Selective Maintenance in System Reliability with Random Costs of Repairing and Replacing the Components

In this paper we consider the problem of determining the optimum number of repairable and replaceable components to maximize a system's reliability when both, the cost of repairing the components and the cost of replacement of components by new ones, are random. We formulate it as a problem of non-linear stochastic programming. The solution is obtained through Chance Constrained programming. We also consider the problem of finding the optimal maintenance cost for a given reliability requirement of the system. The solution is then obtained by using Modified E-model. A numerical example is solved for both the formulations.     

A family of estimators of population variance in two-occasion rotation patterns

Abstract

In this article, we have considered the problem of estimation of population variance on current (second) occasion in two occasion successive (rotation) sampling. A class of estimators of population variance has been proposed and its asymptotic properties have been discussed. The proposed class of estimators is compared with the sample variance estimator when there is no matching from the previous occasion and the Singh et al. (2013) estimator. Optimum replacement policy is discussed. It has been shown that the suggested estimator is more efficient than the Singh et al. (2013) estimator and a usual unbiased estimator when there is no matching. An empirical study is carried out in support of the present study.     

Use of several auxiliary variables in estimating the population mean in a two-occasion rotation pattern

ABSTRACT

This paper addresses the problem of estimation of the population mean on the current (second) occasion in two-occasion successive sampling. Utilizing the readily available information on several auxiliary variables on both occasions and the information on the study variable from the previous occasion, an estimation procedure of the population mean on the current occasion has been proposed. Theoretical properties of the proposed estimator have been investigated. Optimum replacement policy to the proposed estimator has been discussed. The proposed estimator has been compared empirically with the sample mean estimator, when there is no matching and the optimum estimator which is a linear combination of the means of the matched and unmatched portions of the sample at the current occasion. Appropriate recommendations have been made for practical applications.     

Influences of Infant‐Directed Speech on Early Word Recognition

When addressing infants, many adults adopt a particular type of speech, known as infant‐directed speech (IDS). IDS is characterized by exaggerated intonation, as well as reduced speech rate, shorter utterance duration, and grammatical simplification. It is commonly asserted that IDS serves in part to facilitate language learning. Although intuitively appealing, direct empirical tests of this claim are surprisingly scarce. Additionally, studies that have examined associations between IDS and language learning have measured learning within a single laboratory session rather than the type of long‐term storage of information necessary for word learning. In this study, 7‐ and 8‐month‐old infants' long‐term memory for words was assessed when words were spoken in IDS and adult‐directed speech (ADS). Word recognition over the long term was successful for words introduced in IDS, but not for those introduced in ADS, regardless of the register in which recognition stimuli were produced. Findings are discussed in the context of the influence of particular input styles on emergent word knowledge in prelexical infants.     

The power functions of the likelihood ratio tests for a simply ordered trend in normal means

Likelihood ratio tests for the homogeneity of k normal means with the alternative restricted by an increasing trend are considered as well as the likelihood ratio tests of the null hypothesis that the means satisfy the trend. While the work is primarily a survey of results concerning the power functions of these tests, the extensions of some results to the case of not necessarily equal sample sizes are presented. For the case of known or unknown population variances, exact expressions are given for the power functions for k=3,4, and approximations are discussed for larger k. The topics of consistency, bias and monotonicity of the power functions are included. Also, Bartholomew's conjectures concerning minimal and maximal powers are investigated, with results of a new numerical study given.     

Measuring Accessibility for Inclusive Development: A Census Based Index

State is often involved in the challenging process of judicious allocation and apportioning of resources for an inclusive growth through creating infrastructure and ensuring accessibility- the “ability of the people to reach and engage in opportunities and activities”. The issue at the heart of the debate concerns with the “opportunities” available in a geographic area and the inhabitants’ use of those opportunities in terms of their “behaviour”. The extant literature suggests that the dominant component of the accessibility is mobility infrastructure. The present paper argues that the impact of the human development and the information infrastructure should also be considered. This paper uses the Indian census data of 2001 and develops the methodology for creating an accessibility index for a geographic unit. The paper also discusses the use of the accessibility index (AI) as a tool for evaluating the efficacy of a public policy initiative towards decreasing the exclusion of geographic units. Validation of the tool is done using the patient inflow data at a large charitable hospital in Central India and household level employment data from National Rural Employment Guarantee Scheme (NREGS).     

A Class of Estimators Using Auxiliary Information for Estimating Finite Population Variance in Presence of Measurement Errors

This article addresses the problem of estimating the population variance using auxiliary information in the presence of measurement errors. When the measurement error variance associated with study variable is known, a class of estimators of the population variance using auxiliary information has been proposed. We obtain the bias and mean squared errors of the suggested class of estimators upto the terms of order n ^?1, and also optimum estimators in asymptotic sense of the class with approximate mean squared error formula.     

Double Sampling Ratio-product Estimator of a Finite Population Mean in Sample Surveys

It is well known that two-phase (or double) sampling is of significant use in practice when the population parameter(s) (say, population mean X¯) of the auxiliary variate x is not known. Keeping this in view, we have suggested a class of ratio-product estimators in two-phase sampling with its properties. The asymptotically optimum estimators (AOEs) in the class are identified in two different cases with their variances. Conditions for the proposed estimator to be more efficient than the two-phase sampling ratio, product and mean per unit estimator are investigated. Comparison with single phase sampling is also discussed. An empirical study is carried out to demonstrate the efficiency of the suggested estimator over conventional estimators.