On the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty hypercube

Hsieh and Yu (2007) first claimed that an injured n-dimensional hypercube Q _n contains (n?1?f)-mutually independent fault-free Hamiltonian cycles, where f≤n?2 denotes the total number of permanent edge-faults in Q _n for n≥4, and edge-faults can occur everywhere at random. Later, Kueng et al. (2009a) presented a formal proof to validate Hsieh and Yu’s argument. This paper aims to improve this mentioned result by showing that up to (n?f)-mutually independent fault-free Hamiltonian cycles can be embedded under the same condition. Let F denote the set of f faulty edges. If all faulty edges happen to be incident with an identical vertex s, i.e., the minimum degree of the survival graph Q _n ?F is equal to n?f, then Q _n ?F contains at most (n?f)-mutually independent Hamiltonian cycles starting from s. From such a point of view, the presented result is optimal. Thus, not only does our improvement increase the number of mutually independent fault-free Hamiltonian cycles by one, but also the optimality can be achieved.     

Accounting Performance and Capacity Investment Decisions: Evidence from California Hospitals

Capacity decisions involve trade‐offs between the cost of capacity and the opportunity costs of lost sales. Accounting researchers posit that accounting performance provides sufficient information about these trade‐offs and thus can be used to formulate simple rules to assist capacity decisions. Empirical research has not examined the role of accounting information in capacity investment decisions at the department level in a multiproduct firm in the presence of social costs. Empirical analyses using department‐level data from California hospitals for the period 1998–2005 show that hospitals are more likely to make capacity investments in departments with high accounting performance. However, in the presence of demand variability, the association between accounting performance and capacity investment is attenuated because of the resulting increase in noise in accounting performance measures. Thus, the weight on accounting performance as a decision tool for capital investments reduces when there is demand variability. Another factor that reduces the weight on accounting performance is capacity utilization. Higher capacity utilization can lead to turning away or rerouting of patients to other hospitals and negatively impacts reputation and quality of care, which increases the hospital's social costs. Hence, hospitals do not require high accounting performance before investing in a department with high capacity utilization. This empirical evidence of the role of accounting performance in capacity investment decisions fills a gap in the capacity investment literature and furthers our understanding of the interactions between accounting performance and the operational determinants of firms’ capacity investment behavior.     

Maximum Chi-Square Generally Weighted Moving Average Control Chart for Monitoring Process Mean and Variability

In this article, we propose a new control chart called the maximum chi-square generally weighted moving average (MCSGWMA) control chart. This control chart can effectively combine two generally weighted moving average (GWMA) control charts into a single one and can detect both increases as well as decreases in the process mean and/or variability simultaneously. The average run length (ARL) characteristics of the MCSGWMA and maximum exponentially weighted moving average (MaxEWMA) charts are evaluated by performing computer simulations. The comparison of the ARLs shows that the MCSGWMA control chart performs better than the MaxEWMA control chart.     

Shelf-life and its estimation in drug stability studies

One important property of any drug product is its stability over time. Drug stability studies are routinely carried out in the pharmaceutical industry in order to measure the degradation of an active pharmaceutical ingredient of a drug product. One important study objective is to estimate the shelf-life of the drug; the estimated shelf-life is required by the US Food and Drug Administration to be printed on the package label of the drug. This involves a suitable definition of the true shelf-life and the construction of an appropriate estimate of the true shelf-life. In this paper, the true shelf-life T_β is defined as the time point at which 100β% of all the individual dosage units (e.g. tablets) of the drug have the active ingredient content no less than the lowest acceptable limit L, where β and L are prespecified constants. The value of T_β depends on the parameters of the assumed degradation model of the active ingredient content and so is unknown. A lower confidence bound T?_β for T_β is then provided and used as the estimated shelf-life of the drug.     

The Lehmann Model with Time-dependent Covariates

Consider the Lehmann model with time-dependent covariates, which is different from Cox’s model. We find out that (1) the parameter space for β under the Lehmann model is restricted, and the maximum point of the parametric likelihood for β may lie outside the parameter space; (2) for some particular time-dependent covariate, under the standard generalized likelihood the semiparametric maximum likelihood estimator (SMLE) is inconsistent and we propose a modified generalized likelihood which leads to the consistent SMLE.     

Some sequential selection procedures for good regression models

In the past decade a number of fixed sampling methods have been developed for selecting the "best" or at least a "good" subset of vaiable in regression analysis. We are interested in deriving a sequential selection procedure to select a subset of a random size including equations. Tables for an example are given at the end of this paper     

Hamiltonicity of hypercubes with a constraint of required and faulty edges

Let R and F be two disjoint edge sets in an n-dimensional hypercube Q _n . We give two constructing methods to build a Hamiltonian cycle or path that includes all the edges of R but excludes all of F. Besides, considering every vertex of Q _n incident to at most n−2 edges of F, we show that a Hamiltonian cycle exists if (A) |R|+2|F|≤2n−3 when |R|≥2, or (B) |R|+2|F|≤4n−9 when |R|≤1. Both bounds are tight. The analogous property for Hamiltonian paths is also given. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday. Lih-Hsing Hsu’s research project is partially supported by NSC 95-2221-E-233-002. Shu-Chung Liu’s research project is partially supported by NSC 90-2115-M-163-003 and 95-2115-M-163-002. Yeong-Nan Yeh’s research project is partially supported by NSC 95-2115-M-001-009.     

Statistical analysis of firm interdependence using duration data—parametric approach

A pioneer first enters the market as the monopolist and later experiences the competition when a similar product is brought to the market by the competitor. In 2012, Wang and Xie suggested to decompose the pioneer survival to “monopoly” and “competition” durations and estimate the two survivals of the pioneer individually with the competitor's survival via regression analysis. In their article, several regression analyses were performed to study the effect of order entry to the pioneer and the later entrant in different market status. Using the same datasets from their study, our main interest is to investigate the interdependent relationship between two competitive firms and study whether the market pioneer and the later entrant can benefit from the competition. The major contribution of this article is that the interdependence between two competitive firms is explicitly expressed and three survival durations can be estimated in one model. The proposed method relates the survival times of two competitive firms to pioneer's monopoly time and some observable covariates via proportional hazard model, and incorporates frailty variables to capture the interdependence in the competition. This article demonstrates a new method that formulates the interdependence between competitive firms and shows data analyses in the industries of newspapers and high technology.     

Missing genetic information in case-control family data with general semi-parametric shared frailty model

Case-control family data are now widely used to examine the role of gene-environment interactions in the etiology of complex diseases. In these types of studies, exposure levels are obtained retrospectively and, frequently, information on most risk factors of interest is available on the probands but not on their relatives. In this work we consider correlated failure time data arising from population-based case-control family studies with missing genotypes of relatives. We present a new method for estimating the age-dependent marginalized hazard function. The proposed technique has two major advantages: (1) it is based on the pseudo full likelihood function rather than a pseudo composite likelihood function, which usually suffers from substantial efficiency loss; (2) the cumulative baseline hazard function is estimated using a two-stage estimator instead of an iterative process. We assess the performance of the proposed methodology with simulation studies, and illustrate its utility on a real data example.