Estimation of nonseparable models with censored dependent variables and endogenous regressors

In this article we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalize the identification argument put forward in Altonji, Ichimura, and Otsu (2012 Altonji, J. G., Ichimura, H., Otsu, T. (2012). Estimating derivatives in nonseparable models with limited dependent variables. Econometrica 80:1701–1719.[Crossref], [Web of Science ®] , [Google Scholar]), construct a nonparametric estimator, characterize its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. Identification is constructive and is achieved through a control function approach. We show that the estimator is consistent and asymptotically normally distributed. The Monte Carlo results are encouraging.     

Robustness to non-normality and autocorrelation of individuals control charts

This paper studies the effects of non-normality and autocorrelation on the performances of various individuals control charts for monitoring the process mean and/or variance. The traditional Shewhart X chart and moving range (MR) chart are investigated as well as several types of exponentially weighted moving average (EWMA) charts and combinations of control charts involving these EWMA charts. It is shown that the combination of the X and MR charts will not detect small and moderate parameter shifts as fast as combinations involving the EWMA charts, and that the performana of the X and MR charts is very sensitive to the normality assumption. It is also shown that certain combinations of EWMA charts can be designed to be robust to non-normality and very effective at detecting small and moderate shifts in the process mean and/or variance. Although autocorrelation can have a significant effect on the in-control performances of these combinations of EWMA charts, their relative out-of-control performances under independence are generally maintained for low to moderate levels of autocorrelation.     

Selecting the normal population with the smallest variance: A restricted subset selection rule

Consider k( ? 2) normal populations whose means are all known or unknown and whose variances are unknown. Let σ²_[1] ? ??? ? σ_[k]² denote the ordered variances. Our goal is to select a non empty subset of the k populations whose size is at most m(1 ? m ? k ? 1) so that the population associated with the smallest variance (called the best population) is included in the selected subset with a guaranteed minimum probability P* whenever σ²_[2]/σ_[1]² ? δ* > 1, where P* and δ* are specified in advance of the experiment. Based on samples of size n from each of the populations, we propose and investigate a procedure called R_BCP. We also derive some asymptotic results for our procedure. Some comparisons with an earlier available procedure are presented in terms of the average subset sizes for selected slippage configurations based on simulations. The results are illustrated by an example.     

学分绩点制在武汉七所部属高校的实践与探索

学分绩点制是一种能客观衡量学生学习质量的教学管理制度。学分绩点制在武汉地区七校联合办学实践中的应用,为联合办学的可持续发展提供了有益的探索。     

An EWMA chart for monitoring process mean

In the statistical process control literature, there exists several improved quality control charts based on cost-effective sampling schemes, including the ranked set sampling (RSS) and median RSS (MRSS). A generalized cost-effective RSS scheme has been recently introduced for efficiently estimating the population mean, namely varied L RSS (VLRSS). In this article, we propose a new exponentially weighted moving average (EWMA) control chart for monitoring the process mean using VLRSS, named the EWMA-VLRSS chart, under both perfect and imperfect rankings. The EWMA-VLRSS chart encompasses the existing EWMA charts based on RSS and MRSS (named the EWMA-RSS and EWMA-MRSS charts). We use extensive Monte Carlo simulations to compute the run length characteristics of the EWMA-VLRSS chart. The proposed chart is then compared with the existing EWMA charts. It is found that, with either perfect or imperfect rankings, the EWMA-VLRSS chart is more sensitive than the EWMA-RSS and EWMA-MRSS charts in detecting small to large shifts in the process mean. A real dataset is also used to explain the working of the EWMA-VLRSS chart.     

Transition probabilities and ARL performance of Six Sigma zone control charts

In this article, Six Sigma zone control charts (SSZCCs) are proposed for world class organizations. The transition probabilities are obtained using the Markov chain approach. The Average Run Length (ARL) values are then presented. The ARL performance of the proposed SSZCCs and the standard Six Sigma control chart (SSCC) without zones or run rules is studied. The ARL performance of these charts is then compared with those of the other standard zone control charts (ZCCs), the modified ZCC and the traditional Shewhart control chart (SCC) with common run rules. As expected, it is shown that the proposed SSZCC outperforms the standard SSCC without zones or run rules for process shifts of any magnitude. When compared to the other standard ZCCs and the Shewhart chart with common run rules, it is observed that the proposed SSZCCs have much higher false alarm rates for smaller shifts and hence they prevent unwanted process disturbances. The application of the proposed SSZCC is illustrated using a real time example.     

The effect of autocorrelation on the ewma maxmin tolerance limits

Amin et al. (1999) developed an exponentially weighted moving average (EWMA) control chart, based on the smallest and largest observations in each sample. The resulting plot of the extremes suggests that the MaxMin EWMA may also be viewed as smoothed tolerance limits. Tolerance limits are limits that include a specific proportion of the population at a given confidence level. In the context of process control, they are used to make sure that production will not be outside specifications. Amin and Li (2000) provided the coverages of the MaxMin EWMA tolerance limits for independent data. In this article, it is shown how autocorrelation affects the confidence level of MaxMin tolerance limits, for a specified level of coverage of the population, and modified smoothed tolerance limits are suggested for autocorrelated processes.     

An Improved Distribution-free EWMA Mean Chart

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used here. In this article, we propose an improved asymmetric EWMA mean chart based on a simple statistic to monitor process mean shift. We explored the sampling properties of the new monitoring statistic and calculated the average run lengths of the proposed asymmetric EWMA mean chart. We recommend the proposed improved asymmetric EWMA mean chart because the average run lengths of the modified charts are more accurate and reasonable than those of the five existed mean charts. A numerical example of service times with a right skewed distribution from a service system of a bank branch is used to illustrate the application of the improved asymmetric EWMA mean chart and to compare it with the five existing mean charts. The proposed chart showed better detection performance than those of the five existing mean charts in monitoring and detecting shifts in the process mean.     

Multivariate process dispersion monitoring without subgrouping

The memory-type adaptive and non-adaptive control charts are among the best control charts for detecting small-to-moderate changes in the process parameter(s). In this paper, we propose the Crosier CUSUM (CCUSUM), EWMA, adaptive CCUSUM (ACCUSUM) and adaptive EWMA (AEWMA) charts for efficiently monitoring the changes in the covariance matrix of a multivariate normal process without subgrouping. Using extensive Monte Carlo simulations, the length characteristics of these control charts are computed. It turns out that the ACCUSUM and AEWMA charts perform uniformly and substantially better than the CCUSUM and EWMA charts when detecting a range of shift sizes in the covariance matrix. Moreover, the AEWMA chart outperforms the ACCUSUM chart. A real dataset is used to explain the implementation of the proposed control charts.     

Conditional design of the EWMA median chart with estimated parameters

The exponentially weighted moving average (EWMA) chart is often designed assuming the process parameters are known. In practice, the parameters are rarely known and need to be estimated from Phase I samples. Different Phase I samples are used when practitioners construct their own control chart's limits, which leads to the “Phase I between-practitioners” variability in the in-control average run length (ARL) of control charts. The standard deviation of the ARL (SDARL) is a good alternative to quantify this variability in control charts. Based on the SDARL metric, the performance of the EWMA median chart with estimated parameters is investigated in this paper. Some recommendations are given based on the SDARL metric. The results show that the EWMA median chart requires a much larger amount of Phase I data in order to reduce the variation in the in-control ARL up to a reasonable level. Due to the limitation of the amount of the Phase I data, the suggested EWMA median chart is designed with the bootstrap method which provides a good balance between the in-control and out-of-control ARL values.