A robust process capability index

The existing process capability indices (PCI's) assume that the distribution of the process being investigated is normal. For non-normal distributions, PCI's become unreliable in that PCI's may indicate the process is capable when in fact it is not. In this paper, we propose a new index which can be applied to any distribution. The proposed indexC_f:, is directly related to the probability of non-conformance of the process. For a given random sample, the estimation of C_f boils down to estimating non-parametrically the tail probabilities of an unknown distribution. The approach discussed in this paper is based on the works by Pickands (1975) and Smith (1987). We also discuss the construction of bootstrap confidence intervals of C_f: based on the so-called accelerated bias correction method (BC _a:). Several simulations are carried out to demonstrate the flexibility and applicability of C_f:. Two real life data sets are analyzed using the proposed index.     

On the Alias Method for Generating Random Variables from a Discrete Distribution

The alias method of Walker is a clever, new, fast method for generating random variables from an arbitrary, specified discrete distribution. A simple probabilistic proof is given, in terms of mixtures, that the method works for any discrete distribution with a finite number of outcomes. A more efficient version of the table-generating portion of the method is described. Finally, a brief discussion on efficiency of the method is given. We believe that the generality, speed, and simplicity of the method make it attractive for use in generating discrete random variables.     

Long-Term Earnings Differentials Between African American and White Men by Educational Level

This paper investigates long-term earnings differentials between African American and white men using data that match respondents in the Survey of Income and Program Participation to 30 years of their longitudinal earnings as recorded by the Social Security Administration. Given changing labor market conditions over three decades, we focus on how racial differentials vary by educational level because the latter has important and persistent effects on labor market outcomes over the course of an entire work career. The results show that the long-term earnings of African American men are more disadvantaged at lower levels of educational attainment. Controlling for demographic characteristics, work disability, and various indicators of educational achievement does not explain the lower long-term earnings of less-educated black men in comparison to less-educated white men. The interaction arises because black men without a high school degree have a larger number of years of zero earnings during their work careers. Other results show that this racial interaction by educational level is not apparent in cross-sectional data which do not provide information on the accumulation of zero earnings over the course of 30 years. We interpret these findings as indicating that compared to either less-educated white men or highly educated black men, the long-term earnings of less-educated African American men are likely to be more negatively affected by the consequences of residential and economic segregation, unemployment, being out of the labor force, activities in the informal economy, incarceration, and poorer health.     

Toward Probabilistic Prediction of Flash Flood Human Impacts

This article focuses on conceptual and methodological developments allowing the integration of physical and social dynamics leading to model forecasts of circumstance‐specific human losses during a flash flood. To reach this objective, a random forest classifier is applied to assess the likelihood of fatality occurrence for a given circumstance as a function of representative indicators. Here, vehicle‐related circumstance is chosen as the literature indicates that most fatalities from flash flooding fall in this category. A database of flash flood events, with and without human losses from 2001 to 2011 in the United States, is supplemented with other variables describing the storm event, the spatial distribution of the sensitive characteristics of the exposed population, and built environment at the county level. The catastrophic flash floods of May 2015 in the states of Texas and Oklahoma are used as a case study to map the dynamics of the estimated probabilistic human risk on a daily scale. The results indicate the importance of time‐ and space‐dependent human vulnerability and risk assessment for short‐fuse flood events. The need for more systematic human impact data collection is also highlighted to advance impact‐based predictive models for flash flood casualties using machine‐learning approaches in the future.     

Morality as a Verb: The Process of Moral Development Within the “Family Culture”

The purpose of this paper was to examine many different theories of moral development, view their similarities and differences, and expand upon the role of the family in teaching morality. There have been many stage theories developed in order to understand the process of moral development. In addition, many researchers have criticized the stage models for not adequately incorporating the role of culture in shaping a child's moral stance. We believe that the child's family (not necessarily an American Western view of the family) is crucial in directly and indirectly translating cultural values to children. We review some prominent stage theories to moral development as a point of departure for looking at the crucial role of the family culture. The family teaches morality to children by finding a balance between the forces of individuation and connection.