Mark Bebbington

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We propose computationally tractable formal mathematical definitions for the 'useful period' of lifetime distributions with bathtub shaped hazard rate functions. Detailed analysis of the reduced additive Weibull hazard rate function illustrates its utility for identifying such useful periods. Examples of several other bathtub shaped hazard rate functions(More)
Aging and mortality is usually modeled by the Gompertz-Makeham distribution, where the mortality rate accelerates with age in adult humans. The resulting parameters are interpreted as the frailty and decrease in vitality with age. This fits well to life data from 'westernized' societies, where the data are accurate, of high resolution, and show the effects(More)
Although failure data are usually treated as being continuous, they may have been collected in a discrete manner, or in fact be discrete in nature. Reliability models with bathtub-shaped hazard rate are fundamental to the concepts of burn-in and maintenance, but how well do they incorporate discrete data? We explore discrete versions of the additive Weibull(More)
A linked stress release model is proposed for the analysis of spatial interaction of earthquake occurrences through stress transfer within a large area of the Earth’s crust. As an example, the model is used for statistical analysis for the Japanese historical earthquakes in central Japan and offshore in the Nankai and Sagami troughs with magnitude M ≥ 6.5(More)
Wireless channels introduce burst errors as well as random errors to digitally modulated links. Proper characterization of these errors is necessary, as it not only clearly identifies the channel itself but also is of utmost importance to system designers utilizing these channels. For example, it is then possible to attempt to eliminate these errors by(More)
Loss networks have long been used to model various types of telecommunication network , including circuit-switched networks. Such networks often use admission controls, such as trunk reservation, to optimize revenue or stabilize the behaviour of the network. Unfortunately, an exact analysis of such networks is not usually possible, and reduced-load(More)
Admission controls, such as trunk reservation, are often used in loss networks to optimize their performance. Since the numerical evaluation of performance measures is complex, much attention has been given to nding approximation methods. The Erlang Fixed Point Approximation, which is based on an independent blocking assumption, has been used for networks(More)
The New Zealand Food Safety Authority sampling protocol for compliance inspection of imported food products is evaluated for its ability to provide consumer protection. The sampling protocol involves both partial testing of imported consignments and complete skipping inspection of consignments based on the quality history. The risk posed by the strategies(More)