title: Prior Robustness for Bayesian Implementation of the Fault Tree Analysis

authors: Joshi, Chaitanya

subjects: Science & Technology

abstract: We propose a prior robustness approach for the Bayesian implementation of the fault tree analysis (FTA). FTA is often used to evaluate risk in large, safety critical systems but has limitations due to its static structure. Bayesian approaches have been proposed as a superior alternative to it, however, this involves prior elicitation, which is not straightforward. We show that minor misspecification of priors for elementary events can result in a significant prior misspecification for the top event. A large amount of data is required to correctly update a misspecified prior and such data may not be available for many complex, safety critical systems. In such cases, prior misspecification equals posterior misspecification. Therefore, there is a need to develop a robustness approach for FTA, which can quantify the effects of prior misspecification on the posterior analysis. Here, we propose the first prior robustness approach specifically developed for FTA. We not only prove a few important mathematical properties of this approach, but also develop easy to use Monte Carlo sampling algorithms to implement this approach on any given fault tree with and and/or or gates. We then implement this Bayesian robustness approach on two real-life examples: a spacecraft re-entry example and a feeding control system example. We also provide a step-by-step illustration of how this approach can be applied to a real-life problem.

text: Prior Robustness for Bayesian Implementation of the Fault Tree Analysis We propose a prior robustness approach for the Bayesian implementation of the fault tree analysis (FTA). FTA is often used to evaluate risk in large, safety critical systems but has limitations due to its static structure. Bayesian approaches have been proposed as a superior alternative to it, however, this involves prior elicitation, which is not straightforward. We show that minor misspecification of priors for elementary events can result in a significant prior misspecification for the top event. A large amount of data is required to correctly update a misspecified prior and such data may not be available for many complex, safety critical systems. In such cases, prior misspecification equals posterior misspecification. Therefore, there is a need to develop a robustness approach for FTA, which can quantify the effects of prior misspecification on the posterior analysis. Here, we propose the first prior robustness approach specifically developed for FTA. We not only prove a few important mathematical properties of this approach, but also develop easy to use Monte Carlo sampling algorithms to implement this approach on any given fault tree with and and/or or gates. We then implement this Bayesian robustness approach on two real-life examples: a spacecraft re-entry example and a feeding control system example. We also provide a step-by-step illustration of how this approach can be applied to a real-life problem.

year: 2018

title: Miners’ and prospectors’ skills in general and at Te Aroha in particular

authors: Hart, Philip

abstract: Mining was a skilled occupation, and untrained men were poor miners. A variety of skills were required to trace ore and to develop safe and well-operated mines. Mine managers needed not only to understand all aspects of mining but also required knowledge of geology and an understanding of treatment processes. Ensuring safety was paramount. And ideally, in some circumstances they should have the fortitude to stand up to their directors. 
In the small mines of the Te Aroha district, as elsewhere, managers worked alongside miners, which could be bad for discipline. Examples are cited of managers who were unfairly dismissed for not finding high-grade ore. It was vital for the welfare of the industry that all their reports were accurate and not adjusted to suit share trading. Until late in the nineteenth century, managers were appointed because of their experience, but from 1887 onwards training was required, though for a time some very competent managers were granted certificates of competency without having to pass examinations in technical subjects. For long a preference was expressed for ‘practical’ men rather than the newly trained, and in the 1890s overseas experts were commonly ridiculed.
An ability to trace payable ore on the surface and underground was vital, and also one of the most difficult tasks facing both prospectors and miners. Untrained prospectors were notable for misunderstanding geology and wasting their efforts, as illustrated by some over-optimistic amateurs who failed to find anything of value despite years of effort. But even experienced men struggled to find good ore – hardly surprisingly because of its rarity. At least such men were not tempted by some of the more esoteric prospecting methods tried.
Because many in the mining industry realized their lack of knowledge, they were enthusiastic to learn from visiting lecturers and the schools of mines that were established in the 1880s. And several became inventors, with not all their inventions being limited just to the mining industry.

text: Miners’ and prospectors’ skills in general and at Te Aroha in particular Mining was a skilled occupation, and untrained men were poor miners. A variety of skills were required to trace ore and to develop safe and well-operated mines. Mine managers needed not only to understand all aspects of mining but also required knowledge of geology and an understanding of treatment processes. Ensuring safety was paramount. And ideally, in some circumstances they should have the fortitude to stand up to their directors. 
In the small mines of the Te Aroha district, as elsewhere, managers worked alongside miners, which could be bad for discipline. Examples are cited of managers who were unfairly dismissed for not finding high-grade ore. It was vital for the welfare of the industry that all their reports were accurate and not adjusted to suit share trading. Until late in the nineteenth century, managers were appointed because of their experience, but from 1887 onwards training was required, though for a time some very competent managers were granted certificates of competency without having to pass examinations in technical subjects. For long a preference was expressed for ‘practical’ men rather than the newly trained, and in the 1890s overseas experts were commonly ridiculed.
An ability to trace payable ore on the surface and underground was vital, and also one of the most difficult tasks facing both prospectors and miners. Untrained prospectors were notable for misunderstanding geology and wasting their efforts, as illustrated by some over-optimistic amateurs who failed to find anything of value despite years of effort. But even experienced men struggled to find good ore – hardly surprisingly because of its rarity. At least such men were not tempted by some of the more esoteric prospecting methods tried.
Because many in the mining industry realized their lack of knowledge, they were enthusiastic to learn from visiting lecturers and the schools of mines that were established in the 1880s. And several became inventors, with not all their inventions being limited just to the mining industry.

year: 2016

title: Maori syllabus and the curriculum documents: A critical analysis. Part 1: Tihe Mauri Ora

authors: Crombie, Winifred

subjects: Te reo Māori

abstract: This paper presents, within the context of ongoing debates on syllabus design, a critical analysis of Tihē Mauri Ora, a syllabus document produced by the New Zealand Ministry of Education to support the teaching and learning of the Māori language in schools in New Zealand. It includes a number of suggestions in relation to any future documents prepared with similar intent.

text: Maori syllabus and the curriculum documents: A critical analysis. Part 1: Tihe Mauri Ora This paper presents, within the context of ongoing debates on syllabus design, a critical analysis of Tihē Mauri Ora, a syllabus document produced by the New Zealand Ministry of Education to support the teaching and learning of the Māori language in schools in New Zealand. It includes a number of suggestions in relation to any future documents prepared with similar intent.

year: 2001