Chand K. Midha

Construction of some asymmetrical orthogonal arrays

A method of construction of asymmetrical orthogonal arrays of strength two is described. The method exploits difference matrices and a special type of orthogonal arrays. Several families of asymmetrical orthogonal arrays are obtained through the method. An open problem relating to the construction of a class of asymmetrical orthogonal arrays is proposed and comments on partial solutions to the problem are made. A conjecture on an upper bound to the number of constraints in a class of arrays is also made.

STATISTICAL ANALYSIS OF OLEFINS YIELD IN FIXED BED CONVERSION OF DIMETHYL ETHER

ABSTRACT Selective conversion of dimethyl ether to lower olefins is a process of commercial significance. Lower olefins are intermediates in the conversion of dimethyl ether to higher hydrocarbons. Conversion of dimethyl ether to hydrocarbons has significant advantages over its counterpart methanol conversion process in the areas of heat duties, hydrocarbon selectivities, product yield, and reactor size The present work examines the effect of key process variables on the dimethyl ether conversion to lower olefins in a fixed bed reactor system. The effect of process variables, namely reactor temperature, reactor pressure, feed dilution with nitrogen, and the weight hourly space velocity of dimethyl ether has been investigated using a 24 full factorial experimental design, with three replicates of the center point of the design. The estimates of significant main and interactive effects have been quantified using the Yates algorithm and conducting F-tests. A computational model has been formulated to predict...

Cyclic Group Divisible Designs

New cyclic solutions of several group divisible incomplete block designs arc presented, A new group divisible desian is reported whose solution is also cyclic. We also present non-isomorphic solutions of several group divisible designs listed in the catalogue of Clatworthy (1973).

Modified Clopper-Pearson Confidence Interval for Binomial Proportion

We introduce expected coverage probability as a measure for constructing confidence intervals for the binomial proportion, p. We propose a model based confidence interval for p using the expected coverage probabilities of the Clopper-Pearson interval. The method provides intervals comparable or better than the alternative intervals, such as the Wilson, Agresti-Coull and Jeffreys intervals.

Optimal Supersaturated Designs for sm Factorials in N ≢ 0 (mod s) Runs

Supersaturated designs (SSDs) offer apotentially 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(χ2) criterion. The literature reports on SSDs have concentrated mainly on balanced designs. For s-level SSDs, the restriction of the number of runs N being only a multiple of s is really not required for the purpose of use of such designs. Just like when N is a multiple of s and the design ensures orthogonality of the factor effects with the mean effect, in the case of N not a multiple of s, we ensure near orthogonality of each of the factors with the mean. In this article we consider s-level E(χ2)-optimal designs for N ≡ n (mod s), 0 ≤ n ≤ s − 1. We give an explicit lower bound on E(χ2). We give the structures of design matrices that attain the lower bounds. Some combinatorial methods for constructing E(χ2)-optimal SSDs are provided.

Optimal Supersaturated Designs for s m Factorials in (mod s) Runs

Supersaturated designs (SSDs) offer apotentially 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(χ2) criterion. The literature reports on SSDs have concentrated mainly on balanced designs. For s-level SSDs, the restriction of the number of runs N being only a multiple of s is really not required for the purpose of use of such designs. Just like when N is a multiple of s and the design ensures orthogonality of the factor effects with the mean effect, in the case of N not a multiple of s, we ensure near orthogonality of each of the factors with the mean. In this article we consider s-level E(χ2)-optimal designs for N ≡ n (mod s), 0 ≤ n ≤ s − 1. We give an explicit lower bound on E(χ2). We give the structures of design matrices that attain the lower bounds. Some combinatorial methods for constructing E(χ2)-optimal SSDs are provided.

Construction of Nested Incomplete Block Designs

Nested balanced incomplete block designs were introduced by Preece (1967). Generalization of these designs were studied by Home! and Robinson (1975). In this communication, we present some systematic methods of construction of nested balanced and partially balanced incomplete block designs. These methods unify and generalize some of the existing ones.

A Generalized Formula for Variance in Unequal Probability Sampling

A variance formula is given for a general class of estimators for any fixed sample size design. A formula for an unbiased estimator of the variance is also provided. These results generalize the Yates-Grundy variance formula of the Horvitz-Thompson estimator.

Preliminary Statistical Analysis of PAH-Contaminated Soils

Current research has proven bioremediation to be extremely effective for the cleanup of contaminated soils. Although bioremediation is effective, it still faces serious doubts on its implementation at a full-scale site. This is primarily due to minute differences encountered with each specific microbial species, supplemental nutrients, and the interaction between microbe and nutrient used at each site. The objective of this research was to determine the statistical significance of the choice of microorganism, nutrient solution, and their respective interaction effects. Specifically, the use of three different bacteria and three supplemental nutrient solutions was investigated for the remediation of soil contaminated with polycyclic aromatic hydrocarbons.