Ram C. Dahiya

Estimating the parameters of a non-homogeneous Poisson-process model for software reliability

A stochastic model (G-O) for the software failure phenomenon based on a nonhomogeneous Poisson process (NHPP) was suggested by Goel and Okumoto (1979). This model has been widely used but some important work remains undone on estimating the parameters. The authors present a necessary and sufficient condition for the likelihood estimates to be finite, positive, and unique. A modification of the G-O model is suggested. The performance measures and parametric inferences of the new model are discussed. The results of the new model are applied to real software failure data and compared with G-O and Jelinski-Moranda models. >

Estimation of the Mean of the Selected Population

Abstract Let X i1, X i2, …,X in, i = 1, 2, be a pair of independent random samples from normal populations with means θi , and common known variance τ2. Suppose we select the population which provides the larger sample mean. In this article our main aim is to investigate different estimators for the mean of the selected population. Two different estimators are suggested by Sarkadi [9] and Putter and Rubinstein [8]. Two alternative estimators are suggested here and the bias and the mean square error of all the different types of estimators are tabled and compared.

Goodness of Fit Tests for the Gamma and Exponential Distributions

Goodness of fit tests based on generalized minimum x 2 techniques are developed for the gamma and exponential distributions. The power of these tests has been found for several alternative families of distributions by utilizing the asymptotic non-null distribution of the test statistic. The tests behave very well for the types of alternatives considered here. Applications to some failure data of Proschan (1963) are included for illustrative purposes.

Estimating the Zero Class from a Truncated Poisson Sample

Abstract A procedure for estimating the zero class from a truncated Poisson sample is developed. Asymptotic normality of the estimator is proved so that a confidence interval for the missing zero class can be obtained. An example is given to illustrate the results obtained.

How Many Classes in the Pearson Chi-Square Test?

Abstract The asymptotic non-null distribution is obtained for the modified form of the Pearson chi-square statistic studied by Dahiya and Gurland [3]. By utilizing this result the power is obtained for specific alternative distributions in testing for normality. This enables recommendations to be made as to the number of class intervals to be employed in applying the aforementioned modification of the Pearson chi-square test of normality.

Estimation of parameters of mixed failure time distribution from censored data

Here, we consider estimation of parameters of a mixture of binomial and exponential populations. The exact bias and mean square error (MSE) of the estimator is derived and computed for different values of parameters. It is also shown that the exact MSE approaches to asymptotic MSE as n increases.

Estimation in a truncated bivariate poisson distribution

Moment estimators for parameters in a truncated bivariate Poisson distribution are derived in Hamdan (1972) for the special case of λ1 = λ2, Where λ1, λ2 are the marginal means. Here we derive the maximum likelihood estimators for this special case. The information matrix is also obtained which provides asymptotic covariance matrix of the maximum likelihood estimators. The asymptotic covariance matrix of moment estimators is also derived. The asymptotic efficiency of moment estimators is computed and found to be very low.

Estimating the Parameters of a Gamma Distribution.

Generalized minimum chi-square estimators of the parameters involved in a gamma distribution are obtained, and their asymptotic generalized variance is compared with that of maximum likelihood estimators.

Estimation of Reliability After Corrective Action

Asymptotic distributions of several estimators, proposed in the literature for estimating reliability after corrective action, are derived here. Furthermore, the maximum likelihood estimators for the special case of equal failure probabilities are obtained. Some of the estimators appearing in the literature are shown to be not s-consistent.

Adaptive Exponential Smoothing Models for Reliability Estimation

Four methods are discussed for determining the smoothing parameters in an adaptive exponential smoothing model which is used to assess reliability of a complex system tested in stages. The adaptive model is defined as Ri = ?iri + (1 - ?i)Ri-1, i = 2,...k, where Ri-1 is the assessed reliability at stage (i -1), ri is the ratio of the number of successes to the number of trials at stage i. Among the four procedures given here for determining the smoothing parameters xi two empirical methods and an empirical Bayes procedure are considered in some detail including a numerical example in which these techniques are compared.