Purpose: When designing an input-output system susceptible to noise, engineers assume a functional relation between the input and the output. The Taguchi method, which uses a dynamic, robust parameter design (RPD) to evaluate the robustness of the input-output relation against noise, is employed. This study aims to address extending the scope of use of a dynamic RPD.Methodology/Approach: A target system in a typical dynamic RPD can be interpreted as one in which the relation between the input and the output is a linear model, and the output error follows a normal distribution. However, an actual system often does not conform to this premise. Therefore, we propose a new analysis approach that can realize a more flexible system design by applying a response surface methodology (RSM) based on a generalized linear model (GLM) to dynamic RPD.Findings: The results demonstrate that 1) a robust solution can be obtained using the proposed method even for a typical dynamic RPD system or an actual system, and 2) the target function can be evaluated using an adjustment parameter.Research Limitation/implication: Further analysis is required to determine which factor(s) in the estimated process model largely contribute(s) to changes in the adjustment parameter.Originality/Value of paper: The applicability of typical dynamic RPD is limited. Hence, this study’s analytical process provides engineers with greater design flexibility and deeper insights into dynamic systems across various contexts.Category: Research paperKeywords: robust parameter design; dynamic system; generalized linear model; response surface methodology; Taguchi method

Purpose: In this paper, we propose a method to classify and detect normal, known anomalies, and unknown anomalies by combining the expectation–maximisation (EM-λ) algorithm and the Mahalanobis–Taguchi (MT) method.Methodology/Approach: The proposed method learns normal data that are expected to be homogeneous and known abnormal data and performs classification and detection by parameter estimation using the EM-λ algorithm. Conventional methods perform analysis based on parameter estimation using the EM algorithm. However, the EM algorithm can degrade classification accuracy if it does not assume that the data fits the model's generative process.Findings: We verify the performance of the proposed method using artificially generated data and real-world bean data for classification as data that do not satisfy this assumption. The validation results show up to 6% improvement over the conventional method in classification accuracy and unknown anomaly discrimination accuracy.Research Limitation/implication: We try various patterns for the parameter of the proposed method in the verification. However, this way is computationally expensive.Originality/Value of paper: Conventional methods perform analysis based on parameter estimation using the EM algorithm. Our proposal method seeks to improve accuracy by using the EM-λ algorithm for parameter estimation, which is expected to improve classification accuracy when the data do not conform to the generative assumptions of the EM algorithm's model.

Purpose: The causality search Taguchi (CS-T) method was proposed to support system selection in a robust parameter design. However, the target of the analysis is likely to be quasi-experimental data. This can be difficult to analyse with the CS-T method. Therefore, this study proposes a new analysis approach that can perform a more accurate knowledge search by applying the instrumental variable.Methodology/Approach: Using the CS-T method, appropriate knowledge search is difficult with quasi-experimental data, including endogeneity. We examined an analytical process that addresses the endogeneity between mechanism and output by utilizing the control and noise factors that constitute the mechanism as instrumental variables.Findings: The results show that 1) the proposed method has sufficient practical accuracy, even for quasi-experimental data including endogeneity; and 2) the extracted mechanism is less likely to fluctuate depending on the number of experimental conditions used. Moreover, we can clarify the position of the CS-T and proposed methods in system selection.Research Limitation/Implication: We perform estimation under the assumption that the threshold is known. However, the extracted mechanism may change depending on the threshold; this requires discussing how to determine them.Originality/Value of paper: Technological development requires a high degree of engineer sophistication. However, this study’s analytical process allows conducting more accurate knowledge search in a realistic and systematic way without requiring a high level of engineer input.

<title>Abstract</title>In the game of baseball, each pitcher throws various types of pitches, such as cutter, curve ball, slider, and splitter. Although the type of a given pitch may be inferred by audience and/or obtained from the TrackMan data, the actual pitch type (i.e., the pitch type declared by the pitcher) may not be known. Classification of pitch types is a challenging task, as pitched baseballs may have different kinematic characteristics across pitchers even if the self-declared pitch types are the same. In addition, there is a possibility that the kinematic characteristics of pitched baseballs are identical even if the self-declared pitch types are different. In this study, we aimed to classify TrackMan data of pitched baseballs into pitch types by applying the Variational Bayesian Gaussian Mixture Models technique. We also aimed to analyze the kinematic characteristics of the classified pitch types and indices related to batting performance while pitching each pitch type. The results showed that the pitch types could not be accurately classified solely by kinematic characteristics, but with consideration of the characteristics of the fastball the accuracy improves substantially. This study could provide a basis for the development of a more accurate automatic pitch type classification system.

