Modelling multi-scale microstructures with combined Boolean random sets: A practical contribution

Boolean random sets are versatile tools to match morphological and topological properties of real structures of materials and particulate systems. Moreover, they can be combined in any number of ways to produce an even wider range of structures that cover a range of scales of microstructures through intersection and union. Based on well-established theory of Boolean random sets, this work provides scientists and engineers with simple and readily applicable results for matching combinations of Boolean random sets to observed microstructures. Once calibrated, such models yield straightforward three-dimensional simulation of materials, a powerful aid for investigating microstructure property relationships. Application of the proposed results to a real case situation yield convincing realisations of the observed microstructure in two and three dimensions

Prediction intervals for reliability growth models with small sample sizes

Engineers and practitioners contribute to society through their ability to apply basic scientific principles to real problems in an effective and efficient manner. They must collect data to test their products every day as part of the design and testing process and also after the product or process has been rolled out to monitor its effectiveness. Model building, data collection, data analysis and data interpretation form the core of sound engineering practice.After the data has been gathered the engineer must be able to sift them and interpret them correctly so that meaning can be exposed from a mass of undifferentiated numbers or facts. To do this he or she must be familiar with the fundamental concepts of correlation, uncertainty, variability and risk in the face of uncertainty. In today's global and highly competitive environment, continuous improvement in the processes and products of any field of engineering is essential for survival. Many organisations have shown that the first step to continuous improvement is to integrate the widespread use of statistics and basic data analysis into the manufacturing development process as well as into the day-to-day business decisions taken in regard to engineering processes.The Springer Handbook of Engineering Statistics gathers together the full range of statistical techniques required by engineers from all fields to gain sensible statistical feedback on how their processes or products are functioning and to give them realistic predictions of how these could be improved

A New Approach for Computing the Bandwidth Statistics of Avalanche Photodiodes

A new approach for characterizing the avalanche-buildup-time-limited bandwidth of avalanche photodiodes (APDs) is introduced which relies on the direct knowledge of the statistics of the random response time. The random response time is the actual duration of the APD’s finite buildup-limited random impulse response function. A theory is developed characterizing the probability distribution function (PDF) of the random response time. Recurrence equations are derived and numerically solved to yield the PDF of the random response time. The PDF is then used to compute the mean and the standard deviation of the bandwidth. The dependence of the mean and the standard deviation of the bandwidth on the APD mean gain and the ionization coefficient ratio is investigated. Exact asymptotics of the tail of the PDF of the response time are also developed to aid the computation efficiency. The technique can be readily applied to multiplication models which incorporate dead space and can be extended to cases for which the carrier ionization coefficient is position dependent

A Method for the Combination of Stochastic Time Varying Load Effects

The problem of evaluating the probability that a structure becomes unsafe under a combination of loads, over a given time period, is addressed. The loads and load effects are modeled as either pulse (static problem) processes with random occurrence time, intensity and a specified shape or intermittent continuous (dynamic problem) processes which are zero mean Gaussian processes superimposed 'on a pulse process. The load coincidence method is extended to problems with both nonlinear limit states and dynamic responses, including the case of correlated dynamic responses. The technique of linearization of a nonlinear limit state commonly used in a time-invariant problem is investigated for timevarying combination problems, with emphasis on selecting the linearization point. Results are compared with other methods, namely the method based on upcrossing rate, simpler combination rules such as Square Root of Sum of Squares and Turkstra's rule. Correlated effects among dynamic loads are examined to see how results differ from correlated static loads and to demonstrate which types of load dependencies are most important, i.e., affect' the exceedance probabilities the most. Application of the load coincidence method to code development is briefly discussed.National Science Foundation Grants CME 79-18053 and CEE 82-0759