This paper is concerned with the optimal control of a production inventory system with deteriorating items. It is assumed that the deterioration rate follows the two-parameter Weibull distribution. The continuous-review and periodic-review policies are investigated. In each case, optimality conditions are derived. Also, numerical illustrative examples are presented.

The exponentiated -parent distribution is a generalization of the standard parent distribution. [7] introduced a simple generalization to weibull distribution namely the exponentiated weibull distribution. The new distribution was applied to analyzing bathtub failure rates lifetime data. In this paper, we consider the standard exponentiated inverted weibull distribution (EIW) that generalizes t...

For the first time, a three-parameter lifetime model, called the Weibull Rayleigh distribution, is defined and studied. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood and least squares methods is used for estimating the model parameters and the observed Fisher’s information matrix is derived. We ill...

A number of global optimisation algorithms rely on the value of the Lipschitz constant of the objective function. In this paper we present a stochastic method for estimating the Lipschitz constant. We show that the largest slope in a fixed size sample of slopes has an approximate Reverse Weibull distribution. Such a distribution is fitted to the largest slopes and the location parameter used as...

Lower bounds are typically used to evaluate the performance of heuristics for solving combinatorial minimization problems. In the absence of tight analytical lower bounds, optimal objective-function values may be estimated statistically. In this paper, extreme value theory is used to construct confidence-interval estimates of the minimum makespan achievable when scheduling nonsimilar groups of ...

In this paper, a new class of five parameter gamma-exponentiated or generalized modified Weibull (GEMW) distribution which includes exponential, Rayleigh, Weibull, exponentiated gamma gamma-modified gamma-Weibull, gamma-Rayleigh and gamma-exponential distributions as special cases is proposed studied. Mathematical properties including moments, mean deviations, Bonferroni Lorenz curves, order st...

In this paper, the test purpose will be to assess whether or not the accelerated model proposed by Eyring will be able to translate results for the shape and scale parameters of an underlying Weibull model, obtained under two accelerating using conditions, to expected normal using condition results for these parameters. The product being analyzed is a new type of insulate fluid, and the acceler...

In many applications of failure time data analysis, it is important to perform inferences about the median of the distribution function in situations of failure time data modeling with skewed distribution. For failure time distributions where the median of the distribution function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties...

In this article, we introduce a method for monitoring the Weibull shape parameter β with type II (failure) censored data. The control limits depend on the sample size, the number of censored observations, the target average run length, and the stable value of β. The method assumes that the scale parameter α is constant during each sampling period, which is true under rational subgrouping. The p...

A method is described for the calculation of the three-parameter Weibull distribution function from censored samples. The method introduces a data driven technique based on an adapted Gaussian like kernel to match the censoring scheme. The method minimizes the Cramer von Mises distance from a non-parametric density estimate and the parametric estimate at the order statistics. The maximum likeli...