Teaching reliability theory with the Computer Algebra System Maxima

The use of the Computer Algebra System MAXIMA as a teaching aid in an MSc lecture course in Reliability Theory is described here. Extracts from student handouts are used to show how the ideas in Reliability Theory are developed and how they are intertwined with their applications implemented in MAXIMA. Three themes from the lectures will be used in the demonstration to illustrate this: (1) Approximations, (2) Markov Modelling, (3) Laplace Transform Techniques. It will be demonstrated in the presentation that MAXIMA is a good tool for the task, since it is fairly easy to learn & use; it is well documented; it has extensive facilities; it is mature and won't undergo sudden (and perhaps undesirable) ‘upgrades’ causing compatibility problems; it is available for any operating system; and, finally, it can be freely downloaded from the Web. MAXIMA is a useful tool also in Reliability research for certain tasks. This latter feature provides a seamless link from teaching to research – an important feature in postgraduate education. Introduction The author has taught over successive years a one–semester lecture course entitled Reliability Modelling and Analysis (RMA) to MSc students. Students come from various academic background but all have a computing-related first degree. The RMA module, which is optional, is designed to prepare students for solving reliability-related problems in their own fields of specialisation. It is assumed that students have some prior knowledge of Probability and Statistics. A common initial standard in the basics is achieved by helping the weaker student on a one–to–one basis with reference to any standard textbook in Probability and Statistics. It was clear to the author at the outset that computing activities, in some form, should be part of this lecture course for the following reasons: (a) Students have a common interest and background in computers. (b) The syllabus permits the coursework component for computer usage to be specified. (c) In the author’s experience, computer generated course material enlivens the presentation and makes the ‘dry’, i.e. formal, mathematics-based material more acceptable to non–mathematicians. (d) In an applied course, the real life relevance should be emphasized by pertinent examples and exercises. There is room here for the traditional ‘paper–and–pencil’ work, but, to avoid boredom, they have to be accompanied by computer-based activities.