Economic and economic statistical designs for three-level control charts

In some situations, an appropriate quality measure uses three or more discrete levels to classify a product characteristic. For these situations, some control charts have been developed based on statistical criteria regardless of economic considerations. In this paper, we develop economic and economic statistical designs (ESD) for 3-level control charts. We apply the cost model proposed by Costa and Rahim.[Economic design of X charts with variable parameters: the Markov chain approach, J Appl Stat 28 (2001), 875–885] Furthermore, we assume that the length of time that the process remains in control is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply a genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. A numerical example is provided to illustrate the performance of the proposed models and to compare the cost of the pure economic and ESD for three-level control charts. A sensitivity analysis is also conducted in this numerical example.     

A note on spectral estimation for ARMA processes

The standard frequency domain approximation to the Gaussian likelihood of a sample from an ARMA process is considered. The Newton-Raphson and Gauss-Newton numerical maximisation algorithms are evaluated for this approximate likelihood and the relationships between these algorithms and those of Akaike and Hannan explored. In particular it is shown that Hannan's method has certain computational advantages compared to the other spectral estimation methods considered     

A bootstrap control chart for inverse Gaussian percentiles

The conventional Shewhart-type control chart is developed essentially on the central limit theorem. Thus, the Shewhart-type control chart performs particularly well when the observed process data come from a near-normal distribution. On the other hand, when the underlying distribution is unknown or non-normal, the sampling distribution of a parameter estimator may not be available theoretically. In this case, the Shewhart-type charts are not available. Thus, in this paper, we propose a parametric bootstrap control chart for monitoring percentiles when process measurements have an inverse Gaussian distribution. Through extensive Monte Carlo simulations, we investigate the behaviour and performance of the proposed bootstrap percentile charts. The average run lengths of the proposed percentage charts are investigated.     

Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution

In this paper, we propose a multiple deferred state repetitive group sampling plan which is a new sampling plan developed by incorporating the features of both multiple deferred state sampling plan and repetitive group sampling plan, for assuring Weibull or gamma distributed mean life of the products. The quality of the product is represented by the ratio of true mean life and specified mean life of the products. Two points on the operating characteristic curve approach is used to determine the optimal parameters of the proposed plan. The plan parameters are determined by formulating an optimization problem for various combinations of producer's risk and consumer's risk for both distributions. The sensitivity analysis of the proposed plan is discussed. The implementation of the proposed plan is explained using real-life data and simulated data. The proposed plan under Weibull distribution is compared with the existing sampling plans. The average sample number (ASN) of the proposed plan and failure probability of the product are obtained under Weibull, gamma and Birnbaum–Saunders distributions for a specified value of shape parameter and compared with each other. In addition, a comparative study is made between the ASN of the proposed plan under Weibull and gamma distributions.     

A comparative study of confidence intervals for negative binomial proportion

In this paper, we investigate four existing and three new confidence interval estimators for the negative binomial proportion (i.e., proportion under inverse/negative binomial sampling). An extensive and systematic comparative study among these confidence interval estimators through Monte Carlo simulations is presented. The performance of these confidence intervals are evaluated in terms of their coverage probabilities and expected interval widths. Our simulation studies suggest that the confidence interval estimator based on saddlepoint approximation is more appealing for large coverage levels (e.g., nominal level≤1% ) whereas the score confidence interval estimator is more desirable for those commonly used coverage levels (e.g., nominal level>1% ). We illustrate these confidence interval construction methods with a real data set from a maternal congenital heart disease study.     

Phase-II monitoring and diagnosing of multivariate categorical processes using generalized linear test-based control charts

In this paper, two control charts based on the generalized linear test (GLT) and contingency table are proposed for Phase-II monitoring of multivariate categorical processes. The performances of the proposed methods are compared with the exponentially weighted moving average-generalized likelihood ratio test (EWMA-GLRT) control chart proposed in the literature. The results show the better performance of the proposed control charts under moderate and large shifts. Moreover, a new scheme is proposed to identify the parameter responsible for an out-of-control signal. The performance of the proposed diagnosing procedure is evaluated through some simulation experiments.     

The economic design of multivariate binomial EWMA VSSI control charts

Since multi-attribute control charts have received little attention compared with multivariate variable control charts, this research is concerned with developing a new methodology to employ the multivariate exponentially weighted moving average (MEWMA) charts for m-attribute binomial processes; the attributes being the number of nonconforming items. Moreover, since the variable sample size and sampling interval (VSSI) MEWMA charts detect small process mean shifts faster than the traditional MEWMA, an economic design of the VSSI MEWMA chart is proposed to obtain the optimum design parameters of the chart. The sample size, the sampling interval, and the warning/action limit coefficients are obtained using a genetic algorithm such that the expected total cost per hour is minimized. At the end, a sensitivity analysis has been carried out to investigate the effects of the cost and the model parameters on the solution of the economic design of the VSSI MEWMA chart.     

A股上市公司变相财务操纵对行业估值的影响

关于上市公司利润操控的相关研究主要是将净利润作为一个事关操控的敏感指标,但在监管与被监管双方努力的博弈下,其可被操纵的潜力已被充分挖掘。从实证角度关注上市公司财务操纵的其他可操作途径,其中就包括一些看似合理的变相财务操纵手段。按照2001年中国证监会公布的《上市公司行业分类指引》,把我国上市企业分为13个行业,对不同行业内企业2003—2013年部分主观可操控的财务指标与其所在行业的平均市盈率进行格兰杰因果检验和回归分析,结果表明,一些行业内企业的部分财务指标与其所在行业的平均市盈率存在领先与滞后关系,并且影响作用显著。     

A general inversion theorem for cointegration

A generalization of the Granger and the Johansen Representation Theorems valid for any (possibly fractional) order of integration is presented. This Representation Theorem is based on inversion results that characterize the order of the pole and the coefficients of the Laurent series representation of the inverse of a matrix function around a singular point. Explicit expressions of the matrix coefficients of the (polynomial) cointegrating relations, of the Common Trends and of the Triangular representations are provided, either starting from the Moving Average or the Auto Regressive form. This contribution unifies different approaches in the literature and extends them to an arbitrary order of integration. The role of deterministic terms is discussed in detail.