Construction of closed interval for process capability indices Cpu,Cpl, and Spk based on Boole’s inequality and de Morgan’s laws

ABSTRACT

Considerable effort has been spent on the development of confidence intervals for process capability indices (PCIs) based on the sampling distribution of the PCI or the transferred PCI. However, there is still no definitive way to construct a closed interval for a PCI. The aim of this study is to develop closed intervals for the PCIs C_pu, C_pl, and S_pk based on Boole's inequality and de Morgan's laws. The relationships between different sample sizes, the significance levels, and the confidence intervals of the PCIs C_pu, C_pl, and S_pk are investigated. Then, a testing model for interval estimation for the PCIs C_pu, C_pl, and S_pk is built as a powerful tool for measuring the quality performance of a product. Finally, an applied example is given to demonstrate the effectiveness and applicability of the proposed method and the testing model.     

The effects of tact training on stereotypic vocalizations in children with autism

This study was a systematic extension of Karmali, Greer, Nuzzulo-Gomez, Ross, and Rivera-Valdes (2005) and Ahearn, Clark, MacDonald, and Chung (2007). We investigated the effects of a tact correction procedure on stereotypic vocalizations in 4 children diagnosed with autism who ranged in age from 6 to 16 years. Participants had limited vocal verbal repertoires and were primarily dependent on prompts for the emission of appropriate vocalizations. A multiple-baseline design across participants was used. Data were collected on instances of stereotypic vocalizations and independent tacts during baseline conditions and on instances of stereotypic vocalizations, independent tacts, and echoic-tacts during intervention. Procedural integrity and social validity data were also obtained. The results indicated a decrease in stereotypic vocalizations for 3 of the 4 participants and a slight increase in appropriate vocal verbal behavior (i.e., tacting) for all participants. The study provides support for the use of tact correction procedures to decrease stereotypic vocalizations and increase appropriate vocalizations in children with autism.     

赋权与增能：农民工弱势地位改变的根本途径

农民工①作为一个特殊的群体，为国家和社会的经济发展做出了巨大的贡献，可是他们处于社会的弱势和边缘状态，无法分享经济和社会发展的成果。对此，文章分析了农民工弱势地位的基本表现，农民工弱势地位的产生原因，提出改变农民工弱势地位的途径：赋权和增能。     

Comparison of procedures for fitting the autoregressive order of a vector error correction model

This paper investigates the lag length selection problem of a vector error correction model by using a convergent information criterion and tools based on the Box–Pierce methodology recently proposed in the literature. The performances of these approaches for selecting the optimal lag length are compared via Monte Carlo experiments. The effects of misspecified deterministic trend or cointegrating rank on the lag length selection are studied. Noting that processes often exhibit nonlinearities, the cases of iid and conditionally heteroscedastic errors will be considered. Strategies that can avoid misleading situations are proposed.     

Improved likelihood inferences for Weibull regression model

A general procedure is developed for bias-correcting the maximum likelihood estimators (MLEs) of the parameters of Weibull regression model with either complete or right-censored data. Following the bias correction, variance corrections and hence improved t-ratios for model parameters are presented. Potentially improved t-ratios for other reliability-related quantities are also discussed. Simulation results show that the proposed method is effective in correcting the bias of the MLEs, and the resulted t-ratios generally improve over the regular t-ratios.     

An improved two-stage procedure to compare hazard curves

Qiu and Sheng has proposed a powerful and robust two-stage procedure to compare two hazard rate functions. In this paper we improve their method by using the Fisher test to combine the asymptotically independent p-values obtained from the two stages of their procedure. In addition, we extend the procedure to situations with multiple hazard rate functions. Our comprehensive simulation study shows that the proposed method has a good performance in terms of controlling the type I error rate and of detecting power. Three real data applications are considered for illustrating the use of the new method.     

A note on the asymptotic distribution of the process capability index C pmk

Process capability indices have been widely used to evaluate the process performance to the continuous improvement of quality and productivity. The distribution of the estimator of the process capability index C _pmk is very complicated and the asymptotic distribution is proposed by Chen and Hsu [The asymptotic distribution of the processes capability index C _pmk , Comm. Statist. Theory Methods 24(5) (1995), pp. 1279–1291]. However, we found a critical error for the asymptotic distribution when the population mean is not equal to the midpoint of the specification limits. In this paper, a correct version of the asymptotic distribution is given. An asymptotic confidence interval of C _pmk by using the correct version of asymptotic distribution is proposed and the lower bound can be used to test if the process is capable. A simulation study of the coverage probability of the proposed confidence interval is shown to be satisfactory. The relation of six sigma technique and the index C _pmk is also discussed in this paper. An asymptotic testing procedure to determine if a process is capable based on the index of C _pmk is also given in this paper.     

Corrected maximum likelihood estimators in heteroscedastic symmetric nonlinear models

In this article, we derive general matrix formulae for second-order biases of maximum likelihood estimators (MLEs) in a class of heteroscedastic symmetric nonlinear regression models, thus generalizing some results in the literature. This class of regression models includes all symmetric continuous distributions, and has a wide range of practical applications in various fields such as engineering, biology, medicine and economics, among others. The variety of distributions with different kurtosis coefficients than the normal may give more flexibility in the choice of an appropriate distribution, particularly to accommodate outlying and influential observations. We derive a joint iterative process for estimating the mean and dispersion parameters. We also present simulation studies for the biases of the MLEs.     

Developing social work students’ professional identity: the role of England’s Professional Capabilities Framework

ABSTRACT

Developing professional identity is a key aim of social work education. This paper argues that the Professional Capabilities Framework (PCF) – a holistic, capability approach to student assessment used in England’s social work education programmes – is ideally placed to promote the development of students’ professional identities. The paper discusses two research studies, each of which was stimulated by significant policy changes in England’s social work profession. The author draws out the implications of both studies for supporting social work students to develop their professional identities. It is concluded that the PCF is valued by practice educators as an assessment and teaching tool, while acknowledging that its future is uncertain due to the lack of continuity impacting on England’s social work profession. This paper is equally of relevance for social work educators outside the UK who may be developing and evaluating their assessment approaches and also for those experiencing the impact of rapid policy changes in their own countries.     

Numerical evaluation of tests based on different heteroskedasticity-consistent covariance matrix estimators

This article considers the issue of performing tests in linear heteroskedastic models when the test statistic employs a consistent variance estimator. Several different estimators are considered, namely: HC0, HC1, HC2, HC3, and their bias-adjusted versions. The numerical evaluation is performed using numerical integration methods; the Imhof algorithm is used to that end. The results show that bias-adjustment of variance estimators used to construct test statistics delivers more reliable tests when they are performed for the HC0 and HC1 estimators, but the same does not hold for the HC3 estimator. Overall, the most reliable test is the HC3-based one.