Purpose: When applying exponentially weighted moving average (EWMA) multivariate control charts to multivariate statistical process control, in many cases, only some elements of the controlled parameters change. In such situations, control charts applying Lasso are useful. This study proposes a novel multivariate control chart that assumes that only a few elements of the controlled parameters change.
Methodology/Approach: We applied Lasso to the conventional likelihood ratio-based EWMA chart; specifically, we considered a multivariate control chart based on a log-likelihood ratio with sparse estimators of the mean vector and variance-covariance matrix.
Findings: The results show that 1) it is possible to identify which elements have changed by confirming each sparse estimated parameter, and 2) the proposed procedure outperforms the conventional likelihood ratio-based EWMA chart regardless of the number of parameter elements that change.
Research Limitation/Implication: We perform sparse estimation under the assumption that the regularization parameters are known. However, the regularization parameters are often unknown in real life; therefore, it is necessary to discuss how to determine them.
Originality/Value of paper: The study provides a natural extension of the conventional likelihood ratio-based EWMA chart to improve interpretability and detection accuracy. Our procedure is expected to solve challenges created by changes in a few elements of the population mean vector and population variance-covariance matrix.

&lt;p&gt;&lt;strong&gt;Purpose:&lt;/strong&gt; Condition-based maintenance requires an accurate detection of unknown yet-to-have-occurred anomalies and the establishment of anomaly detection procedure for sensor data is urgently needed. Sensor data are noisy, and a conventional analysis cannot always be conducted appropriately. An anomaly detection procedure for noisy data was therefore developed.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Methodology/Approach:&lt;/strong&gt; In a conventional Mahalanobis–Taguchi method, appropriate anomaly detection is difficult with noisy data. Herein, the following is applied: 1) estimation of a statistical model considering noise, 2) its application to anomaly detection, and 3) development of a corresponding analysis framework.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Findings:&lt;/strong&gt; Engineers can conduct anomaly detection through the measurement and accumulation, analysis, and feedback of data. Especially, the two-step estimation of the statistical model in the analysis stage helps because it bridges technical knowledge and advanced anomaly detection.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Research Limitation/implication:&lt;/strong&gt; A novel data-utilisation design regarding the acquired quality is provided. Sensor-collected big data are generally noisy. By contrast, data targeted through conventional statistical quality control are small but the noise is controlled. Thus various findings for quality acquisition can be obtained. A framework for data analysis using big and small data is provided.&lt;/p&gt;&lt;strong&gt;Originality/Value of paper:&lt;/strong&gt; The proposed statistical anomaly detection procedure for noisy data will improve of the feasibility of new services such as condition-based maintenance of equipment using sensor data.

<p>To derive useful information from complicated data, many hybrid modeling strategies that combine nonparametric and parametric methods have been proposed. In this study, we propose a new hybrid modeling strategy that combines the random forest and the x-means methods using linear regression analysis. This strategy is referred to as XR regression.This study has three purposes: to improve the performance of a strategy of hybrid modeling using the random forest method, to determine an optimal class automatically using the x-means method, and to compare the prediction accuracy of this method with that of other existing methods.To determine the characteristics of XR regression, we compare its prediction accuracy with that of the existing methods using Monte Carlo simulations.The simulation results show that XR regression has a high performance in any situation, especially in data sets that include interaction effects.</p>

<p></p><p>High-dimensional data sets have been used extensively in recent years. However, their use is computationally expensive, and model features are difficult to capture. Thus, it is necessary to construct a simple and appropriate model. The least absolute shrinkage and selection operator (Lasso) can estimate several regression coefficients as exactly zero, making it possible to estimate a model and select variables at the same time. However, several problems exist. The decision procedure for the tuning parameter, which is the coefficient of the penalty term, is not established, and it is difficult to determine the value of the estimated model.</p><p>In this paper, we consider a model evaluation method and a selection method for the tuning parameter. We investigate selection methods for the most appropriate tuning parameter and model evaluation methods using the model evaluation indexes RSS, AIC, BIC, and Mallows's Cp. Let several regression coefficients be zero and vary the number of zeroes. Then, we observe the performances of the evaluation indexes. Furthermore, we observe their performances when the values of the regression coefficients are close to zero and confirm them by simulation.</p>

