Testing the nonrandomness of breakage at a chromosome band is an essential step for identifying a fragile site. In this paper, we propose a method derived by using the relationship between the binomial and F distributions for testing nonrandomness. The method is simple in calculation. It was applied to the detection of fragile sites for Chinese patients with colorectal carcinoma.

The process personnel always seeks the opportunity to improve the processes. One of the essential steps for process improvement is to quickly recognize the starting time or the change point of a process disturbance. Different from the traditional normally distributed assumption for a process, this study considers a process which follows a gamma distribution. This study proposes an effective approach to estimate the change point of a gamma process. The proposed approach combines the commonly used S control chart with the maximum likelihood (ML) technique. This study applies the Monte Carlo technique to determine the upper and lower control limits for a gamma process when the S control chart is used to monitor a gamma process. The fruitful results with the use of the proposed approach are also demonstrated.

The meta-analysis of P-values is a widely used method in integrating information from multiple studies, and much research has focused on combining P-values. Among the established approaches, Fisher's test may be the most popular one. Many studies have been devoted to extending or modifying Fisher's statistic. For example, Lancaster’s variation of Fisher’s method may outperform the weighted Z-test and recently has drawn noteworthy attention. In this study, we first extend Lancaster's statistic by incorporating a weighting scheme. An approximation and an algorithm that are suitable for use under both independence and dependence assumptions are proposed for calculating the distribution of the weighted Lancaster statistic. The relationships between this method and existing ones are discussed. An application of the main results to a linkage test method in human gene mapping is then provided to show its use.

The fraction nonconforming, which follows a binomial distribution, is one of the most critical quality characteristics of attribute processes. In addition, the multivariate binomial process plays an important role in industries due to the enormous diversity of quality characteristics. A multivariate binomial process is deemed out of control when it triggers a signal in a multivariate statistical process control chart. However, it is difficult to determine which quality characteristic triggers the nonconforming shift. In contrast to most current studies that identify the contributors of shifts in multivariate normal processes, this study discusses the contributors of fraction nonconforming shifts in multivariate binomial processes. First, a test that can be applied to detect outliers in a multivariate binomial distribution is proposed. In addition, a stepwise test method that can be used to determine the contributors of fraction nonconforming shifts in a multivariate binomial process is then developed. Numerical results indicate that the method proposed is effective in determining the contributors of fraction nonconforming shifts for a multivariate binomial process.

The achievable capacity index (ACI) is a simple and efficient approach for estimating the profitability of newsboy-type products, wherein profitability is defined as the probability of achieving the target profit by optimizing the order quantity. At present, the ACI is applicable to single retail stores (i.e., single demand) but not to multiple sales channels (i.e., multiple demand). This paper presents an integrated achievable capacity index (IACI) by which to measure the aggregate profitability of multiple mutually independent channels under normally distributed demand. An unbiased IACI estimator is also developed, to which is applied the Taylor expansion to approximate its sampling distribution, wherein the sizes, means, and variances of demand differ in each channel. Furthermore, overestimates due to sampling error are avoided by deriving the lower confidence bound for the IACI. This paper also provides generic tables to aid managers seeking conservative estimates of profitability. The applicability of the proposed scheme is demonstrated numerically using a real-world example involving an own-branding-and-manufacturing (OBM) enterprise with multiple owned channels.