Kashinath Chatterjee

Some search designs for symmetric and asymmetric factorials

Abstract This paper describes the construction of search designs involving a larger number of factors from those involving smaller numers of factors. Some search designs for symmetric factorials have been proposed. These results may be utilized for the construction of search designs for the series s r × w m − r where s and w are any positive integers.

A lower bound for the centred L 2-discrepancy on combined designs under the asymmetric factorials

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 L 2-discrepancy of combined designs under a general foldover plan is obtained, which can be used as a benchmark for searching optimal foldover plans. All of our results are the extended ones of Ou et al. [Lower bounds of various discrepancies on combined designs, Metrika 74 (2011), pp. 109–119] for symmetric designs to asymmetric designs. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.

Construction of supersaturated designs involving s-level factors

Abstract Supersaturated designs for searching active factors in screening experiments involving several factors at two levels have been considered by several authors. This paper considers the construction of supersaturated designs for s m experiments, s ⩾2. Two classes of designs for searching one and two active factors respectively are provided.

Lower Bounds for the Uniformity Pattern of Asymmetric Fractional Factorials

The objective of this article is to study the issue of the projection discrepancy (Fang and Qin, 2005; Ma et al. 2003), which has wide application to the field of fractional factorials. Fang and Qin (2005) and Zhang and Qin (2006) derived some properties of the projection properties of two-level factorials. Here we extend their results to asymmetric factorials. Some lower bounds of projection discrepancy of asymmetrical factorials are also obtained.

Graph-theoretic techniques in D-optimal design problems

Abstract We solve several problems in D-Optimal Design Theory using techniques from Graph Theory and Combinatorics. The techniques involve relating the value of a determinant of a 0–1 matrix with the number of certain perfect matchings in a bipartite graph.

Search designs for searching for one among the two-and three-factor interaction effects in the general symmetric and asymmetric factorials

This paper describes the construction of search designs which permit the estimation of the general mean and main-effects, and allow the search for and estimation of one possibly unknown non-zero effect among the two-and three-factor interactions in the general symmetric and asymmetric factorial set-up.

Bayes estimation for exponential distributions with common location parameter and applications to multi-state reliability models

ABSTRACT 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 location parameter but different scale parameters. We show that the limits of the Bayes estimators of both location and scale parameters under suitable priors are the maximum likelihood estimators as given by Ghosh and Razmpour [15]. We use the Bayes estimators to determine the multi-state stress–strength reliability of a system having states between 0 and 1. We derive the uniformly minimum variance unbiased estimators of the reliability function. Interval estimation using the bootstrap method is also considered. Under the squared error loss function and linex loss function, risk comparison of the reliability estimators is carried out using extensive simulations.

Excitations in doped quantum dot driven by periodically fluctuating impurity domain

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. The investigation also reveals the maximization in the excitation rate for some typical range of values of dopant location and dopant strength.

Optimality of orthogonally blocked diallels with specific combining abilities

Optimality of orthogonally blocked complete diallel crosses for estimating general combining abilities is investigated when the model also includes specific combining abilities. It is proved that these designs remain optimal even in the presence of specific combining abilities. Three new series of orthogonally blocked designs are also reported.

Stress–strength models with more than two states under exponential distribution

ABSTRACT 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) introduced the stress–strength reliability in a different framework assigning more than two states to the system depending on the difference between strength and stress values. Unlike Eryılmaz (2011), the present article deals with the ratio of the strength and stress values when the stress and strength follow independent exponential distributions. This article presents in detail the estimation aspect of the multistate stress–strength reliability function.