Confidence interval for the mean of the exponential distribution,based on grouped data

When the available data from an exponential distribution are grouped, the maximum likelihood estimator (MLE) for the mean and several modified MLE have been discussed in literature. However, little work has been done on interval estimators based on such grouped data. This paper derives the asymptotic property of a statistic which is used to construct an approximate confidence interval for the mean. The width of this approximate confidence interval, based on grouped data, is compared with those based on complete samples, and samples with type-I and type-II censoring. The limits of the ratios of these widths are derived when the sample size approaches infinity. The approximate confidence interval from grouped data is wider than those from complete and censored samples. However, Monte Carlo simulation indicates that the proposed method based on grouped data is adequate, considering the restricted information in this case     

Analysis of grouped and censored data from step-stress life test

This paper studies statistical analysis of grouped and censored data obtained from a step-stress accelerated life test. We assume that the stress change times in the step-stress life test are fixed and the lifetimes observed are type I censored. Maximum likelihood estimates and asymptotic confidence intervals for model parameters are obtained. We provide an asymptotic statistical test for the cumulative exposure model based on the grouped and type I censored data. We also present the optimum test plan for a simple step-stress test when the lifetime under constant stress is assumed exponential. Finally we give an application of our methods by applying our analysis process to a real life data set. The proposed statistical methodology is especially useful when intermittent inspection is the only feasible way of checking the status of test units during a step-stress test.     

Estimation of average survival time of a process having an exponential lifetime model for time censored data

Censoring is almost mandatory, especially in dealing with costly sophisticated items in a life testing experiment. Assuming the survival times to be distributed exponentially with two parameters we have proposed an estimator using a preliminary test of significance for the estimation of average survival time of the time censored life data. The bias and mean square error of the proposed estimator have been studied. Based on some mathematical results and an empirical study, recommendations have been made regarding the use of proposed estimator.     

Estimation of parameters of life from progressively censored data using Burr-XII model

Based on progressively Type-II censored samples, the maximum likelihood, and Bayes estimators for some lifetime parameters (reliability, and hazard functions), as well as the parameters of the Burr-XII model, are derived. The Bayes estimators are obtained using both the symmetric (Squared Error, SE) loss function, and asymmetric (LINEX, and General Entropy, GE) loss functions. This was done with respect to the conjugate prior for the one shape parameter, and discrete prior for the other parameter of this model. Also the existence, uniqueness, and finiteness of the ML parameter estimates for this type of censoring are discussed. A practical example consisting of data from an accelerated test on insulating fluid reported by Nelson (1982) was used for illustration, and comparison. Finally, some numerical results using simulation study concerning different sample sizes, and progressive censoring schemes were reported.     

Sequential interval estimation procedures for the mean exponential survival time and reliability function

The problems of confidence interval estimation are considered (a) for estimating the mean of a one-parameter exponential distribution and (b) for estimating the reliability function associated with the one-parameter exponential distribution. For the estimation problem (a), the confidence interval of ‘preassigned width and coverage probability’ is considered. For the estimation problem (b), the confidence interval of ‘fixed-ratio width and preassigned coverage probability’ is proposed. The failure of the fixed sample size procedures to deal with these estimation problems is established and sequential procedures are proposed to deal with them. The proposed sequential procedures are proved to be ‘asymptotically efficient and consistent’ in the Chow-Robbins [Chow and Robbins, Ann. Math. Statist. 36,457–462 (1965)] sense. Asymptotic distributions of the stopping times are derived and second-order approximations are obtained for the average sample numbers associated with them.     

Estimation of average life for negative exponential distribution

This paper deals with the problem of average life estimation when the life times follow negative exponential distribution. A minimum mean square error estimator belonging to the class of linear combination of complete sufficient statistics has been obtained. The estimator thus obtained requires knowledge of coefficient of variation. The effect of using a guessed value of coefficient of variation on the estimator has also been studied.     

Interval estimation from censored and masked system-failure data

The author addresses confidence interval (CI) estimation in a competing risk (or multiple failure mode) framework where sample data are singly time-censored on the right and partially masked. A three-component series system with exponentially-distributed component-failure times is considered in order to represent cases involving full as well as partial masking. The approximate CIs considered are based on: asymptotic-normal theory for maximum likelihood estimators; cube-root transformation of the exponential distribution rate parameter; and inverted likelihood ratio tests. The small-sample coverage properties of these approximate CIs are estimated via computer simulation. These results also apply to models where component-failure times are Weibull distributed with known shape parameters     

Estimation of the mean of a quantized signal

The accuracy with which the mean of an analog signal can be estimated from the mean after quantization by an analog/digital converter is examined. The mean of the quantized signal is a good measure of the mean of the input, down to lower values of input noise than is commonly supposed.     

Maximum likelihood estimates, from censored data, for mixed-Weibulldistributions

An algorithm for estimating the parameters of mixed-Weibull distributions from censored data is presented. The algorithm follows the principle of the MLE (maximum likelihood estimate) through the EM (expectation and maximization) algorithm, and it is derived for both postmortem and non-postmortem time-to-failure data. The MLEs of the nonpostmortem data are obtained for mixed-Weibull distributions with up to 14 parameters in a five-subpopulation mixed-Weibull distribution. Numerical examples indicate that some of the log-likelihood functions of the mixed-Weibull distributions have multiple local maxima; therefore the algorithm should start at several initial guesses of the parameters set. It is shown that the EM algorithm is very efficient. On the average for two-Weibull mixtures with a sample size of 200, the CPU time (on a VAX 8650) is 0.13 s/iteration. The number of iterations depends on the characteristics of the mixture. The number of iterations is small if the subpopulations in the mixture are well separated. Generally, the algorithm is not sensitive to the initial guesses of the parameters     

