Lennart Råde

Reliability survival equivalence

Abstract The concept of reliability equivalence is extended to the case when the survival function is used as performance measure of a reliability system. Reliability equivalence factors are calculated for a single component and for two component series and parallel systems. These factors are solutions to transcendent equations which are solved and the solutions graphed with Mathematica.

Probability and Flow Graphs

Summary This paper uses a number of examples to show how probability problems can be solved with the aid of flow graphs. This method has been used with great success by R. A. Howard in his recent work on dynamic probabilistic systems. The approach in this article is somewhat different from Howards, as the use of flow graphs here is combined with the collective marks method. The problems solved have to do with renewal processes in discrete and continuous time.

On the Use of Generating Functions and Laplace Transforms in Applied Probability Theory

Summary This article is concerned with the application of probability generating functions and Laplace transforms to the solution of specific probability problems. In particular, it presents the interpretation (or collective marks) method of van Dantzig and Runnenburg. With this method, generating functions and Laplace transforms can be interpreted as probabilities and these can often be obtained directly, without having first to derive a recursion formula or a differential equation. It is demonstrated how this method can be used to derive the binomial, the Poisson and the compound Poisson distributions, and it is also applied to the thinning of renewal streams and to some stochastic service systems.

A consecutive k-out-of-n reliability system in random environment

Abstract Linear and circular consecutive k-out-of-n reliability system are assumed to be situated in a random environment such that shocks generated by the environment will cause failure with probability p to one randomly chosen component. Explicit formulas for k = 2 and 3 are derived for generating functions and expectations and variances for the system time to failure. An equivalene between linear and circular systems is derived.

Waiting for HTHT.. .HT and geometric transforms

It is shown how geometric transforms (probability generating functions) can be used to study the expected number of tosses until HTHT.. .HT.

Random walks on the hexagon

This paper gives several examples of how flow graphs can be used to determine the probability distribution of certain random variables. All the examples deal with random walks on the hexagon. Ideas for further such examples are listed at the end of the paper.

Mathematical education at European universities of technology

The results from a survey of certain features of mathematical education of engineering students at some European universities and colleges of technology are reported.

Copenhagen ‘85: a report on the second European Seminar on Mathematics in Engineering Education

This paper reviews the presentations and activities of the second seminar organized by the working group on mathematics in engineering education, which took place in March 1985 at the Danish Engineering Academy.

A reliability problem treated by the additional event method

Abstract The additional event method (or method of collective marks) is used to derive the joint distribution of time to non-availability and number of served customers for a reliability system undergoing failure and repair.

The impact of computers on teaching stochastics to engineering students

Examples indicating how a micro‐computer or programmable calculator may be used as a didactical tool to enrich the teaching of probability and statistics to engineering students are presented.