# Kashinath ChatterjeeAugusta University · Biostatistics and Data Science

Kashinath Chatterjee

PhD

## About

123

Publications

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664

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## Publications

Publications (123)

Two-symbol supersaturated designs (SSDs) are two-symbol arrays in which the number of rows is no larger than the number of columns. In this paper, a lower bound for the E(2) value of SSDs that are not necessarily balanced is derived. The sharpness of the newly derived lower bound is analyzed theoretically by using constructions of E(2)-optimal SSDs...

In the present article, a double generally weighted moving average
(DGWMA) control chart based on a three-parameter logarithmic
transformation is proposed for monitoring the process variability,
namely the S2-DGWMA chart. Monte-Carlo simulations are utilized
in order to evaluate the run-length performance of the S2-DGWMA
chart. In addition, a detai...

Control charts are very popular quality tools used to detect and control industrial process deviations in Statistical Process Control. In the current paper, we propose a new single memory-type control chart, called the maximum triple exponentially weighted moving average chart (referred as Max-TEWMA chart), that simultaneously detects both upward a...

Many studies have shown that industrial as well as non-industrial business organisations present a growing need of robust and more efficient multivariate monitoring schemes in order to be able to monitor several quality characteristics simultaneous. To monitor two or more parameters simultaneously, several monitoring schemes are used concurrently i...

In many real-world applications, there is a functional relationship between a response variable and one or more explanatory variables. In such situations, classical quality monitoring schemes will not be able to provide accurate information about the process. To solve this problem, the literature recommends the use of regression monitoring tools kn...

In this article, we extend the single exponentially weighted moving average (EWMA) semicircle (EWMA-SC) chart to a single double EWMA semicircle chart, called the DEWMA-SC control chart. The run length (RL) characteristics of the proposed chart are computed through Monte-Carlo simulations. A detailed comparative study is conducted to compare the pe...

The exponentially weighted moving average (EWMA) control chart is a very popular memory-type chart and also effective in detecting small shifts in the process mean. Several modifications of the EWMA chart, such as the double and triple EWMA charts (regarded as DEWMA and TEWMA charts, respectively) have been developed to enhance its performance in d...

Statistical process monitoring (SPM) is mostly populated with univariate control charts used to monitor a single variable (or quality characteristic). Nowadays, industries and online environments are filled with processes in which two or more quality characteristics are related. In such situations, univariate control charts are replaced with multiv...

In many real applications, the quality characteristics of interest, such as the number of nonconformities in a production unit or the annual incidence rate, may follow the Poisson distribution. In the present article, we propose a triple exponentially weighted moving average control chart for monitoring Poisson processes (regarded as PTEWMA chart)....

This paper considers the construction of mixed-level supersaturated split-plot designs (SSSPDs) which are very useful in screening situations where the number of factors is larger than the number of available observations and several of these factors have levels that they are hard to change. As a benchmark of obtaining optimal SSSPDs, lower bounds...

Control charts are widely known quality tools used to detect and control industrial process deviations in Statistical Process Control. In the current paper, we propose a new single memory-type control chart, called the maximum double generally weighted moving average chart (referred as Max-DGWMA), that simultaneously detects shifts in the process m...

The paper deals with estimating the stress-strength reliability of a system where the stress and strength random variables follow two-parameter exponential distributions with different location and scale parameters assuming all parameters are unknown. We derive the maximum likelihood estimator, uniformly minimum variance unbiased estimator, and Bay...

This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors. An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix. The admissibility of designs is also considered and a s...

The moving average (MA) control chart is a memory-type scheme and effective for monitoring small and moderate shifts in the process mean. Several modifications of the MA chart, such as the double MA (DMA) and the triple MA (TMA) charts, have been introduced to improve the detection ability of the MA chart. In the present article, we propose the qua...

The repetitive sampling scheme is utilized in control charts to
enhance their detection ability in process shifts. Their performance is
usually evaluated under the assumption that the process parameters
are known. In this article, we investigate the performance of the X
and S^2 charts under repetitive sampling when the process parameters are estima...