Estimation in the 2-parameter exponential distribution with priorinformation

This paper proposes a class of estimators for the scale parameter and for the mean of a 2-parameter exponential distribution, which is important in life testing and reliability theory, given a prior estimate of the scale parameter. The class of estimators for the scale parameter is motivated by the work of Jani (1991). These estimators have smaller mean square error than the classical estimators for all values of the location parameter, and for values of the scale parameter in a neighborhood of the prior estimate. Numerical computations indicate that certain of these estimators substantially improve the classical estimators for values of the scale parameter near the prior estimate, especially for small sample sizes     

Nonparametric confidence bounds, using censored data, on the meanresidual life

An approach to inverting confidence bounds on the failure rate to obtain conservative nonparametric confidence statements about the mean residual life (MRL) for type I and II censoring and random right (left) censoring is described. A mild nonparametric condition of increasing (or decreasing) MRL is used. The condition of increasing (or decreasing) MRL is not required for the whole time axis. All example which uses type II censored data is included     

Testing exponentiality based on the Kullback-Leibler information with the type II censored data

We express the joint entropy of order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint entropy of the type II censored data. Then we establish a goodness of fit test statistic based on the Kullback-Leibler information with the type II censored data, and compare its performance with some leading test statistics. A Monte Carlo simulation study shows that the proposed test statistic shows better powers than some leading test statistics against the alternatives with monotone increasing hazard functions.     

机要数据分析与数据保护方法

机要数据存在于某个范围内,在未经许可的情况下不得访问,这些数据直接关系到各个政府、企业、研究机构的核心机密,甚至威胁到国家安全。按照数据特点的不同,机要数据通常包括:机要文件、电子图纸、财务资料、专利技术、运营统计。 机要数据的主要存在形式包括:办公类电子文件,常见的格式有DOC、XLS、MDB、WPS、PDF 等;图形类文件,常见的图类型文件通常保存的格式比较特殊,且基本都使用特定的应用程序打开。 机要数据主要分布在机要类政府部分、研究类机构、制造型企业、财务部门。 对于这种机要数据存在的网络环境,通常存在以下特点:…     

Admissibility of a conditionally specified test procedure for time censored life data

A test procedure may have a sufficiently large power and size under control, but its use is not advisable unless it is admissible. In other words, the admissibility of a test procedure is a desirable property in addition to having size and power. In this paper, the necessary and sufficient conditions for the admissibility of a conditionally-specified test procedure, for testing the scale parameter called ‘average life’ in a two-parameter exponential distribution under time censoring, have been derived.     

指数分步场合分组数据下简单步加试验的极大似然估计

对指数分布场合下的寿命分布进行研究,简单步进应力加速寿命试验中,在观察时间间隔不相等的条件下,对所获得的分组数据为寿命数据,给出加速方程中未知参数的极大似然估计（MLE）,从而计算出常应力下产品的平均寿命。     

Estimation of scale parameters for two exponential distributions[reliability theory]

The scale parameter of the exponential distribution is estimated using conditional specification. When there are two censored samples available for estimating the scale parameter, a preliminary test is usually used to determine whether to pool the samples or to use the individual minimum-variance unbiased estimator. This latter estimator (usual preliminary-test estimator) is studied. The optimum levels of significance and their corresponding critical values for the preliminary test are obtained on the basis of the minimax regret criterion. A preliminary-test shrinkage estimator is proposed, and the optimum values of its shrinkage estimator is proposed, and the optimum values of its shrinkage coefficients are obtained. For a mean-square-error criterion of goodness of estimation, the preliminary-test shrinkage estimator is better than the usual preliminary-test estimator     

Maximum likelihood estimation of the Burr XII parameters with censored and uncensored data

This paper presents the methodology for obtaining point and interval estimates of the parameters of the Burr Type XII distribution with multiple-censored and singly-censored data (Type I censoring or Type II censoring) as well as complete data, using the maximum likelihood method. The basis is the likelihood expression for multiple-censored data. The other types of censoring and complete data are treated as special cases. A FORTRAN language program was used. Some illustrative examples are included.     

CSCC for the mean and standard deviation of non-normally distributed life test data

In this paper Cumulative Sum Control Charts (CSCC) have been constructed for the mean and standard deviation of non-normally distributed life test data. The parameters of the V-mask have been determined and finally the expression for the Average Run Length is derived.     

Goodness-of-fit tests based on spacings for progressively type-II censored data from a general location-scale distribution

There has been extensive research on goodness-of-fit procedures for testing whether or not a sample comes from a specified distribution. These goodness-of-fit tests range from graphical techniques, to tests which exploit characterization results for the specified underlying model. In this article, we propose a goodness-of-fit test for the location-scale family based on progressively Type-II censored data. The test statistic is based on sample spacings, and generalizes a test procedure proposed by Tiku . The distribution of the test statistic is shown to be approximated closely by a s-normal distribution. However, in certain situations it would be better to use simulated critical values instead of the s-normal approximation. We examine the performance of this test for the s-normal and extreme-value (Gumbel) models against different alternatives through Monte Carlo simulations. We also discuss two methods of power approximation based on s-normality, and compare the results with those obtained by simulation. Results of the simulation study for a wide range of sample sizes, censoring schemes, and different alternatives reveal that the proposed test has good power properties in detecting departures from the s-normal and Gumbel distributions. Finally, we illustrate the method proposed here using real data from a life-testing experiment. It is important to mention here that this test can be extended to multi-sample situations in a manner similar to that of Balakrishnan et al.