarily the definition of components and of faults on different system levels. Given these terms the rest of any modeling needs basic logical operations, mostly AND and OR, and delays, and often some counting (of time or events). All of these basic operations are offered by a fairly simple kind of Petri net (PN), i.e., timed stochastic Petri nets, allowing also for the modeling of immediate activities and of such with a deterministic delay. In this half-tutorial paper it is shown how such Petri nets modeling, i.e., the construction of the relevant nets, works in practice. No math will be needed for that. Several typical engineering virtues are needed; primarily imagination as to how to (i) find simple solutions, since often nonelegant solutions can be correct too, (ii) compose larger PN from elementary building blocks, and (iii) the ability to model the real world by interpreting the so-called tokens of a PN intelligently in different places of one and the same PN. In the appendix it is shown how the PN can also help in the analytical analysis of nonrepairable systems. In that context they are superior to state graphs since they show state durations explicitly.

After discussing a few derivations of the canonical, i.e., unique, polynomial form of a Boolean function, various interesting applications of this form are discussed. Mainly, the polynomial form is shown to be very useful for a deeper understanding of switching functions with emphasis on fault tolerant electronics systems.

It is shown how the property of being monotonous of any invariables combinational switching function can be checked by evaluating n possibly ternary functions of binary variables in a simple way. Those functions are then shown to play a key role in the sensitivity analysis of stochastic Boolean functions.