In the present article, we propose a generally weighted moving average control chart based on a three-parameter logarithmic transformation for monitoring shifts in the process variability (regarded as S2-GWMA chart). Monte Carlo simulations are used to evaluate its performance in terms of the run-length distribution. A comparison study versus the S...

Parametric (or traditional) control charts are based on the assumption that the
quality characteristic of interest follows a specific distribution. However, in many
applications, there is a lack of knowledge about the underlying distribution. To
this end, nonparametric (or distribution-free) control charts have been developed in recent years. In th...

Control charts based on the sample mean X are used for monitoring shifts in the process mean under the assumption that the process standard deviation is stable or well estimated. However, in many applications, this assumption is violated. In this case, t control charts are preferred as they are robust to changes in the process standard deviation. I...

At the primary stage of most of scientific investigations, supersaturated designs (SSDs) are extremely cost-effective to scientists and engineers. Booth and Cox [Booth KHV, Cox DR. Some systematic supersaturated designs. Technometrics. 1962;4:489–495] proposed E(s2) as a criterion for comparing several SSDs. It is to be remarked that E(s2) fails to...

Control charts are widely known quality tools used to detect and control industrial process deviations in statistical process control. In the current paper, we propose a new single memory‐type control chart, called the sum of squares triple exponentially weighted moving average control chart (referred as SS‐TEWMA chart), that simultaneously detects...

Nonparametric (or distribution‐free) control charts are used for monitoring processes where there is a lack of knowledge about the underlying distribution. In this article, a triple exponentially weighted moving average control chart based on the signed‐rank statistic (referred as TEWMA‐SR chart) is proposed for monitoring shifts in the location pa...

Control charts are widely applied in many manufacturing processes to monitor the quality characteristic of interest. Recently, a homogeneously weighted moving average (HWMA) control chart was proposed as an improvement of the exponentially weighted moving average (EWMA) chart for efficiently monitoring of small shifts in the process mean. In the pr...

The modified exponentially weighted moving average (MEWMA) control chart has been proposed in the literature in an effort to improve the performance of the classical EWMA chart. In this article, we study in more detail the MEWMA chart using various values of its additional design parameter and we also propose the double MEWMA (DMEWMA) chart for mon...

A mixed exponentially weighted moving average (EWMA)–progressive mean (PM) control chart (regarded as MEP) has been recently proposed in the literature for monitoring the process mean. Unfortunately, the variance of MEP statistic is incorrect. In this article, we provide the correct variance of charting statistic along with the corresponding contro...

Nonparametric control charts are used in process monitoring when there is insufficient information about the form of the underlying distribution. In this article, we propose a triple exponentially weighted moving average (TEWMA) control chart based on the sign statistic for monitoring the location parameter of an unknown continuous distribution. Th...

Control charts are very popular quality tools used to detect and control industrial process deviations in statistical process control. The current paper presents a new triple exponentially weighted moving average (TEWMA) control chart for monitoring the process dispersion (named as S 2 ‐TEWMA chart), based on a three‐parameter logarithmic transform...

Time between events (TBE) charts are used in high‐yield processes where the rate of occurrences is very low. In the current article, we propose a triple exponentially weighted moving average control chart to monitor TBE (regarded as triple exponentially weighted moving average TEWMA‐TBE chart) modeled by a gamma distribution. One‐ and two‐sided sch...

We propose a combinatorial construction method for setting up informative experiments with both restricted randomisation and a large number of factors. The supersaturated split-plot designs are very useful in screening situations where the number of factors is larger than the number of available observations and several of these factors have levels...

This paper considers the R-optimal design problem for a linear Haar-wavelet regression
model. It is proved that the proposed designs are R-optimal by means of the equivalence theorem.

Quality control charts are extensively used to monitor processes. The EWMA chart is a good alternative to the Shewhart chart to quickly detect small and moderate shifts in the process mean. The DEWMA charting procedure is an enhanced approach for the EWMA chart and performs much better, especially for small and moderate shifts. In this article, we...

