• Communications for Statistical Applications and Methods
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• v.21 no.1
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• pp.1-9
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• 2014

This paper discusses the problem of estimation of finite population mean in double sampling for stratification. In fact, ratio and product type exponential estimators of population mean are proposed in double sampling for stratification. The biases and mean squared errors of proposed estimators are obtained upto the first degree of approximation. The proposed estimators have been compared with usual unbiased estimator, ratio and product estimators in double sampling for stratification. To judge the performance of the proposed estimators an empirical study has been carried out.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.539-557
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• 1998

This article is concerned with the problem of estimating the mean of a one-parameter exponential family through sequential sampling in three stages under quadratic error loss. This more general framework differs from those considered by Hall (1981) and others. The differences are : (i) the estimator and the final stage sample size are dependent; and (ii) second order approximation of a continuously differentiable function of the final stage sample size permits evaluation of the asymptotic regret through higher order moments. In particular, the asymptotic regret can be expressed as a function of both the skewness $\rho$ and the kurtosis $\beta$ of the underlying distribution. The conditions on $\rho$ and $\beta$ for which negative regret is expected are discussed. Further results concerning the stopping variable N are also presented. We also supplement our theoretical findings wish simulation results to provide a feel for the triple sampling procedure presented in this study.

• Journal of Korean Society for Quality Management
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• v.23 no.4
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• pp.13-27
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• 1995

This paper considers the design of life test sampling plans based on Type II censored accelerated life tests. The lifetime distribution of products is assumed to be exponential. An estimator of acceleration factor between use condition stress and an accelerated level of stress higher than use condition stress is assumed to be known. The critical value for lot acceptance and the number of failure before censoring which satisfy the producer's and consumer's risk requirements are determined. The properties of the proposed life test sampling plans are investigated.

• Journal of Korean Institute of Industrial Engineers
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• v.17 no.1
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• pp.95-108
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• 1991

For the case where the lifetime at a constant stress level has exponential distribution, optimal accelerated life test plans are developed under the assumptions of intermittent inspection and Type I censoring. In a optimal plan, the low and high stress levels, the proportion of test units allocated and the inspection times at each stress are determined such that the asymptotic variance of the maximum likelihood estimator of logarithmic transformed mean at the use condition is minimized. In addition to the optimal plan in which numerical technique to solve the set of nonlinear equations must be employed to determine inspection times at each stress level, we also propose another plans which employ equally-spaced or equal probability inspection schemes at two overstress levels of corresponding optimal one. For both optimal and proposed plans, computational results indicate that the asymptotic variance of the estimated mean at the use stress is insensitive to number of inspections at overstress levels for the range of parameter values considered.

• Journal of the Korean Operations Research and Management Science Society
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• v.21 no.1
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• pp.115-129
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• 1996

A reliability Acceptance Sampling Plan (RASP) is developed for testing the exponential mean lifetime under the periodic (i. e., equally-spaced) inspection and Type I censoring. Under the periodic inspection, the exact sampling distribution of maximum likelihood (ML) estimator of mean can not be derived. Hence sample size and acceptance criterion are determined by the algorithm proposed on the basis of Monte Carlo simulation such that the producer's and consumer's risks are satisfied for given censoring time and number of inspections. In addition, the developed RASP is compared in terms of sampling size, OC curve, and expected completion time. The effects for the RASP by the chosen inspection scheme are also discussed.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.37-45
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• 1999

In this paper, we consider two components system having Marshall-Olkin's bivariate exponential model. For the bivariate random censorship, we obtain maximum likelihood estimators of parameters and system reliability. And we propose the methods of homogeniety and independence tests using asymptotic normality. Also we compute the estimators and p-values of the testings through Monte Carlo simulation.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.3
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• pp.459-471
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• 1996

This paper considers ramp tests for exponential lifetime distribution when there are limitations on test stress and test time. The inverse power law and a cumulative exposure model are assumed. Maximum likelihood (ML) estimators of model parameters and their asymptotic covariance matrix are obtained. The optimum ramp test plans are also found which minimize the asymptotic variance of the ML estimator of the log mean life at design constant stress. For selected values of the design parameters, tables useful for finding optimal test plans are given. The effect of the pre-estimates of design parameters is studied.

• Journal of Korean Society for Quality Management
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• v.24 no.2
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• pp.77-86
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• 1996

In this paper, we consider the problem of testing independence in the absolutely continuous bivariate exponential distribution of Block and Basu(1974). We construct a bootstrap procedure for testing zero and non-zero values of the parameter ${\lambda}_3$ which measures the degree of dependence and compare the power of the bootstrap test with likelihood ratio test(LRT) by Gupta et al.(1984) and the test based on maximum likelihood estimator(MLE) $\hat{{\lambda}}_3$ by Hanagal and Kale(1991) for small and moderate sample sizes.

• International Journal of Reliability and Applications
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• v.4 no.4
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• pp.171-181
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• 2003

This paper proposes a U-test statistic for the problem of testing that a life distribution is exponential against the alternative that it is harmonic new better (worse) than used in expectation upper tail HNBUET (HNWUET), but not exponential on complete data. Selected critical values are tabulated for sample sizes n =5(1)60. The asymptotic normality of the statistic is proved and a comparison is made of the asymptotic efficiency between the statistic and other statistics. The power of the test is studied by simulation. A test for HNBUET in the case of randomly right-censored data is also considered. An application of the proposed test statistic in medical sciences is given.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.23-31
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• 2002

A scale parameter is the principal parameter to be estimated, since it corresponds to one of the main reliability characteristics, namely the average time to failure. To provide robustness of scale estimators to gross errors in the data, we apply the Huber minimax approach in time to failure models of the statistical reliability theory. The minimax valiance estimator of scale is obtained in the important particular case of the exponential distribution.