Weibull Lifetime Distribution Research Articles

DESIGN OF FAILURE-CENSORED ACCELERATED LIFE-TEST SAMPLING PLANS FOR LOGNORMAL AND WEIBULL DISTRIBUTIONS

This paper considers the design of life-test sampling plans based on failure-censored accelerated life tests for products with lognormal and Weibull lifetime distributions. Two levels of stress higher than the use condition stress, high and low, are used. The sample size, sample proportion allocated to each stress level, and the lot acceptability constant which satisfy the producer's risk and consumer's risk and minimize the generalized asymptotic variance of the maximum likelihood estimators of the model parameters are obtained. The properties of the proposed sampling plans are investigated.

The inverse power law model for the lifetime of a mylar-polyurethane laminated dc hv insulating structure

Results of an accelerated test on the lifetime of a mylar-polyurethane laminated dc high voltage insulating structure are reported. This structure consists of mylar ribbons placed side by side in a number of layers, staggered and glued together with a polyurethane adhesive. The lifetime until breakdown as a function of extremely high values of voltage stress is measured and represented by a mathematical model, the inverse power law model with a 2-parameter Weibull lifetime distribution. The statistical treatment of the data — either by graphical or by analytical methods — allowed us to estimate the lifetime distribution and confidence bounds for any required normal voltage stress. The laminated structure under consideration is, according to the analysis, a very reliable dc hv insulating material, with a very good life performance according to the inverse power law model, and with an exponent of voltage stress equal to 6. A large insulator of cylindrical shape with this kind of laminated structure can be constructed by winding helically a mylar ribbon in a number of layers.

An accelerated life test model with the inverse power law

Abstract Constant and progressive stress accelerated life test models based on the inverse power law and Weibull lifetime distributions are proposed in which the Weibull scale parameter at use condition has a gamma prior distribution and other parameters are unknown constants. Bayes and maximum likelihood methods are used to estimate the model parameters. Monte Carlo study is performed to investigate the behaviour of the estimators.

An informative bayesian prediction for the weibull lifetime distribution

Suppose components have lifetimes which follow a Weibull distribution with both scale and shape parameters unknown. Given the first r (r fixed) failure times of a sample of n components (type 2 censoring), predictions are to be made on the failure times of the remaining components in the sample (one sample prediction) and the lifetimes of unused components (two sample prediction). An outline is given of the general Bayesian approach for this problem using an informative Bayesian prior for both parameters. Iterative procedures involving considerable computation are necessary for calculating prediction bounds, but some simplification is possible on restricting the shape parameter to a finite number of values. Numerical examples are used to illustrate the procedure.

An Informative Bayesian Prediction for the Weibull Lifetime Distribution

An Informative Bayesian Prediction for the Weibull Lifetime Distribution

Bayesian One-Sample Prediction for the Two-Parameter Weibull Lifetime Distribution

Bayesian One-Sample Prediction for the Two-Parameter Weibull Lifetime Distribution

Sequential determination of inspection epochs for reliability systems with general lifetime distributions

AbstractThe problem of determining the optimal inspection epoch is studied for reliability systems in which N components operate in parallel. Lifetime distribution is arbitrary, but known. The optimization is carried with respect to two cost factors: the cost of inspecting a component and the cost of failure. The inspection epochs are determined so that the expected cost of the whole system per time unit per cycle will be minimized. The optimization process depends in the general case on the whole failure history of the system. This dependence is characterized. The cases of Weibull lifetime distributions are elaborated and illustrated numerically. The characteristics of the optimal inspection intervals are studied theoretically.