Lee discrepancy has wide applications in design of experiments, which can be used to measure the uniformity of fractional factorials. An improved lower bound of Lee discrepancy for asymmetrical factorials with mixed two-, three- and four-level is presented. The new lower bound is more accurate for a lot of designs than other existing lower bound, w...

The moving average (MA) and double moving average (DMA) control charts are a good alternative to the Shewhart chart to detect small to moderate shifts of the process mean more quickly. In this article, we propose the triple moving average (TMA) control chart to improve the detection ability of the MA chart. It is shown that the proposed chart is mo...

Most control charts have been developed based on the actual distribution of the quality characteristic of interest. However, in many applications, there is a lack of knowledge about the process distribution. Therefore, in recent years, nonparametric (or distribution‐free) control charts have been introduced for monitoring the process location or sc...

A double moving average (DMA) control chart has been proposed in the literature for monitoring the process mean. Several studies have also been done based on this scheme. Unfortunately, the variance of DMA statistic that has been used in these studies is not correct. In this article, we provide the correct variance of the DMA chart and through a si...

Fractional factorial designs are popularly used in different fields of experimentations, which allow experimenters to study large number of potentially relevant factors with relatively small number of experimental units but suffer from the fact that some of the effects are aliased with some others. In order to overcome these drawbacks, the foldover...

In this paper we investigate geometric characterization of optimal designs for random coefficient regression models. We establish a generalization of Elving’s theorem for the D-optimality criterion for estimating the population parameters in random coefficient regression models. We also consider the geometric characterization of D-optimal designs f...

This paper considers estimation of the stress–strength reliability when the stress and strength follow two-parameter exponential distributions having different location parameters and a common scale parameter. All parameters are assumed to be unknown. We derive the uniformly minimum variance unbiased estimator, Bayes estimators and an affine equiva...

In this article, we study the problem of estimating the stress-strength reliability, where the stress and strength variables follow independent exponential distributions with a common location parameter but different scale parameters. All parameters are assumed to be unknown. We derive the MLE, the UMVUE of the reliability parameter. We also derive...

This paper provides a new methodology to construct quantitative screening designs. Some examples of 3-level designs are presented to illustrate the method. The theoretical properties of the derived designs are also explored. An advantage of the presented designs is that they exist in cases where the classical screening designs cannot exist. The abo...

The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two-and three-level design. A formulation of wrap-around L2-discrepancy for the extended designs is developed. As a benchmark of obtaining (nearly) uniform asymmetrical extended designs, a l...

Supersaturated designs (SSDs) constitute an important class of fractional factorial designs that could be extremely useful in factor screening experiments. Most of the existing studies have focused on balanced designs. This paper provides a new lower bound for the \(E(f_{NOD})\)-optimality measure of SSDs with general run sizes. This bound is a gen...

Computer experiments involving quantitative factors at high levels are becoming more and more important in the study of complex experiments arising in the area of science and engineering. Uniform designs are found to be widely applicable in computer experiments in the form of space-filling designs. In this paper, the projection uniformity for quant...

In recent years, both robust parameter designs (RPDs) and supersaturated designs (SSDs) have attracted a great deal of attention. In the present article, a combination of the above two techniques is considered. More precisely, we propose a construction of an effective SSD along with an analysis method in order to deal with the significant problem o...

The objective of this paper is to investigate the issue of projection discrepancy for extended U-type or nearly U-type extended designs along the line of Fang and Qin (2005 Fang, K.T., Qin, H., 2005. Uniformity pattern and related criteria for two-level factorials. Sci. China Ser. A 48 1–11.[CrossRef] [Google Scholar]) based on the centered L2-disc...

The foldover is a useful technique in construction of two-level factorial designs. A foldover design is the follow-up experiment generated by reversing the sign(s) of one or more factors in the initial design. The full design obtained by joining the runs in the foldover design to those of the initial design is called the combined design. In this ar...

