Inference on C pk for autocorrelated data in the presence of random measurement errors

The present paper examines the properties of the C _pk estimator when observations are autocorrelated and affected by measurement errors. The underlying reason for this choice of subject matter is that in industrial applications, process data are often autocorrelated, especially when sampling frequency is not particularly low, and even with the most advanced measuring instruments, gauge imprecision needs to be taken into consideration. In the case of a first-order stationary autoregressive process, we compare the statistical properties of the estimator in the error case with those of the estimator in the error-free case. Results indicate that the presence of gauge measurement errors leads the estimator to behave differently depending on the entity of error variability.     

基于因子分析法的民营企业“两级三维”绩效指标矩阵模型构建与应用研究

民营企业的绩效问题一直倍受业界和学者的关注,但实践中依然存在许多难点.本文基于民营企业部门绩效考核管理实践,提出了民营企业绩效考核的关键问题;在此基础上,针对部门绩效考核指标提取难、执行难等问题,创新性地提出了"公司--部门(中层)"、"管理--执行"间左右互动、层层分解的两级三维指标矩阵模型,并利用因子分析法构建模型对部门二级(B类)绩效指标的提炼进行了实证分析.本文所提出的两级三维指标矩阵模型已经在实证中得到了检验,充分证明了其应用价值.     

Rejoinder

Abstract

In this article several formulae for the approximation of the critical values for tests on the actual values of the process capability indices CPL, CPU, and C_pk are provided. These formulae are based on different approximations of the percentiles of the noncentral t distribution and their performance is evaluated by comparing the values assessed through them from the exact critical values, for several significance levels, test values, and sample sizes. As supported by the obtained results, some of the presented techniques constitute valuable tools in situations where the exact critical values of the tests are not available, since one may approximate them readily and rather accurately through them.     

A Superstructure of Process Capability Indices for Circular Specification Region

Circular specification regions can be seen in processes like hitting a target (in ballistics), drilling a hole (in manufacturing industries) and so on. However, only a few process capability indices are available in the literature to address the problem. Most of these indices, in turn, make some assumptions like equality of variance and independence of the two axes of the circular tolerance region. Since, in most of the cases, these assumptions are not practically viable, in the present article, we have proposed a few of the process capability indices which do not need the above assumptions to be valid. Also, we propose a superstructure which unifies all the proposed indices. Some properties of these indices have been studied including the threshold value and the relationship of the proportion of non-conformance with the member indices of the superstructure. These strengthen the practical utility of the superstructure. Distributional properties like expectations and variances of the member indices of the superstructure are also studied to have a better insight about the indices. A real life example has been discussed to carry out a comparative study of the performance of the existing as well as the newly developed indices.     

A non linear analysis of the preference for preservation of the teeth

Data resulting from behavioral dental research, usually categorical or discretized and having unknown measurement and distributional characteristics, often cannot be analyzed with classical multivariate techniques. A non linear principal components technique called multiple correspondence analysis is presented with its corresponding computer program that can handle this kind of data. The model is described as a form of multidimensional scaling. The technique Is applied in order to establish which factors are associated with an Individual's preference for preservation of the teeth.     

On a Process Capability Index for Asymmetric Specifications

Abstract

Among the process capability indices considered in the literature C _pm is one of the most widely used, despite the fact that its performance often becomes unsatisfactory in the case of processes with asymmetric specifications, i.e., processes whose target value is not located at the midpoint of the specification area. In this article, a new index that is a variant of C _pm , is introduced and shown to overcome this deficiency. In particular, the proposed index performs satisfactorily for processes with symmetric or asymmetric specifications. Moreover, the article compares the suggested index with the existing indices for asymmetric specifications, investigates the distributional properties of its estimator under the assumption of normality and deals with the assessment of confidence intervals using three bootstrap methods. The coverage achieved by each of these methods is investigated via simulation.     

A Comparison of Forecasting Accuracies of Alternative Regional Production Index Methodologies

This article examines the forecasting accuracies of various methods used by Federal Reserve Banks to estimate real value added by regional manufacturing industries. Using Texas manufacturing data and weighted forecasting accuracy measures consistent with index number construction for Texas, obtained results support the use of very simple methods based on the assumption of product exhaustion, allowing for technical change. More complex methods using Cobb-Douglas production functions estimated by Bayesian techniques did not perform as well, not because of lack of conceptual sophistication or appropriate prior information but probably because of the small number of observations and collinearity of the data that are available when constructing regional production indices. These results must be qualified. The weighted forecasting accuracy measures tend to obscure the fact that no one method is uniformly superior to the other methods for all industries. Given industry weights different from those for Texas, the results presented here could be reversed. Confirmation of the conclusions drawn await the results of other regional manufacturing studies.     

Estimation of the Sobol indices in a linear functional multidimensional model

We consider a functional linear model where the explicative variables are known stochastic processes taking values in a Hilbert space, the main example is given by Gaussian processes in L²([0,1])${\mathbb{L}}^2([0,1])$. We propose estimators of the Sobol indices in this functional linear model. Our estimators are based on U-statistics. We prove the asymptotic normality and the efficiency of our estimators and we compare them from a theoretical and practical point of view with classical estimators of Sobol indices.     

Construction of confidence intervals for the Laspeyres price index

In the paper, we present and discuss several methods of the construction of confidence intervals for the Laspeyres price index. We assume that prices of commodities are normally distributed and we consider both independent and dependent prices. Using Monte Carlo simulation, the paper compares the confidence interval computed from a simple econometric model with those obtained based on the Laspeyres density function. Our conclusions can be generalized to other price index formulas.