BATHTUB-TYPE CURVES IN RELIABILITY AND BEYOND

Finding optimal, or at least good, maintenance and repair policies is crucial in reliability engineering. Likewise, describing life phases of human mortality is important when determining social policy or insurance premiums. In these tasks, one searches for distributions to fit data and then makes inferences about the population(s). In the present paper, we focus on bathtub‐type distributions and provide a view of certain problems, methods and solutions, and a few challenges, that can be encountered in reliability engineering, survival analysis, demography and actuarial science.     

SMPD Scenarios of Spatial Distribution of Human Population in China

Three scenarios of spatial distribution of human population in China are developed in the years 2010 and 2020, respectively by means of the method of surface modeling of population distribution (SMPD). Each one of the SMPD scenarios is defined as a plausible alternative future under particular assumptions of elevation, water system, net primary productivity (NPP), urbanization, transport infrastructure development, and population growth. The SMPD scenarios show that if population could freely migrate within the whole China, the balanced ratios of population in the western region, the middle region and the eastern region to total population in the whole China would be 16%, 33% and 52%, respectively.     

100 key research questions for the post‐2015 development agenda

The Sustainable Development Goals (SDGs) herald a new phase for international development. This article presents the results of a consultative exercise to collaboratively identify 100 research questions of critical importance for the post‐2015 international development agenda. The final shortlist is grouped into nine thematic areas and was selected by 21 representatives of international and non‐governmental organisations and consultancies, and 14 academics with diverse disciplinary expertise from an initial pool of 704 questions submitted by 110 organisations based in 34 countries. The shortlist includes questions addressing long‐standing problems, new challenges and broader issues related to development policies, practices and institutions. Collectively, these questions are relevant for future development‐related research priorities of governmental and non‐governmental organisations worldwide and could act as focal points for transdisciplinary research collaborations.     

A generalized negative binomial and applications

A generalized negative binomial distribution is derived from the Markov Bernoulli sequence of successes and failures. We study the properties and applications of this distribution. The properties are illustrated by two examples of discrete time queueing systems. The distribution is then fitted to two data sets, the eruption record of Mt. Sangay, and a record of computer disk failure accesses. In the first case there is a strong serial dependence in the data and the generalized negative binomial provides a good fit, while in the second case, although there is a significant serial dependence, it is insufficient to justify the additional parameter of the distribution. We conclude by demonstrating the usefulness of the distribution in the field of statistical quality control.     

Equity and efficiency in the allocation of the personal social services

This paper investigates two issues of equity in the receipt of the home help service, one about territorial justice, the other about sex discrimination. It uses GHS data for 1980. An argument is developed about the efficiency with which services are targeted on persons who by normative criteria would appear to have most need of them. Efficiency is of two types: horizontal efficiency, the proportion of persons judged in need who receive services; and vertical efficiency, the proportion of services allocated to persons judged in need. The findings are that there is evidence of inequity both between different areas and between the sexes. Metropolitan areas are advantaged compared with rural areas, and this cannot be explained by differences in social support nor by the availability of other domiciliary services. Among the elderly living alone, neither sex is advantaged, but in elderly married couple households the home help service is more frequently provided in the case of a husband caring for a disabled wife than in the case of a wife caring for a disabled husband.     

Rolling with the shakes: an insight into teenagers’ perceptions of recovery after the Canterbury earthquakes

Natural disasters are harmful worldwide events that inflict multiple psychosocial impacts on disaster-exposed individuals. A significant proportion of affected individuals are teenagers (13–18 years old) who, compared with adults, have been historically overlooked in disaster research. The literature is particularly sparse concerning teenagers’ recovery from natural disasters, specifically what recovery means to them and the contributing factors towards their positive recovery. Therefore, the aim of the current study was to gain deeper insight into this largely unexplored area by conducting five focus groups with teenagers (16–18 years) who experienced at least one of the Canterbury, New Zealand, earthquakes since and including the initial September 2010 earthquake. This study directly asked teenagers about their recovery over the three years after the initial earthquakes, with data being analysed using thematic analysis. Two main themes were identified: (1) perceptions of recovery, with three sub-themes (i) knowledge and being less frightened, (ii) talking about the earthquakes and (iii) shift in perspectives; and (2) contributing factors to recovery, with three sub-themes (i) participation in the community response, (ii) returning to school and (iii) the rebuild of Christchurch. These factors provide insight into how we can better support the recovery process for disaster-exposed teenagers to reduce long-term distress.     

Estimating the turning point of a bathtub-shaped failure distribution

The turning point of a hazard rate function is useful in assessing the hazard in the useful life phase and helps to determine and plan appropriate burn-in, maintenance, and repair policies and strategies. For many bathtub-shaped distributions, the turning point is unique, and the hazard varies little in the useful life phase. We investigate the performance of an empirical estimator for the turning point in the case of the modified Weibull distribution, a bathtub-shaped generalization of the Weibull distribution, that has been found to be useful in reliability engineering and other areas concerned with life-time data. We illustrate the theory by means of an example, and also conduct a simulation study to assess the performance of the estimator in practice.