Due to cost constraints, there are often times when balanced designs are not feasible. Unbalanced designs are also used in cases where some treatment combinations may be of particular interest, so the experimenter chooses to sample more heavily from them. A new lower bound for the
A2 -optimality measure that can be applied to both balanced and near...

Sequential experiment is an indispensable strategy and is applied immensely to various fields of science and engineering. In such experiments, it is desirable that a given design should retain the properties as much as possible when few runs are added to it. The designs based on sequential experiment strategy are called extended designs. In this pa...

The objective of this paper is to study U-type designs for Bayesian nonparametric response surface prediction under correlated errors. The asymptotic Bayes criterion is developed in terms of the asymptotic approach of Mitchell, Sacks and Ylvisaker (19946.
Mitchell, T., Sacks, J. and Ylvisaker, D. (1994). Asymptotic Bayes criteria for nonparametric...

The -optimality criterion introduced by Dette (1997) minimizes the volume of Bonferroni -intervals. The present paper is devoted to the construction of -optimal designs for second-order response surface models with predictors. An equivalence theorem are given as an important tool for determining the -optimal designs. The algorithms are given for co...

This paper considers the derivation of a new lower bound for the generalized discrete discrepancy of designs involving mixed level factors. Using mirror mapping and foldover techniques, a simple and efficient construction method of Sudoku-based mixed level uniform designs is proposed. Moreover, the properties of such Sudoku-based mixed level unifor...

This paper considers the estimation of the stress–strength reliability of a multi-state component or of a multi-state system where its states depend on the ratio of the strength and stress variables through a kernel function. The article presents a Bayesian approach assuming the stress and strength as exponentially distributed with a common locatio...

In the stress-strength models, analysis is based on the reliability of the system where the system is either in operational state or in failure state. Eryılmaz (2011)7.
Eryılmaz, S. (2011). A new perspective to stress–strength models. Ann. Inst. Statist. Math., 63(1):101–115.View all references introduced the stress-strength reliability in a differ...

Supersaturated designs (SSDs) are factorial designs in which the number of experimental runs is smaller than the number of parameters to be estimated in the model. While most of the literature on SSDs has focused on balanced designs, the construction and analysis of unbalanced designs has not been developed to a great extent. Recent studies discuss...

The purpose of this article is to introduce a new class of two-level optimal extended designs obtained by adding few runs to an existing two-level uniform design. The extended design is a union of two designs belonging to different classes. New lower bounds to the centered and wrap-around -discrepancies of extended designs are obtained. Some exampl...

This paper considers the problem of estimation of Rp = Pr( Y p > max( Y 1 , …, Y p-1 )) where Y1; Y2; …, Y p are all independent random variables following one parameter exponential distributions. As an application, Rp is the stress-strength reliability of a component having strength Y p and is subjected to several independent stresses Y1; Y2; …, Y...

This paper considers an extension of -optimality to model-robust optimal design, where a prior probability is set on a class of candidate linear models. A generalization of Elfving’s theorem is proved, which gives a geometrical characterization of model-robust -optimal designs. An equivalence theorem is presented and used to check optimality of des...

Supersaturated designs (SSDs) are defined as fractional factorial designs whose experimental run size is smaller than the number of main effects to be estimated. While most of the literature on SSDs has focused only on main effects designs, the construction and analysis of such designs involving interactions has not been developed to a great extent...

The objective of this paper is to study the issue of the generalized projection discrepancy along the line of Qin et al. (J Stat Plan Inference 142:1170–1177, 2012) based on generalized discrete discrepancy measure proposed by Chatterjee and Qin (J Stat Plan Inference 141:951–960, 2011). We shall study the projection properties for general asymmetr...

