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This article provides a new estimator of the exponential mean life which makes use of a preliminary test of hypothesis on the scale parameter for certain life test situations where a guess of the parameter value is available from past studies. Expressions for the bias and mean square error of the proposed estimator are derived. Generalization of this result to a class of weighted estimators is also considered. [ABSTRACT FROM AUTHOR]

The use of Patnaik's [28] chi-square approximation to the noncentral chi-square distribution and the Wilson-Hilferty [321 transformation of chi-square to approximate normality are explored as a simple, efficient means of finding k-order-statistic confidence bounds on parameters and reliability of the one- and two-parameter negative exponential distributions. An important implication of the results leads to obtaining simple closed-form approximations to percentiles of the beta distribution either with integer or noninteger parameters. The general methodology is also used to approximate confidence or prediction intervals for the time of the kth exponential failure based on r

In many studies there is believed to be a trend in a categorical variate with a continuous variate. Often in these cases it is desired to test for the trend using k groups farmed from the continuous variable. This article is concerned with the grouping problem where the goal is essentially to maximize the asymptotic efficiency of the test. Optimal classes are given for k = 2, 3, 4, 5 and 6 for the uniform, normal and exponential distributions. Also, the number of groups to use and the "robustness" of the optimal grouping are investigated. It is noted that the "mathematical problem" in determining the optimal classes appears in other studies; a rationale for this is presented. [ABSTRACT FROM AUTHOR]

Several classes of efficiency-robust linear unbiased estimators of location based an k sample quantiles are defined. The efficiencies of these estimators under the normal, logistic, and double exponential distributions are computed for sample sizes n = 20, 30, 40, 50, 100, infinity, and subsamples of size k = 2, 6, 10, 20. These results are then discussed in relation to other research in efficiency-robust estimation. [ABSTRACT FROM AUTHOR]

This paper investigates the properties of the minimum variance unbiased (M.V.U) and maximum likelihood (M.L.) estimators of the reliability functions of systems composed of two subsystems connected in series. The study falls into two parts, one for the Poisson case and one for the exponential case. In each of these cases the situations are distinguished between, where the two subsystems are identical and situations subsystems are different. In the Poisson case under minimum variance unbiased estimators a system A is considered which is composed of two subsystems connected in series. Failure time points of the subsystem follow a Poisson process with intensity. An experiment is performed on n independent replicates of each of the considered subsystems over a period of length. Under the exponential case, a system A is considered, same as Poisson case which consists of two subsystems connected in series. Failure time points of the two subsystems follow a Poisson process. Independent observations are available on the interfailure time lengths; namely, the life-lengths of the subsystems.

Minimum variance unbiased estimators of reliability are developed for a series, parallel, and standby redundant system where the components are from a single exponentially distributed population. It is assumed that sampling information has been censored with respect to number of failures or test time. [ABSTRACT FROM AUTHOR]

Statistical properties of the bivariate exponential distribution are investigated. Maximum likelihood and method of moments type estimates are obtained and compared with the estimates given by Arnold. The method of moments type estimates are easy to compute and highly efficient, whereas the maximum likelihood estimates are computationally inconvenient. The problem of testing for correlation in the bivariate exponential distribution is also investigated. [ABSTRACT FROM AUTHOR]

We introduce a normal scores test for ordered alternatives among k treatments in the randomized block design. For k = 2 or 3, the test is equivalent to a standard test due to Page [5]. For k is greater than or equal to 4, the test differs from Page's and is often more efficient. As k arrow right Infinity the Pitman asymptotic relative efficiency of the normal scores test compared to Page's test tends to Infinity for uniform and exponential populations. For normal, uniform and exponential populations, this efficiency exceeds 1 for k is greater than or equal to 4. We present a table of .01, .05, and .10 critical values for k = 4, n = 1(1)10 and k=5, n= 1(1)5. [ABSTRACT FROM AUTHOR]