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Parts manufacturers use sudden death testing to reduce the testing time of experiments. The sudden death testing plan in the literature can only be applied when all observations of failure time/parameters are crisp. In practice however, it is noted that not all measurements of continuous variables are precise. Therefore, the existing sudden death test plan can be applied if failure data/or parameters are imprecise, incomplete, and fuzzy. The classical statistics have the special case of neutrosophic statistics when there are no fuzzy observations/parameters. The neutrosophic fuzzy statistics can be applied for the testing of manufacturing parts when observations are imprecise, incomplete and fuzzy. In this paper, we will design an original neutrosophic fuzzy sudden death testing plan for the inspection/testing of the electronic product or parts manufacturing. We will assume that the lifetime of the product follows the neutrosophic fuzzy Weibull distribution. The neutrosophic fuzzy operating function will be given and used to determine the neutrosophic fuzzy plan parameters through a neutrosophic fuzzy optimization problem. The results of the proposed neutrosophic fuzzy death testing plan will be implemented with the aid of an example.

The Weibull distribution is a very applicable model for the lifetime data. In this paper, we have investigated inference on the parameters of Weibull distribution based on record values. We first propose a simple and exact test and a confidence interval for the shape parameter. Then, in addition to a generalized confidence interval, a generalized test variable is derived for the scale parameter when the shape parameter is unknown. The paper presents a simple and exact joint confidence region as well. %for the scale and shape parameters. In all cases, simulation studies show that the proposed approaches are more satisfactory and reliable than previous methods. All proposed approaches are illustrated using a real example.

The present paper is concerned with using  Bayesian and E-Bayesian method of estimation to find estimates for the shape parameter of Exponentiated Inverted Weibull distribution. These estimators are derived by using different loss functions. In this paper, Bayesian estimates are derived by using informative prior.

The present paper is concerned with using  Bayesian and E-Bayesian method of estimation to find estimates for the shape parameter of Exponentiated Inverted Weibull distribution. These estimators are derived by using different loss functions. In this paper, Bayesian estimates are derived by using informative prior.

Budget limitations have reduced the number of military components available for testing, and time constraints have reduced the amount of time available for actual testing resulting in many items still operating at the end of test cycles. These two factors produce small test populations (small sample size) with heavily censored data. The assumption of normal approximation for estimates based on these small sample sizes reduces the accuracy of confidence bounds of the probability plots and the associated quantities. This creates a problem in acquisition analysis because the confidence in the probability estimates influences the number of spare parts required to support a mission or deployment or determines the length of warranty ensuring proper operation of systems. This thesis develops a method that simulates small samples with censored data and examines the error of the Fisher-Matrix (FM) and the Likelihood Ratio Bounds (LRB) confidence methods of two test populations (size 10 and 20) with three, five, seven and nine observed failures for the Weibull distribution. This thesis includes a Monte Carlo simulation code written in S-Plus that can be modified by the user to meet their particular needs for any sampling and censoring scheme. To illustrate the approach, the thesis includes a catalog of corrected confidence bounds for the Weibull distribution, which can be used by acquisition analysts to adjust their confidence bounds and obtain a more accurate representation for warranty and reliability work.

Two new goodness-of-fit tests are developed for the three-parameter Weibull distribution with known shape parameter. These procedures eliminate the need for estimating the unknown location and scale parameters prior to initiating the tests and are easily adapted for censored data. This is accomplished by employing the Anderson-Darling and Cramer-von Mises statistics based on the normalized spacings of the sample data. Critical values of the new tests are obtained for common significance levels by large Monte Carlo simulations for shapes 0.5(0.5)4.0 and sample sizes 5(5)40 with up to 40% censoring (Type II) from the left and/or right. An extensive Monte Carlo power study is also conducted to compare the two tests with each other and with their prominent competitors. The competitors include another spacings test, Z*, and the modified Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling EDF tests. Results show the Anderson-Darling spacings test is the preferred test for the three-parameter Weibull distribution with known shape parameter.

Estimates of the Weibull distribution parameters were made employing the mean ranks estimator; the estimates were repeated using the median ranks estimator. These estimates were compared to known values of the Weibull distribution parameters. This made it possible to compare the results obtained using either estimator (mean ranks or median ranks) and to determine the relative merits of using either estimator. The study made use of a digital computer and employed Monte-Carlo techniques to simulate Weibull distributed failure times. These failure times may represent tank-automotive component failures.

Estimates of the Weibull distribution parameters were made employing the mean ranks estimator; the estimates were repeated using the median ranks estimator. These estimates were compared to known values of the Weibull distribution parameters. This made it possible to compare the results obtained using either estimator (mean ranks or median ranks) and to determine the relative merits of using either estimator. The study made use of a digital computer and employed Monte-Carlo techniques to simulate Weibull distributed failure times. These failure times may represent tank-automotive component failures.

The paper develops a Monte Carlo technique which, with a digital computer, determines confidence limits for system reliability of complex systems containing components characterized by the Weibull distribution. The component distribution shape and scale parameters are estimated by the method of maximum likelihood from component failure times while the location parameter is assumed known. The asymptotic distribution of these maximum likelihood estimators and a Monte Carlo simulation are used to determine confidence limits on system reliability. As an example, confidence limits are calculated for two systems of up to eight components in combinations of series and parallel configurations using 99, 499, 999, and 2999 simulations. Accuracy of the confidence limits is found to be satisfactory after being checked by a method using a double Monte Carlo technique.