A generalization of the log-series distribution

A new generalized logarithmic series distribution (GLSD) with two parameters is proposed.The proposed model is flexible enough to describe short-tailed as well as long-tailed data.Some recurence relations for its probabilities and the factorial moments are presente.These recurrence relations are utilized to obtain the minimum chi-square estimators for the parmaters.Maximum likelihood estimators and some other estimators based on first few moments and probabilities are also suggested.Asymptotic relative efficiency of some of these estimators is also obtained and compared.Two test statistics based on the minimum chi-square estimators fo testing some hypotheses regarding the GLSD are proposed.The fit of the model and the application of the test statistics are exemplified by some data sets.Finally, a graphical method is suggested for differentiating between the ordinary logarithmic series distribution and the GLSD.     

Estimation of the parameters in a truncated normal distribution

This paper deals with the estimation of the parameters of doubly truncated and singly truncated normal distributions when truncation points are known. We derive, for these families, a necessary and sufficient condition for the maximum likelihood estimator(MLE) to be finite. Furthermore, the probability of the MLE being infinite is positive. A simulation study for single truncation is carried out to compare the modified maximum likelihood estimator, and the mixed estimator.     

Bi-directional system analysis under copula-coverage approach

Reliability assessment is a major step, toward the development of fault-tolerant computing system. In different fields of engineering and physical/ailed sciences, researchers or engineers have several reliability approaches for the better performance of the system. By assuming different types of time trends, failure modes and repair effects, the legion stochastic model has been developed for repairable system. This study shows a novel concept for three state fault tolerant repairable systems with two types of repair. This research predicts the effect of the coverage factor using Gumbel-Hougaard family of copula approach on reliability characteristics of the designed system.     

A Bayesian approach to mixture cure models with spatial frailties for population‐based cancer relative survival data

As the treatments of cancer progress, a certain number of cancers are curable if diagnosed early. In population‐based cancer survival studies, cure is said to occur when mortality rate of the cancer patients returns to the same level as that expected for the general cancer‐free population. The estimates of cure fraction are of interest to both cancer patients and health policy makers. Mixture cure models have been widely used because the model is easy to interpret by separating the patients into two distinct groups. Usually parametric models are assumed for the latent distribution for the uncured patients. The estimation of cure fraction from the mixture cure model may be sensitive to misspecification of latent distribution. We propose a Bayesian approach to mixture cure model for population‐based cancer survival data, which can be extended to county‐level cancer survival data. Instead of modeling the latent distribution by a fixed parametric distribution, we use a finite mixture of the union of the lognormal, loglogistic, and Weibull distributions. The parameters are estimated using the Markov chain Monte Carlo method. Simulation study shows that the Bayesian method using a finite mixture latent distribution provides robust inference of parameter estimates. The proposed Bayesian method is applied to relative survival data for colon cancer patients from the Surveillance, Epidemiology, and End Results (SEER) Program to estimate the cure fractions. The Canadian Journal of Statistics 40: 40–54; 2012 © 2012 Statistical Society of Canada     

Models and Methods to Support a New Type of Inventory Performance Measure: The ESWSO

When analyzing a reorder point, order quantity (r, Q) inventory systems, one important question that often gets very little, if any, attention is: When a stockout occurs, how large is it? This paper is directed at researchers and practicing inventory planners with two objectives. First, we provide several models and algorithms to compute the Expected Shortages When a Stockout Occurs (ESWSO) for a variety of stochastic environments. We show that when ESWSO, is used in conjunction with the traditional fill rate measures it greatly enhances a planners ability to plan for shortages. Second, we develop two cost‐minimizing inventory models—one addressing the backorder and the other the shortage scenario—to show how the ESWSO can be seamlessly integrated into an inventory‐cost framework to specify lot sizes and safety stocks.     

The Impact of Imperfect Processes on Production Run Times

This paper investigates the interaction between the economics of production and imperfections in the production process. Specifically, this paper is the first to devise a model in an attempt to provide managers with guidelines to choose the appropriate production run times to buffer against both the production of defective items and stoppages occurring due to machine breakdowns. In addition to providing several structural properties of the model, we show that a manager will always incur a cost penalty when (s)he uses the results of two oft‐cited models‐the EMQ (Economic Order/Manufacturing Quantity) and the NR‐E (No‐Resumption, Exponential machine breakdown)‐to determine production run times.     

Planned Lead Times in Multistage Systems

This study investigates the impact of planned lead times on performance in multistage manufacturing where material requirements planning is used in a make-to-stock environment. We simulate a variety of different operating environments and find: (1) planned lead times are important to customer service levels under all operating environments examined, but have a smaller impact on inventory investment; (2) tight due dates introduced by short planned lead times hurt customer service without saving much inventory; (3) small increases to tight planned lead times improve customer service substantially with small inventory increases; (4) co-component inventories change with planned lead times, and disparity between such inventories is a sign of poor timing coordination; (5) the fixed order quantity rule performs better than the periodic order quantity rule; and (6) tall product structure and large lot sizes require particular attention to planned lead times. The findings also extend the current understanding of planned lead times by including uncertainties such as forecast error, yield loss, and equipment reliability. The study concludes with a way to diagnose and improve poorly set planned lead times.