The antioxidant activities with respect to the 2,2-diphenyl-1-picrylhydrazyl (DPPH)-radical scavenging activity and reducing activity were assessed and compared for seven edible leafy vegetables (Enhydra fluctuans, Glinus oppositifolius, Amaranthus sp.1, Amaranthus sp.2, Amaranthus spinosus, Ipomoea aquatica and Corchorus sp.) widely consumed in In...

This paper considers R-optimal approximate designs for random coefficient regression models. An equivalence theorem for the R-optimality is provided for random coefficient regression models. Explicit expressions for R-optimal designs under linear regression models are presented for illustration.

This paper considers the R-optimal design problem for multi-factor regression models. It is shown that the product-type designs are optimal for the Kronecker product type models with complete interactions. For the general intra-class models, the optimal designs can be obtained by a mixture of the optimum designs for the conditional models. There ex...

Consider a linear regression model with both quantitative and qualitative factors and an kk-dimensional response variable y whose components are equicorrelated for each observation. The D-optimal design problem is investigated when the levels of the qualitative factor interact with the quantitative factors. It is shown that the determinant of the i...

This paper considers the study of the optimality of the extended design generated by adding few runs to an existing E(χ2)E(χ2)-optimal mixed-level supersaturated design. This paper covers the work of Gupta et al. (2010, 2012) on extended two-level and ss-level supersaturated designs as two special cases. A lower bound to E(χ2)E(χ2) has been obtaine...

Search designs form an important class of experimental designs that allow the identifying of the true model, consisting of a set of factorial effects, among many. Most of the work in this field has been made in the cases where there are at most one or two two-factor interaction effects considered nonnegligible. This article focuses on model identif...

Abtsrcat
Search designs form an indispensable tool under model uncertainty. However, the progress in this area has been limited due to com- plexities of checking the necessary rank condition for search designs. Designs for searching two two-factor and one three-factor interaction effects under a tree structure in the presence of the general mean an...

The purpose of the present work is to extend the work of Gupta et al. (2010) to s-level column balanced supersaturated designs. Addition of runs to an existing E(χ2)-optimalE(χ2)-optimal supersaturated design and to study the optimality of the resulting design is an important issue. This paper considers the study of the optimality of the resulting...

We study the uniformity of two-level U-type designs based on the centered and wrap-around L-2-discrepancies. Based on the known formulation of the measures of uniformity, we present some new lower bounds to centered and wrap-around L-2-discrepancies, which can be used as benchmarks in searching uniform U-type designs or helping to proof that a good...

The objective of this paper is to study the issue of the projection discrepancy along the line of Liu (2002) and Fang and Qin (2005) based on discrete discrepancy measure proposed in Qin and Fang (2004), which has wide application to the field of fractional factorials. Here we also study the projection properties for q-level factorials and provide...

The present paper deals with E(fNOD)-optimalE(fNOD)-optimal multi-level supersaturated designs. We present a new technique for the construction of supplementary difference sets. Based on the new supplementary difference sets, we also provide E(fNOD)-optimalE(fNOD)-optimal multi-level supersaturated designs with a large number of columns when compar...

Supersaturated designs (SSDs) offer a potentially useful way to investigate many factors with only a few experiments during the preliminary stages of experimentation. A popular measure to assess multilevel SSDs is the E(χ) criterion. The literature reports on SSDs have concentrated mainly on balanced designs. For s-level SSDs, the restriction of th...

Lee discrepancy has been employed to measure the uniformity of fractional factorials. In this paper, we further study the statistical justification of Lee discrepancy on asymmetrical factorials. We will give an expression of the Lee discrepancy of asymmetrical factorials with two- and three-levels in terms of quadric form, present a connection betw...

The foldover is a useful technique in the construction of two-level factorial designs for follow-up experiments. To search an optimal foldover plans is an important issue. In this paper, for a set of asymmetric fractional factorials such as the original designs, a lower bound for centred L2-discrepancy of combined designs under a general foldover p...

This paper considers the issue of optimality of fractional factorial experiments involving m factors each at two levels. The optimality criteria used here is the type 1 criteria, due to Cheng (1978), which include the D- and A-criteria. It is shown that if there exists an orthogonal array OA(n−ℓ,m,2,3), ℓ=1,2, then there exists an n-run type 1 opti...

