Application of Multivariate Analysis to Increase the Yield of Dry Cell Batteries

In an organization, the manufacturing process of a dry cell battery was suffering from the problem of frequent stoppages in the assembly line. The complete battery manufacturing operation is highly automated and mechanized. It was suspected that excessive variation in overall height of bobbin was the major reason for such stoppages. The bobbin, the inside part of a dry cell battery acting as cathode, is formed by the battery extrusion process. A planned experiment was carried out on the extrusion process that identified the setting of extrusion machines and the amount of water content in the cathode mixture as the parameters causing variation in the bobbin characteristics. The problem of frequent stoppages was eliminated when appropriate action was taken on these two parameters. Finally, multivariate and univariate control schemes were developed for online control of the bobbin characteristics.     

Union–intersection principle and constrained statistical inference

Most statistical models arising in real life applications as well as in interdisciplinary research are complex in their designs, sampling plans, and associated probability laws, which in turn are often constrained by inequality, order, functional, shape or other restraints. Optimality of conventional likelihood ratio based statistical inference may not be tenable here, although the use of restricted or quasi-likelihood has spurred in such environments. S.N. Roy's ingenious union–intersection principle provides an alternative avenue, often having some computational advantages, increased scope of adaptability, and flexibility beyond conventional likelihood paradigms. This scenario is appraised here with some illustrative examples, and with some interesting problems of inference on stochastic ordering (dominance) in parametric as well as beyond parametric setups.     

Regression models for analyzing clustered binary and continuous outcomes under an assumption of exchangeability

Scientific experiments commonly result in clustered discrete and continuous data. Existing methods for analyzing such data include the use of quasi-likelihood procedures and generalized estimating equations to estimate marginal mean response parameters. In applications to areas such as developmental toxicity studies, where discrete and continuous measurements are recorded on each fetus, or clinical ophthalmologic trials, where different types of observations are made on each eye, the assumption that data within cluster are exchangeable is often very reasonable. We use this assumption to formulate fully parametric regression models for clusters of bivariate data with binary and continuous components. The regression models proposed have marginal interpretations and reproducible model structures. Tractable expressions for likelihood equations are derived and iterative schemes are given for computing efficient estimates (MLEs) of the marginal mean, correlations, variances and higher moments. We demonstrate the use the ‘exchangeable’ procedure with an application to a developmental toxicity study involving fetal weight and malformation data.     

Some remarks on classical and bayesian reliability estimation of binomial and poisson distributions

The problems of estimating the reliability function and Pr{X₁+...+X_k ≤ Y} are considered. The random variables X’s and Y are assumed to follow binomial and Poisson distributions. Classical estimators available in the literature are discussed and Bayes estimators are derived. In order to obtain the estimators of these parametric functions, the basic role is played by the estimators of factorial moments of the two distributions.     

Response to the COVID-19: Understanding implications of government lockdown policies

The rising number of COVID-19 cases and economic implications of lockdown measures indicate the tricky balancing act policy makers face as they implement the subsequent phases of 'unlock'. We develop a model to examine how lockdown and social distancing measures have influenced the behavioral conduct of people. The current situation highlights that policy makers need to focus on bringing awareness and social restraint among people rather than going for stringent lockdown measures. We believe this work will help the policy makers gain insights into the troubled COVID-19 times ahead, and based on the estimates, they can frame policies to navigate these wild waves in the best possible way.     

“The Past in the Present: Mills,Tocqueville and the Necessity of History”

Historical sociology has achieved a reasonable degree of respectability in the discipline, and there is much interesting work being produced. But a pronounced aspect of much of this work is an indifference to the question of the value of studying the past as a way to understanding the present. This article argues that, rather than trying to outdo the historians by producing “better,” more theoretically sophisticated history, sociologists would better advance the case for historical sociology by showing how any particular historical study helps illuminate contemporary concerns. The article draws upon the writings of C. Wright Mills and Alexis de Tocqueville to show not just the need for historical sociology but also as indications of how this might best be done.     

Robustness of tests for directional mean

In this paper we study the robustness of the likelihood ratio, circular mean and circular trimmed mean test functionals in the context of tests of hypotheses regarding the mean direction of circular normal and wrapped normal distributions. We compute the level and power breakdown properties of the three test functionals and compare them. We find that the circular trimmed mean test functional has the best robustness properties for both the above-mentioned distributions. The level and power properties of the test statistics corresponding to these functionals are also studied. Two examples with real data are given for illustration. We also consider the problem of testing the mean direction of the von-Mises–Fisher distribution on the unit sphere and explore the robustness properties of the spherical mean direction and likelihood ratio test functionals.     

Estimating parameters of a selected Pareto population

Let Π₁,…,Π_k be k populations with Π_i being Pareto with unknown scale parameter α_i and known shape parameter β_i;i=1,…,k. Suppose independent random samples (X_i1,…,X_in), i=1,…,k of equal size are drawn from each of k populations and let X_i denote the smallest observation of the ith sample. The population corresponding to the largest X_i is selected. We consider the problem of estimating the scale parameter of the selected population and obtain the uniformly minimum variance unbiased estimator (UMVUE) when the shape parameters are assumed to be equal. An admissible class of linear estimators is derived. Further, a general inadmissibility result for the scale equivariant estimators is proved.