Lakshmi N. Upadhyaya

Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean Y of the study character y, an estimator using a transformed auxiliary variable has been defined. The bias and mean-squared error (MSE) of the proposed estimator have been obtained. The regions of preference have been obtained under which it is better than usual unbiased estimator y, the ratio estimator y R = yX/x, SISODIA and DWIVEDI (1981) estimator y s = y(X + C x )/(x + C x ) and SINGH and KAKRAN (1993) estimator y k = y[X + β 2 (x)]/x + β 2 (x)]. An empirical study has been carried out to demonstrate the superiority of the suggested estimator over the others.

Improved Ratio and Product Exponential Type Estimators

This paper addresses the problem of estimating the population mean using auxiliary information. Improved versions of Bahl and Tuteja (1991) ratio and product exponential type estimators have been proposed and their properties studied under large sample approximation. It has been shown that the proposed ratio and product exponential type estimators are more efficient than those considered by Bahl and Tuteja (1991) estimators, conventional ratio and product estimators and the usual unbiased estimator under some realistic conditions. An empirical study has been carried out to judge the merits of the suggested estimators over others. Theoretical and empirical results are sound and quite illuminating compared to other estimators.

Application of fuzzy time series in prediction of time between failures & faults in software reliability assessment

Since last seventies, various software reliability growth models (SRGMs) have been developed to estimate different measures related to quality of software like: number of remaining faults, software failure rate, reliability, cost, release time, etc. Most of the exiting SRGMs are probabilistic. These models have been developed based on various assumptions. The entire software development process is performed by human being. Also, a software can be executed in different environments. As human behavior is fuzzy and the environment is changing, the concept of fuzzy set theory is applicable in developing software reliability models. In this paper, two fuzzy time series based software reliability models have been proposed. The first one predicts the time between failures (TBFs) of software and the second one predicts the number of errors present in software. Both the models have been developed considering the software failure data as linguistic variable. Usefulness of the models has been demonstrated using real failure data.

Software fault prediction using Nonlinear Autoregressive with eXogenous Inputs (NARX) network

This paper explores a new approach for predicting software faults by means of NARX neural network. Also, a careful analysis has been carried out to determine the applicability of NARX network in software reliability. The validation of the proposed approach has been performed using two real software failure data sets. Comparison has been made with some existing parametric software reliability models as well as some neural network (Elman net and TDNN) based SRGM. The results computed shows that the proposed approach outperformed the other existing parametric and neural network based software reliability models with a reasonably good predictive accuracy.

Effect of change point and imperfect debugging in software reliability and its optimal release policy

This article presents a software reliability growth model based on non-homogeneous Poisson process. The main focus of this article is to deliver a method for software reliability modelling incorporating the concept of time-dependent fault introduction and fault removal rate with change point. Also in this article, a cost model with change point has been developed. Based on the cost model optimal release policy with change point has been discussed. Maximum likelihood technique has been applied to estimate the parameters of the model. The proposed model has been validated using some real software failure data. Comparison has been made with models incorporating change point and without change point. The application of the proposed cost model has been shown using some numerical examples.

Estimation of the Population Standard Deviation Using Auxiliary Information

SYNOPTIC ABSTRACT This paper proposes a class of estimators for estimating population standard deviation using auxiliary information in sample surveys. The large sample expressions for the bias and variance of the estimators are derived and the minimum variance obtained. An empirical study is carried out to demonstrate the performance of the constructed estimators over usual standard deviation estimator.

Transfer function modelling in software reliability

This paper demonstrates the applicability of transfer function model in the field of software reliability. Here a stepwise procedure for fitting a transfer function model has been described and then the prediction of remaining faults in software has been done using the built in model. Some real life data have been used for illustration purpose.

A Generalized Family of Transformed Ratio-Product Estimators for Variance in Sample Surveys

This article advocates the problem of estimating the population variance of the study variable y using information on certain known parameters of the auxiliary variable x. A family of ratio-product-type estimators for population variance of the study variable y is defined. In addition to many estimators, usual unbiased estimator , Isaki (1983), Upadhyaya and Singh (1999) estimators, and Kadilar and Cingi (2006) estimators are shown as members of the proposed class of estimators. Asymptotic expressions for bias and mean squared error of the proposed class of estimators have been obtained. An empirical study is carried out to show the performance of the various estimators of generated from the proposed class of estimators over usual unbiased estimator .

Best Subset Selection of ARMA and ARIMA Models for Software Reliability Estimation

Abstract Many software reliability models have been proposed during last three decades. Almost all these software reliability models have been developed based on many assumptions. One approach for development of assumption free software reliability model is time series. In this paper ARMA and ARIMA models have been developed for predicting software reliability. The proposed models have been validated using some real software failure data.

A Class of Estimators of Population Variance Using Auxiliary Information in Sample Surveys

This article advocates the problem of estimating the population variance of the study variable using information on certain known parameters of an auxiliary variable. A class of estimators for population variance using information on an auxiliary variable has been defined. In addition to many estimators, usual unbiased estimator, Isakis (1983), Upadhyaya and Singhs (1999), and Kadilar and Cingis (2006) estimators are shown as members of the proposed class of estimators. Asymptotic expressions for bias and mean square error of the proposed class of estimators have been obtained. An empirical study has been carried out to judge the performance of the various estimators of population variance generated from the proposed class of estimators over usual unbiased estimator, Isakis (1983), Upadhyaya and Singhs (1999) and Kadilar and Cingis (2006) estimators.