İnci Batmaz

Review: A review of data mining applications for quality improvement in manufacturing industry

Many quality improvement (QI) programs including six sigma, design for six sigma, and kaizen require collection and analysis of data to solve quality problems. Due to advances in data collection systems and analysis tools, data mining (DM) has widely been applied for QI in manufacturing. Although a few review papers have recently been published to discuss DM applications in manufacturing, these only cover a small portion of the applications for specific QI problems (quality tasks). In this study, an extensive review covering the literature from 1997 to 2007 and several analyses on selected quality tasks are provided on DM applications in the manufacturing industry. The quality tasks considered are; product/process quality description, predicting quality, classification of quality, and parameter optimisation. The review provides a comprehensive analysis of the literature from various points of view: data handling practices, DM applications for each quality task and for each manufacturing industry, patterns in the use of DM methods, application results, and software used in the applications are analysed. Several summary tables and figures are also provided along with the discussion of the analyses and results. Finally, conclusions and future research directions are presented.

CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization

Regression analysis is a widely used statistical method for modelling relationships between variables. Multivariate adaptive regression splines (MARS) especially is very useful for high-dimensional problems and fitting nonlinear multivariate functions. A special advantage of MARS lies in its ability to estimate contributions of some basis functions so that both additive and interactive effects of the predictors are allowed to determine the response variable. The MARS method consists of two parts: forward and backward algorithms. Through these algorithms, it seeks to achieve two objectives: a good fit to the data, but a simple model. In this article, we use a penalized residual sum of squares for MARS as a Tikhonov regularization problem, and treat this with continuous optimization technique, in particular, the framework of conic quadratic programming. We call this new approach to MARS as CMARS, and consider it as becoming an important complementary and model-based alternative to the backward stepwise algorithm. The performance of CMARS is also evaluated using different data sets with different features, and the results are discussed.

Comparison of missing value imputation methods in time series: the case of Turkish meteorological data

This study aims to compare several imputation methods to complete the missing values of spatio–temporal meteorological time series. To this end, six imputation methods are assessed with respect to various criteria including accuracy, robustness, precision, and efficiency for artificially created missing data in monthly total precipitation and mean temperature series obtained from the Turkish State Meteorological Service. Of these methods, simple arithmetic average, normal ratio (NR), and NR weighted with correlations comprise the simple ones, whereas multilayer perceptron type neural network and multiple imputation strategy adopted by Monte Carlo Markov Chain based on expectation–maximization (EM-MCMC) are computationally intensive ones. In addition, we propose a modification on the EM-MCMC method. Besides using a conventional accuracy measure based on squared errors, we also suggest the correlation dimension (CD) technique of nonlinear dynamic time series analysis which takes spatio–temporal dependencies into account for evaluating imputation performances. Depending on the detailed graphical and quantitative analysis, it can be said that although computational methods, particularly EM-MCMC method, are computationally inefficient, they seem favorable for imputation of meteorological time series with respect to different missingness periods considering both measures and both series studied. To conclude, using the EM-MCMC algorithm for imputing missing values before conducting any statistical analyses of meteorological data will definitely decrease the amount of uncertainty and give more robust results. Moreover, the CD measure can be suggested for the performance evaluation of missing data imputation particularly with computational methods since it gives more precise results in meteorological time series.

Clustering current climate regions of Turkey by using a multivariate statistical method

In this study, the hierarchical clustering technique, called Ward method, was applied for grouping common features of air temperature series, precipitation total and relative humidity series of 244 stations in Turkey. Results of clustering exhibited the impact of physical geographical features of Turkey, such as topography, orography, land–sea distribution and the high Anatolian peninsula on the geographical variability. Based on the monthly series of nine climatological observations recorded for the period of 1970–2010, 12 and 14 clusters of climate zones are determined. However, from the comparative analyses, it is decided that 14 clusters represent the climate of Turkey more realistically. These clusters are named as (1) Dry Summer Subtropical Semihumid Coastal Aegean Region; (2) Dry-Subhumid Mid-Western Anatolia Region; (3 and 4) Dry Summer Subtropical Humid Coastal Mediterranean region [(3) West coast Mediterranean and (4) Eastern Mediterranean sub-regions]; (5) Semihumid Eastern Marmara Transition Sub-region; (6) Dry Summer Subtropical Semihumid/Semiarid Continental Mediterranean region; (7) Semihumid Cold Continental Eastern Anatolia region; (8) Dry-subhumid/Semiarid Continental Central Anatolia Region; (9 and 10) Mid-latitude Humid Temperate Coastal Black Sea Region [(9) West Coast Black Sea and (10) East Coast Black Sea sub-regions]; (11) Semihumid Western Marmara Transition Sub-region; (12) Semihumid Continental Central to Eastern Anatolia Sub-region; (13) Rainy Summer Semihumid Cold Continental Northeastern Anatolia Sub-region; and (14) Semihumid Continental Mediterranean to Eastern Anatolia Transition Sub-region. We believe that this study can be considered as a reference for the other climate-related researches of Turkey, and can be useful for the detection of Turkish climate regions, which are obtained by a long-term time course dataset having many meteorological variables.

