Data mining driven DMAIC framework for improving foundry quality – a case study

Six Sigma Define-Measure-Analyze-Improve-Control (DMAIC) methodology has been widely used across industries as the best systematic and data driven problem solving approach for quality improvement. Statistical Design of Experiment (DOE) is used in the ‘Improve’ stage for obtaining optimal process settings for significant variables contributing towards quality improvement. But, DOE is an offline activity requiring time and other resources for conducting experiments and analyses. Further, there are many small and medium scale enterprises that cannot afford to conduct DOE. Under such practical constraints, it is desirable to apply DMAIC using online process data under day-to-day production situations or with little changes in process settings without compromising production. In this article, we propose a DMAIC framework, driven by data mining techniques for defect diagnosis and quality improvement where historical and online process data can be effectively utilised. We have used two decision tree algorithms namely, Classification and Regression Tree and Chi-squared Automatic Interaction Detection in developing the proposed framework. The proposed approach is applied in an Indian grey iron foundry where conducting DOE is not a feasible option for the management. The result demonstrates a significant reduction in casting defect and validates the practical viability of this approach.     

Semiparametric Stein estimators

Stein [Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In Proc. 3rd Berkeley symp. math. statist. and pro. (pp. 197–206). University of California Press], in his seminal paper, came up with the surprising discovery that the sample mean is an inadmissible estimator of the population mean in three or higher dimensions under squared error loss. The past five decades have witnessed multiple extensions and variations of Stein’s results. In this paper we develop Stein-type estimators in a semiparametric framework and prove their coordinatewise asymptotic dominance over the sample mean in terms of Bayes risks.     

Adjustment costs in labour markets and the distributional effects of trade liberalization: Analytics and calculations for Vietnam

This paper explores the implications of different labour market adjustment formulations for the analysis of trade liberalization across different sectors and households in the Vietnamese economy using computable general equilibrium (CGE) models. The model is calibrated to a model admissible Vietnamese data set for 1997.We use five different adjustment cost treatments in analyzing the effects of trade liberalization in Vietnam. We compare simulation results from each and show how different treatments can significantly affect the distributional impacts of policy reforms, such as the trade liberalization. First, labour is treated as fully mobile across all sectors in the economy. Second, the sectors of economy are broken down into the two blocks of agricultural and industrial-service sectors and labour markets are treated as segmented by sector block. No mobility of labour between blocks is allowed while labour within each sector block remains fully mobile. The third is the same as the second, but movement within each agricultural and industrial-service sector block involves transactions costs. In the fourth, mobility of workers from the agricultural to industrial-service sectors and vice versa is possible with transactions costs. Finally, we calibrate the model with unemployment but no adjustment costs for labour reallocation to explore how model results differ in terms of adjustments in the labour market and welfare effects.Our results indicate significant differences in the impacts from trade liberalization across these cases. The redistributional impact of trade liberalization is sharper against poor rural households with segmented labour markets and with transactions costs, while aggregate efficiency gains are similar to no adjustment cost analyses. The conclusion is the choice of model structure for labour markets is crucially important for the perceived distributional impacts of trade liberalization.     

Study of incompatibility or near compatibility of bivariate discrete conditional probability distributions through divergence measures

Consider a two-dimensional discrete random variable (X, Y) with possible values 1, 2, …, I for X and 1, 2, …, J for Y. For specifying the distribution of (X, Y), suppose both conditional distributions, of X given Y and of Y given X, are provided. Under this setting, we present here different ways of measuring discrepancy between incompatible conditional distributions in the finite discrete case. In the process, we also suggest different ways of defining the most nearly compatible distributions in incompatible cases. Many new divergence measures are discussed along with those that are already known for determining the most nearly compatible joint distribution P. Finally, a comparative study is carried out between all these divergence measures as some examples.     

Kalman filter-based modelling and forecasting of stochastic volatility with threshold

We propose a parametric nonlinear time-series model, namely the Autoregressive-Stochastic volatility with threshold (AR-SVT) model with mean equation for forecasting level and volatility. Methodology for estimation of parameters of this model is developed by first obtaining recursive Kalman filter time-update equation and then employing the unrestricted quasi-maximum likelihood method. Furthermore, optimal one-step and two-step-ahead out-of-sample forecasts formulae along with forecast error variances are derived analytically by recursive use of conditional expectation and variance. As an illustration, volatile all-India monthly spices export during the period January 2006 to January 2012 is considered. Entire data analysis is carried out using EViews and matrix laboratory (MATLAB) software packages. The AR-SVT model is fitted and interval forecasts for 10 hold-out data points are obtained. Superiority of this model for describing and forecasting over other competing models for volatility, namely AR-Generalized autoregressive conditional heteroscedastic, AR-Exponential GARCH, AR-Threshold GARCH, and AR-Stochastic volatility models is shown for the data under consideration. Finally, for the AR-SVT model, optimal out-of-sample forecasts along with forecasts of one-step-ahead variances are obtained.     

SOME SERIES OF EFFICIENCY BALANCED DESIGNS

Two series of efficiency balanced designs with v*+ 1 treatments have been constructed using balanced incomplete block designs having v* treatments.     

On the robustness of the optimum balanced 2m factorial designs of resolution v (given by Srivastava and Chopra) in the presence of outliers

In this paper we study the sensitivity of the optimum balanced resolution V plans for 2^m factorials, to outliers, using the measure suggested by Box and Drapper (1975). We observe that the designs are robust, i.e., have low sensitivity.     

On a robustness property of PBIBD

In this paper we study a robustness property of partially balanced incomplete block designs based on association schemes with m classes (PBIBD(m)) against the unavailability of data in the sense that, when any t (a positive integer) observations are unavailable the design remains connected w.r.t. treatment. We characterize the robustness property of PBIBD(m) completely for m=2 and partially for m=3.     

Incomplete block designs for complete diallel crosses and their analysis

A large number of incomplete block designs for Griffing's complete diallel cross-systems I, II and III, involving from five to 12 lines, are suggested, using two-associate triangular partially balanced incomplete block designs. Analysis of incomplete block designs for complete diallel cross-systems has been carried out assuming the most appropriate model for genetic yield, as advocated by Hinklemnann. This includes estimation of the general combining ability, specific combining ability and reciprocal cross- effects. An illustration of the design for each system is presented.