Identifying and using critical success factors

This article focuses on defining and discussing the concept of critical success factors as input into the environment analysis, resource analysis, and strategy evaluation steps in the strategic planning/strategy development process. The reader is provided with eight possible sources of critical success factors including environmental analysis, analysis of industry structure, industry/business experts, analysis of competition, analysis of dominant firm in the industry, company assessment, temporal/intuitive factors and PIMS results. Examples of CSF's from various sources are provided and a scheme by which the reader can assess the relative importance of identified CSF's is presented.     

Consumer processing of hazard warning information

Using data obtained from a field experiment involving 957 consumers, this study investigates the linkage between hazard warnings and precautionary behavior, as well as the structure of the information about product usage and risks that consumers store in their memories. Through the use of a methodology based on an open-ended memory recall task, we measure how consumer recall of information on product labels is affected by the type and format of the information and infer the structure by which this information is stored in their memory. The methodology also allows us to explore the importance of limitations on consumers' cognitive abilities. In particular, we find that consumers substitute greater recall of risk information for recall of usage information, indicating a tradeoff among the different types of information conveyed on a product label. We also found that in the case of cluttered labels, as typified by many existing product labels, information overload results, which may make labeling ineffective in achieving its intended informational objective.     

Multi‐Echelon Inventory Management under Short‐Term Take‐or‐Pay Contracts

We extend the Clark–Scarf serial multi‐echelon inventory model to include procuring production inputs under short‐term take‐or‐pay contracts at one or more stages. In each period, each such stage has the option to order/process at two different cost rates; the cheaper rate applies to units up to the contract quantity selected in the previous period. We prove that in each period and at each such stage, there are three base‐stock levels that characterize an optimal policy, two for the inventory policy and one for the contract quantity selection policy. The optimal cost function is additively separable in its state variables, leading to conquering the curse of dimensionality and the opportunity to manage the supply chain using independently acting managers. We develop conditions under which myopic policies are optimal and illustrate the results using numerical examples. We establish and use a generic one‐period result, which generalizes an important such result in the literature. Extensions to cover variants of take‐or‐pay contracts are included. Limitations are discussed.     

A competing risks derivation of a mixture model for the analysis of survival data

Boag (1949) and Berkson and Gage (1952) proposed a mixture model for the analysis of survival time data when aproportion of treated patients are cured. This paper presents a derivation of the Boag/Berkson-Gage mixture model as well as a eneralization of the model based on the theory of competing risks. The assumptions underlying the model are stated and discussed and a general likelihood function is obtained. Use of the model is illustrated ith data from the Stanford Heart Transplant Program.     

Statistics of Primes (and Probably Twin Primes) Satisfy Taylor's Law from Ecology

Taylor's law, which originated in ecology, states that, in sets of measurements of population density, the sample variance is approximately proportional to a power of the sample mean. Taylor's law has been verified for many species ranging from bacterial to human. Here, we show that the variance V(x) and the mean M(x) of the primes not exceeding a real number x obey Taylor's law asymptotically for large x. Specifically, V(x) ～ (1/3)(M(x))² as x → ∞. This apparently new fact about primes shows that Taylor's law may arise in the absence of biological processes, and that patterns discovered in biological data can suggest novel questions in number theory. If the Hardy-Littlewood twin primes conjecture is true, then the identical Taylor's law holds also for twin primes. Taylor's law holds in both instances because the primes (and the twin primes, given the conjecture) not exceeding x are asymptotically uniformly distributed on the integers in [2, x]. Hence, asymptotically M(x) ～ x/2, V(x) ～ x²/12. Higher-order moments of the primes (twin primes) not exceeding x satisfy a generalized Taylor's law. The 11,078,937 primes and 813,371 twin primes not exceeding 2 × 10⁸ illustrate these results.     

Applying Cognitive Theory to Statistics Instruction

This article presents five principles of learning, derived from cognitive theory and supported by empirical results in cognitive psychology. To bridge the gap between theory and practice, each of these principles is transformed into a practical guideline and exemplified in a real teaching context. It is argued that this approach of putting cognitive theory into practice can offer several benefits to statistics education: A means for explaining and understanding why reform efforts work; a set of guidelines that can help instructors make well-informed design decisions when implementing these reforms; and a framework for generating new and effective instructional innovations.     

Therapeutic Hypothermia: Quantification of the Transition of Core Body Temperature Using the Flexible Mixture Bent‐Cable Model for Longitudinal Data

Hypothermia which is induced by reducing core body temperature is a therapeutic tool used to prevent brain damage resulting from physical trauma. However, all physiological systems begin to slow down due to hypothermia and this can result in increased risk of mortality. Therefore quantification of the transition of core body temperature to early hypothermia is of great clinical interest. Conceptually core body temperature may exhibit an either gradual or abrupt transition. Bent‐cable regression is an appealing statistical tool to model such data due to the model's flexibility and readily interpretable regression coefficients. It handles more flexibly models that traditionally have been handled by low‐order polynomial models (for gradual transition) or piecewise linear changepoint models (for abrupt change). We consider a rat model to quantify the temporal trend of core body temperature primarily to address the question: What is the critical time point associated with a breakdown in the compensatory mechanisms following the start of hypothermia therapy? To this end, we develop a Bayesian modelling framework for bent‐cable regression of longitudinal data to simultaneously account for gradual and abrupt transitions. Our analysis reveals that: (i) about 39% of rats exhibit a gradual transition in core body temperature; (ii) the critical time point is approximately the same regardless of transition type; and (iii) both transition types show a significant increase of core body temperature followed by a significant decrease.