<p></p><p>Panel data are a sort of multi-dimensional time-series data that consist of several sets of the observation unit as an identical community over time. Panel data include more information than time-series data or cross-section data. Using panel data, we are able to estimate more accurately, increase degrees of freedom, and avoid multi-collinearity.</p><p></p><p>In this paper, we consider a change point problem in panel data. Detection methods for change points in panel data have not been extensively proposed. This paper proposes a detection method for change points in panel data using the Mahalanobis–Taguchi (MT) method (Taguchi (2002)). As the MT method does not assume panel data or time-series data, we must extend the theory of the MT method. Furthermore, when the sample size is small, it is difficult to estimate the covariance matrix precisely (Miyakawa et al. (2007)). In this paper, the MT method is extended using Bayesian inference to resolve the above-mentioned difficulties. Conducting Monte Carlo simulations and a real data analysis, we show that our proposed method is useful.</p>

The intent of robust parameter design is to make a system insensitive to noise factors by choosing optimum levels for the controllable factors. This is conducted by finding the interactions between noise factors and control factors. In general, it is necessary to control the levels of noise factors; however, there are some that cannot be controlled. On the other hand, there are some which can be observed as covariates.<br/>Hirano and Miyakawa (2007) proposed a method based on linear regression to analyze the interactions between a single noise factor and the control factors, when the noise factor is observed as a covariate.<br/>This paper discusses robust parameter designs when multiple noise factors are observed as covariates. We propose two extensions of the Hirano and Miyakawa method: extended methods 1 and 2. We perform Monte Carlo simulations under several data models to estimate the accuracy of these methods. It is shown that the extended methods are able to analyze the interactions between each of the control factors and the noise factors, when multiple noise factors are observed as covariates. Since the noise factors are combined in extended method 1, it cannot detect which noise factor influences the control factors. On the other hand, extended method 2 distinguishes between noise factors, and thus it can detect the interactions between the control factors and each of the noise factors.

The Mahalanobis-Taguchi (MT) method is a standard method of multivariate analysis for detecting anomalies or recognizing patterns. A number of case studies using the MT method have been reported. However, good performance is only obtained when a sufficient number of samples can be ensured; if the number of samples is insufficient, this method has a large probability bias.  In this paper, we first analyze the existing measures of methods, in which performing dimension reduction, such as using variable selection, is common, and show that there are some problems with testing for unknown data. Secondly, we propose two analytical procedures for small sample data in which the detection capability with respect to unknown data is taken into account. In these proposed procedures, when the number of data samples is small compared to the dimensions of the variables, the detection measure in the MT method is replaced by a measure derived through approximating correlation matrices based on probabilistic principal component analysis (PPCA) or by introducing ensemble learning. Finally, based on raw data analysis using the KDDCup99 dataset and simulation results, we consider how the proposed procedures should be applied when multicollinearity occurs and which of these two procedures should be applied according to the data pattern.

This article discusses the asymptotic theory of Taguchi's natural estimators of the signal to noise ratio (SNR) for dynamic robust parameter design. Three asymptotic properties are shown. First, two natural estimators of the population SNR are asymptotically equivalent. Second, both of these estimators are consistent. Finally, both of these estimators are asymptotically normally distributed.

Taguchi's RT method is designed under the assumption that all variables are measured in the same units. Therefore, an appropriate analysis cannot be necessarily done when applying RT method to continuous type data that the variables are measured in different units. This becomes a big problem when adapting RT method to various fields. In this paper, we present a new procedure to apply RT method to continuous type data that the variables have different units. And, which procedures becomes a powerful procedure is verified together with other procedures to which the full discussion has not been performed yet. Firstly, we evaluate the performance of all procedures by analyzing KDDCup99 dataset. Secondly, the feature of procedures that obtain good evaluations is compared and analyzed by simulation in detail. Our experiments with KDDCup99 dataset show that a new procedure has good performance. We also reveal that in a new procedure, it is useful for the analysis to evaluate variables more reasonably than other procedures, and to consider the correlation between variables. This study concludes that a new procedure is one of the powerful procedures and RT method can become a effective method to anomaly detection etc. for high-dimensional data by using it.

Taguchi's T method belongs to the MT (Mahalanobis Taguchi) system. Several methods of MT system are used to detect outliers or extraordinary patterns, while the T method is used to predict future data. Since T method analyzes the same type of data set as the multiple regression analysis, the performance of T method has been compared with that of the multiple regression analysis under several case studies. This paper discusses the features of T method and considers two kinds of improved T methods. Furthermore, prediction accuracies of these methods are calculated by Monte Carlo simulations under several models. It is shown that the improved T methods are always superior to the original T method and that they are superior to the multiple regression analysis when the sample size is not large enough compared to the number of independent variables.

