Patient Safety Mathematics

various mathematics and probability concepts are being used to study various types of safety-related problems. For example, probability distributions are used to represent times to human error in performing various types of time-continuous tasks in the area of safety [3-7]. In addition, the Markov method is used to conduct human performance reliability analysis in regard to engineering systems safety [7-9]. 

This chapter presents various mathematical concepts considered useful to perform mathematical analysis in the area of patient safety. 

2 Range, Mode, Median, Arithmetic Mean, and Mean Deviation 

A set of given patient safety or other data is only useful if it is analyzed properly. Certain characteristics of data play a key role in describing the nature of a given set of data, thus allowing people to make better decisions. This section presents a number of statistical measures considered useful to perform patient safety-related analysis. 

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A large number of probability distributions have been developed in the area of mathematics to perform various types of analysis [15,161. This section presents some of the probability distributions considered useful to perform patient safety-related analysis. 

Table 2.1 presents Laplace transforms of a number of functions considered useful to perform mathematical patient safety analysis [18,19]. 

Professionals working in the area of human factors have developed many mathematical formulas for estimating various types of human factors-related information. Some formulas that are useful for performing patient safety-related analysis are presented below. 

Patient Safety Organizations, Data Sources, and Mathematical Models... 

Mathematical models are often used in engineering to study various types of physical phenomena. Over the years, a large number of mathematical models have been developed to study human reliability and error in engineering systems [2]. Some of fhese models can also be used to study patient safety-related problems. 

This chapter presents various important aspects of patient safety organizations, data sources, and mathematical models useful for performing patient safety analysis. 

Various types of mathematical models have been developed to perform human performance reliability analysis in the area of engineering. Some of these models can also be used in the area of patient safety to conduct human performance reliability analysis. Four of these models are presented below. 

Thus, the main objective of this book is to eliminate the need to consult many different sources to obtain desired information, to provide up-to-date information on the subject, and to demonstrate to the reader how to handle patient safety-related problems by using the methods developed in the area of engineering. The book provides the source of most of the material presented, in references at the end of each chapter. This will be useful to readers who desire to delve deeper into a particular area. The book contains a chapter on mathematical concepts and another chapter on introductory material on safety and human factors considered essential to understand materials presented in subsequent chapters. 

The book is composed of 11 chapters. Chapter 1 presents the various introductory aspects of patient safety including patient safety-related facts and figures, terms and definitions, and sources for obtaining useful information on patient safety. Chapter 2 reviews mathematical concepts considered useful to understand subsequent chapters and covers topics such as mode, median, mean deviation. Boolean algebra laws, probability definition and properties, Laplace transforms, and probability distributions. 

Chapter 10 is devoted to medical device usability. It covers topics such as medical device users and use environments, medical device user interfaces, an approach to develop medical devices effective user interfaces, guidelines to reduce medical device user interface-related errors, guidelines for designing hand-operated devices with respect to cumulative trauma disorder, and useful documents for improving usability of medical devices. Chapter 11 presents three important topics relating to patient safety patient safety organizations, data sources, and mathematical models for performing probabilistic patient safety analysis. 

Complete SA block otherwise known as sinus arrest has no such mathematical relationship. The pauses can last several seconds, and may cause patients to collapse (Fig. 7.15). The pause is normally terminated by an escape beat. As discussed earlier these escape beats originate further down the conduction system and are known as junctional or ventricular escape beats, depending upon their origin. These beats act as a safety net preventing Asystole. Treatment may require the use of drugs such as atropine or the insertion of an artificial pacemaker. 

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