Search designs were first introduced by J.N. Srivastava [Surf. Stat. Des. Lin. Models, Int. Symp. Fort Collins 1973, 507–519 (1975; Zbl 0313.62050)] in order to address the problem of identifying a set of possibly non-negligible interactions. In this paper search designs for 2-level symmetric factorials are considered under the effects hierarchy pr...

We explore the excitation profile of a repulsive impurity doped quantum dot induced by linear and non-linear drift of the dopant location. We have considered Gaussian impurity centers. The investigation reveals the roles subtly played by the region of influence of the dopant in conjunction with the mode of dopant propagation to modulate the excitat...

A design d is called D-optimal if it maximizes det(M d ), and is called MS-optimal if it maximizes tr(M d ) and minimizes tr[(M d )2] among those which maximize tr(M d ), where M d stands for the information matrix produced from d under a given model. In this article, we establish a lower bound for tr[(M d )2] with respect to a main effects model,...

This paper presents an extension of the work of Yue and Chatterjee (2010) about U-type designs for Bayesian nonparametric response prediction. We consider nonparametric Bayesian regression model with p responses. We use U-type designs with n runs, m factors and q levels for the nonparametric multiresponse prediction based on the asymptotic Bayesian...

We explore the excitation profile of a repulsive impurity doped quantum dot induced by a periodically fluctuating impurity domain. We have considered Gaussian impurity centers. The investigation reveals the effects of the dopant coordinate and dopant strength in conjunction with the oscillating impurity domain to modulate the excitation pattern. Th...

The optimality of designs obtained by adding p runs to an orthogonal array is studied for experiments involving m factors each at s levels. The optimality criterion used here is the Type 1 criterion due to C.-S. Cheng [Ann. Stat. 6, 1239–1261 (1978; Zbl 0396.62055)] which is an extension of J. Kiefer’s [Surv. Stat. Des. Lin. Models, Int. Symp. Fort...

In recent years, there has been increasing interest in the study of discrete discrepancy. In this paper, the popular discrete discrepancy is extended to the so-called generalized discrete discrepancy. Connections among generalized discrete discrepancy and other optimality criteria, such as orthogonality, generalized minimum aberration and minimum m...

In this paper, a new lower bound to A2-optimality measure is derived and is applied to multi-level and mixed-level column balanced designs. A2-optimal multi-level and mixed-level designs are obtained by the application of the new lower bound.

A design d is called D-optimal if it maximizes det(Md) and is called MS-optimal if it maximizes tr(Md) and minimizes tr[(Md)] among those which maximize tr(Md), where Md stands for the information matrix produced from d under a given model. In this paper, we establish a lower bound for tr[(Md)] with respect to a main effects model, where d is an s1...

The present work consider the problem of constructing search designs for searching at most two active hidden two-factor interactions in 3n factorial setup under the assumption that the three-factor and higher-order interactions are negligible. The designs presented here are also capable of estimating all the main effects, general mean and the effec...

This paper deals with Bayesian design over U-type designs of n runs and s factors with q levels for nonparametric response surface prediction. The criterion is developed in terms of the asymptotic approach of Mitchell
etal. (Ann Statist 22: 634–651, 1994) for a specific covariance kernel. An optimal design is given in approximate design
theory over...

A new class of saturated, binary row-column designs is proposed. It is shown that these designs are treatment connected in
the sense that these permit the estimability of all contrasts among treatment effects.
Key wordsRow-column designs-saturated-connectedness

Several extensions of the popular E(s 2) criterion of Booth and Cox (19621.
Booth , K. H. V. ,
Cox , D. R. ( 1962 ). Some systematic supersaturated designs . Technometrics 4 : 489 – 495 . [Taylor & Francis Online], [Web of Science ®]View all references) to multilevel supersaturated designs have been advanced in literature. These extensions are no...