This paper discusses the principles of experimental design proposed by R.A. Fisher. They are consisted of three principles which are replication, randomization and local control. This paper investigates the book "The Design of Experiments" written by R.A. Fisher in order to grasp what he considered and how he intended to describe these principles.

Process capability indices (PCI) are widely used in the activities of quality control. This paper discusses the improvement on the natural estimators for the basic PCI's, C_p, C_pL, C_pU and C_pK. <br>Under the squared error loss function, Nagata (1995) showed that the natural estimator for C_p can be uniformly improved on by the estimator which is multiplied by some constant, and gave the degrees of improvement numerically. He also suggested by numerical calculations that the natural estimator for C_pK cannot be improved on by the simple estimator which is multiplied by some constant.<br> In this paper it is shown that the natural estimator for C_pU and C_pL can be uniformly improved on by the estimators which are multiplied by some constant, and the degrees of improvement are given numerically. Furthermore, it is mathematically shown that the natural estimator for C_pK cannot be improved on by any simple estimators which are multiplied by some constant when the sample size is larger than or equal to 7.

RT (Recognition Taguchi) method is the newest among MT (Mahalanobis Taguchi) system. Several application cases have been published, while the properties of RT method have not been studied theoretically so far. The calculation is not complicated and RT method seems to be an attractive procedure with original ideas. However, practitioners should be cautious when they apply it to continuous type data. This paper discusses the following viewpoints. <BR> (1) The dimensions of all variables must be the same. Otherwise, one needs to translate the variables to non-dimension numbers. <BR> (2) The distance used in RT method has an essentially inappropriate property. It takes some large value at the center of the unit space and attains zero at the point of different position from the center. When a new member comes from the center of the unit space, it would be decided that the member is outside of the unit space, which leads to be misleading. <BR> (3) This paper proposes a new distance for RT system, which improves on the abovementioned inappropriate property. This new distance is zero at the center of the unit space, and then increases with variation as a member is getting further from the center.

It is discussed how to educate the practically useful SQC (statistical quality control). When a company holds an in-house training of SQC, there possibly exist several problems, which are the problem of selecting trainees, the problem of preparing adequate homework and examinations, the problem of engaging practical applications, the problem of evaluating the results and the problem of promoting a thoughtful secretary. In order to overcome these problems, a passionate support by the top is necessary and the existence of stars on SQC in the company is desired. As a guidepost for training a star, one particular topic is introduced, which is the way that one interprets the partial regression coefficients in regression equations. Furthermore, several topics which should be considered to use both the Taguchi methods and the SQC effectively are presented.

On Type I Distance of the MT System under the Condition that the Number of the Items is Larger than or Equal to n-1 Yasushi NAGATA/Go HISATOMI Under the condition that there are several linear restrictions (the condition 1) or that the sample size n is smaller than or equal to the number p of the items (the condition 2), the Mahalanobis distance cannot be calculated. In this situation it is called that there exists multicollinearity. Miyakawa and Nagata (Journal of Japanese Society Quality Control, Vol.33) derived two types of distances and recommended using them as a countermeasure against multicollinearity. This paper mathematically shows that the values of the type I distance are the same for the original data of the normal space when p≧n. As a result, the critical value cannot be determined based on the sampling distribution of the type I distance. It is essentially difficult to cope with the condition 2 in compared with the condition 1. Under the condition 2 some information has to be thrown away. This paper suggests the possibility of the methods. Furthermore, this paper also shows that the values of the Mahalanobis distance are the same for p=n-1 although there does not exist multicollinearity.

Let x(1), x(2), …, x(n) be the order statistics of a sample of size n from the exponential distribution with an unknown location-scale parameter (μ,σ). It is shown that usual confidence intervals for σ based on the only statistic Σ^^^n__<i=1>(x(i)-x(1)) can be improved by using the statistic x(1). Further the degree of the improvement is computed numerically.

The process capability indices (CPI) are often used to obtain the information about the production process capability and there are some criteria in determining it, the criteria which are designed for the true values of CPI's. However, since the true values of CPI's are unknown in practice, they are estimated from several data. So the criteria might not be applied to these (point-) estimated values. Confidence intervals for CPI's should be constructed and these results should be taken into consideration. In this paper some useful and practical methods for the interval estimation are given.