Developing a variables repetitive group sampling plan based on process capability index C pk with unknown mean and variance

In this paper, variables repetitive group sampling plans are developed based on the process capability index C _pk when the quality characteristic follows a normal distribution with unknown mean and variance. The sampling plan parameters such as the sample size and the acceptance constant are determined to minimize the average sample number. Symmetric and asymmetric cases, in percent defectives due to two specification limits, are dealt with for specified combinations of acceptable quality level and limiting quality level. Tables are provided and examples are given to use proposed plans in practice.     

Two-Stage Variables Acceptance Sampling Plans Using Process Loss Functions

In this article, a variable two-stage acceptance sampling plan is developed when the quality characteristic is evaluated through a process loss function. The plan parameters of the proposed plan are determined by using the two-point approach and tabulated according to various quality levels. Two cases are discussed when the process mean lies at the target value and when it does not, respectively. Extensive tables are provided for both cases and the results are explained with examples. The advantage of the proposed plan is compared with the existing variable single acceptance sampling plan using the process loss function.     

Diagnostic Checking for GARCH-Type Models

The asymptotic distributions of squared and absolute residual autocorrelations for GARCH model estimated by M-estimators are derived. Two diagnostic tests are developed which can be used to check the adequacy of GARCH model fitted by using M-estimators. Simulation results show that the empirical sizes of both tests are close to the nominal size in most of the cases. The power of test based on absolute residual autocorrelation is found better than test based on squared residual autocorrelations. Our results reveal that there are estimators that can fit GARCH-type models better than the commonly used quasi-maximum likelihood estimator under non normal errors. An application to real data set is also presented.     

Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength

In this paper, we estimate multicomponent stress-strength reliability by assuming Burr-XII distribution. The research methodology adopted here is to estimate the parameter using maximum likelihood estimation. Reliability is estimated using the maximum likelihood method of estimation and results are compared using the Monte Carlo simulation for small samples. Using real data sets we illustrate the procedure clearly.     

Using Heteroscedasticity-Consistent Standard Errors for the Linear Regression Model with Correlated Regressors

The use of heteroscedasticity-consistent covariance matrix (HCCM) estimators is very common in practice to draw correct inference for the coefficients of a linear regression model with heteroscedastic errors. However, in addition to the problem of heteroscedasticity, linear regression models may also be plagued with some considerable degree of collinearity among the regressors when two or more regressors are considered. This situation causes many adverse effects on the least squares measures and alternatively, the ordinary ridge regression method is used as a common practice. But in the available literature, the problems of multicollinearity and heteroscedasticity have not been discussed as a combined issue especially, for the inference of the regression coefficients. The present article addresses the inference about the regression coefficients taking both the issues of multicollinearity and heteroscedasticity into account and suggests the use of HCCM estimators for the ridge regression. This article proposes t- and F-tests, based on these HCCM estimators, that perform adequately well in the numerical evaluation of the Monte Carlo simulations.     

Circular First- and Second-Order Balanced Repeated Measurements Designs

Sharma (1977 Sharma , V. K. ( 1977 ). Change-over designs with complete balance for first and second order residual effect . Canad. J. Statist. 5 : 121 – 132 .[Crossref] , [Google Scholar]) and Aggarwal et al. (2006 Aggarwal , M. L. , Deng , L.-Y. , Jha , M. K. ( 2006 ). Balanced residual treatment effects designs of first and second order . Statist. Probab. Lett. 76 : 597 – 600 .[Crossref], [Web of Science ®] , [Google Scholar]) considered non circular construction of first- and second-order balanced repeated measurements designs. Sharma et al. (2002 Sharma , V. K. , Varghese , C. , Jaggi , S. ( 2002 ). On optimality of change-over designs balanced for first and second order residual effects . Metron 60 : 153 – 162 . [Google Scholar]) constructed circular first- and second-order balanced repeated measurements designs only for a class with parameters (v, p = 3n, n = v ²) and also showed its universal optimality. In this article, we consider circular construction of first- and second-order balanced repeated measurements designs and strongly balanced repeated measurements designs by using the method of cyclic shifts. Some new circular designs with parameters (v, p, n) for cases p = v, p < v and p > v are given.     

Effectiveness of Performance Appraisal: An Integrated Framework

Based on a robust analysis of the existing literature on performance appraisal (PA), this paper makes a case for an integrated framework of effectiveness of performance appraisal (EPA). To achieve this, it draws on the expanded view of measurement criteria of EPA, i.e. purposefulness, fairness and accuracy, and identifies their relationships with ratee reactions. The analysis reveals that the expanded view of purposefulness includes more theoretical anchors for the purposes of PA and relates to various aspects of human resource functions, e.g. feedback and goal orientation. The expansion in the PA fairness criterion suggests certain newly established nomological networks, which were ignored in the past, e.g. the relationship between distributive fairness and organization‐referenced outcomes. Further, refinements in PA accuracy reveal a more comprehensive categorization of rating biases. Coherence among measurement criteria has resulted in a ratee reactions‐based integrated framework, which should be useful for both researchers and practitioners.     

Choosing summary statistics by least angle regression for approximate Bayesian computation

Bayesian statistical inference relies on the posterior distribution. Depending on the model, the posterior can be more or less difficult to derive. In recent years, there has been a lot of interest in complex settings where the likelihood is analytically intractable. In such situations, approximate Bayesian computation (ABC) provides an attractive way of carrying out Bayesian inference. For obtaining reliable posterior estimates however, it is important to keep the approximation errors small in ABC. The choice of an appropriate set of summary statistics plays a crucial role in this effort. Here, we report the development of a new algorithm that is based on least angle regression for choosing summary statistics. In two population genetic examples, the performance of the new algorithm is better than a previously proposed approach that uses partial least squares.     

Influence diagnostics in gamma ridge regression model

In this article, we proposed some influence diagnostics for the gamma regression model (GRM) and the gamma ridge regression model (GRRM). We assess the impact of influential observations on the GRM and GRRM estimates by extending the work of Pregibon [Logistic regression diagnostics. Ann Stat. 1981;9:705–724] and Walker and Birch [Influence measures in ridge regression. Technometrics. 1988;30:221–227]. Comparison of both models is made and demonstrated with the help of a simulation study and a real data set. We report some momentous results in detecting the influential observations and their effects on the GRM and GRRM estimates.