Small response surface designs for metamodel estimation

Abstract The primary objective of this study is to provide the novice researchers in simulation metamodeling with guidance on how to use small designs for metamodel estimation especially when cost effectiveness is a concern. This study was carried out in three phases: First, a group of second-order small designs were evaluated with respect to various criteria. Next, the metamodel of a time-shared computer system was estimated using these designs. Finally, the predictive capabilities of these small designs in giving the best metamodel fit were investigated, and also, the performance of small designs was compared with two large size standard designs. Results indicate that the metamodel estimated using the hybrid design has the best predictive capability among the small designs, and its performance competes with that of the standard designs studied.

Dealing with the least squares regression assumptions in simulation metamodeling

The aim of this study is twofold. The first is to estimate a metamodel for a time-shared computer system using a sequential design procedure. The second is to deal extensively with the least squares regression assumptions during the metamodel development. In the first stage of the experimentation, a first-order metamodel is estimated using the two-level factorial design. Later, the design is augmented with replicated center points for curvature check. Upon the detection of the significance of the curvature, a central composite design is used for fitting a second-order metamodel, which explains the relation between the levels of the input factors, and the response of interest. In both stages, various diagnostic statistical tests such as normality test, variance homogeneity test, lack-of-fit test and etc. are carried out to make sure that the method of least squares is properly and efficiently applied.

Classification models based on Tanaka’s fuzzy linear regression approach: The case of customer satisfaction modeling

Fuzzy linear regression (FLR) approaches are widely used for modeling relations between variables that involve human judgments, qualitative and imprecise data. Tanaka’s FLR analysis is the first one developed and widely used for this purpose. However, this method is not appropriate for classification problems, because it can only handle continuous type dependent variables rather than categorical. In this study, we propose three alternative approaches for building classification models, for a customer satisfaction survey data, based on Tanaka’s FLR approach. In these models, we aim to reflect both random and fuzzy types of uncertainties in the data in different ways, and compare their performances using several classification performance measures. Thus, this study contributes to the field of fuzzy classification by developing Tanaka based classification models.

A metamodeling methodology involving both qualitative and quantitative input factors

Abstract This paper suggests a methodology for developing a simulation metamodel involving both quantitative and qualitative factors. The methodology mainly deals with various strategic issues involved in metamodel estimation, analysis, comparison, and validation. To illustrate how to apply the methodology, a regression metamodel is developed for a client–server computer system. In particular, we studied how the response time is affected by the quantum interval, the buffer size, and the total number of terminals when different queuing disciplines are employed in the operation of the round-robin queue with a limited buffer. The results of the study indicate that the relationship between the response time and the quantitative factors cannot be adequately described by a single metamodel for all queuing disciplines.

Precipitation Modeling by Polyhedral RCMARS and Comparison with MARS and CMARS

Climate change is becoming an ever important issue due to the possibility that it may result in extreme weather events such as floods or droughts. Consequently, precipitation forecasting has similarly gained in significance as it is a useful tool in meeting the increasing need for the efficient management of water resources as well as in preventing disasters before they happen. In the literature, there are various statistical and computational methods used for this purpose, including linear and nonlinear regression, kriging, time series models, neural networks, and multivariate adaptive regression splines (MARS). Among them, MARS stands out as the better performing precipitation modeling method. In this article, we used a recently developed method called robust conic mars (RCMARS), based on MARS (also on CMARS), to forecast precipitation owing to its ability to model complex uncertain data. In CMARS, which was developed as a powerful alternative to MARS, the model complexity is penalized in the form of Tikhonov regularization and studied as a conic quadratic programming. In RCMARS, on the other hand, CMARS is refined further by including the existence of uncertainty in the future scenarios and robustifying it with a robust optimization technique. To evaluate the performance of the RCMARS method, it was applied to build a precipitation model constructed as an early warning system for the continental Central Anatolia Region of Turkey, where drought has been a recurrent phenomenon for the last few decades. Furthermore, the performance of the RCMARS precipitation model was also compared to that of MARS and CMARS. The results indicated that RCMARS builds more accurate, precise, and stable precipitation models compared to those of MARS and CMARS. In addition to these advantageous features of the RCMARS precipitation model, it also provided a good fit to the data. As a result, we propose its use in precipitation forecasting for the region studied.

Second-order experimental designs for simulation metamodeling

The main purpose of this study is to compare the performance of a group of second-order designs such as Box-Behnken, face-center cube, three-level factorial, central composite, minimum bias, and minimum variance plus bias for estimating a quadratic metamodel. A time-shared computer system is used to demonstrate the ability of the designs in providing good fit of the metamodel to the simulation response. First, for various numbers of center runs, these designs are compared with respect to their efficiency, rotatability, orthogonality, robustness, bias, and prediction variance. Next, second-order metamodels are fit to the data collected using these designs. Metamodel fit is investigated using criteria such as average absolute error, PRESS, and the C p statistic. Results indicate that the minimum variance plus bias design is the most promising design to estimate a metamodel for the case studied.