Bivariate degradation analysis of products based on Wiener processes and copulas

Modern highly reliable products usually have complex structure and many functions. This means that they may have two or more performance characteristics. All the performance characteristics can reflect the product's performance degradation over time, and they may be independent or dependent. If the performance characteristics are independent, they can be modelled separately. But if they are not independent, it is very important to find the joint distribution function of the performance characteristics for estimating the reliability of the product as accurately as possible. Here, we suppose that a product has two performance characteristics and the degradation paths of these two performance characteristics can be governed by a Wiener process with a time-scale transformation, and that the dependency of the performance characteristics can be described by a copula function. The parameters of the two performance characteristics and the copula function can be estimated jointly. The model in such a situation is very complicated and analytically intractable and becomes cumbersome from a computational viewpoint. For this reason, the Bayesian Markov chain Monte Carlo method is developed for this problem that allows the maximum-likelihood estimates of the parameters to be determined in an efficient manner. For an illustration of the proposed model, a numerical example about fatigue cracks is presented.     

Evaluation of Beta Generation Algorithms

In this article, we discuss the maximum likelihood estimates (MLEs) for the exponential and Weibull distributions by considering progressive Type-I interval censored data. For exponential distribution, the explicit expression of MLE of failure rate cannot be obtained when the intervals are not equal in length. The direct application of some numerical algorithms, such as the Newton–Raphson algorithm, is non-ideal because of the cumbersome second derivative. We apply some equivalent quantities to obtain the MLE of failure rate of exponential distribution. Based on the equivalent quantities and the Weibull-to-exponential transformation technique, we propose a new algorithm to obtain the MLEs for the parameters of progressive Type-I interval Weibull data. An example reanalysis and some simulation studies are carried out to illustrate the performance of the estimations using the new algorithm.     

On Regression Analysis with Data Cleaning via Trimming,Winsorization, and Dichotomization

ABSTRACT

In a two-variable regression model setup, we examine in this paper the effects of trimming and winsorization and dichotomization of the independent variable on the regression estimates and the efficiency of the regression estimation. These results have direct implications in the accounting literature when dealing with the effects of analyst forecast errors on stock returns.     

Hessian orderings of multivariate normal variance-mean mixture distributions and their applications in evaluating dependent multivariate risk portfolios

Statistical Methods & Applications - In this paper, some stochastic comparison results are developed for the class of multivariate normal variance-mean mixture (NVM) distributions. These...     

Rationing Capacity Between Two Product Classes*

In this paper, we study the capacity allocation problem faced by make-to-order manufacturing firms encountering expected total demand in excess of available capacity. Specifically, we focus on firms' manufacturing short-life-cycle or seasonal products such as high fashion apparel. Using a decision-theory-based approach, we develop a capacity allocation policy that allows such firms to discriminate between two classes of products (one yielding a higher profit contribution per unit of capacity allocated to it than the other), resulting in selective rejection of orders for the class with the lower unit contribution. The effectiveness of capacity rationing is investigated under a wide array of conditions characterized by variations in factors such as the ratio of unit profit contributions of the two product classes, the ratio of total available capacity to expected total demand, the ratio of expected demands between the two classes, and the variability in demand for each product class. The results indicate that capacity rationing is very effective in increasing the total profit, and could therefore serve as a valuable decision tool for managers in such firms.