## Summary:

This course is valuable for anyone who finds a need to understand or apply statistics. The course can serve as a refresher or as a practical introduction. The statistical techniques often used by weapon system analyst are carefully explained. The presentations emphasize the intuitive development and the practical use of the techniques rather than providing academic developments. Weapon System and other examples are used to illustrate and motivate the topics. The course provides a “toolbox” of statistical methodology and the necessary understanding teaches the student to avoid and detect the common mistakes encountered in applying statistics. Participants will be furnished the textbook Statistical Analysis with Excel for Dummies, by Joseph Schmuller Ph.D.

## Course Outline:

1. Introduction—A review of the basics, clarifying notation. Topics include conditional probability and the low base-rate problem, simple probability models, expected values, and how to relate measurements using joint distributions, correlation’s and covariance’s.
2. Reliability Models and Decision-Making—Discrete probability models for use in reliability and other analysis are introduced. False alarm rates, statistical power, P-values, and (R) OC curves commonly seen in computer output are explained. You will master step-by-step procedures for solving problems.
3. Decisions Making Based on Continuous Measurements—Continuous probability models, including the normal, the chi-square and the student “t” are introduced. These models are used for both weapon system accuracy and reliability. You will understand why these models are often used and when to apply them. False alarm rates, statistical power, P-values, and (R) OC curves are explained for data from the normal distribution. An understanding of these topics is necessary for the proper use of statistical software. These topics also provide a fundamental understanding necessary for sample size determination.
4. Confidence Intervals—An analysis of test results requires an understanding of decision making and the use of confidence intervals. You will be able to determine sample size requirements and will be able to understand and present results in different ways. Exact methods for placing confidence intervals on system reliability are presented. These methods are particular useful for highly reliable systems.
5. Comparing Results—Comparing the performance of two systems requires specialized statistical methods that make different assumptions about the nature of the application. You may want to compare rocket motors manufactured by two different venders or to compare a new system to an old one. You will learn to use techniques for small and large samples and paired observations and be able to choose between the different analysis techniques.
6. Linear Regression—You will learn how to use regression to build and investigate models. Regression is often used to model system performance as a function of controlled or environmental variables.
7. Multiple Regression—You will learn how to build complex models for prediction results and for identifying possible cause and effect relationships. Interaction terms, indicator variables and polynomial models will be explained. You will also learn how to evaluate relationships between measurements both in statistical terms and in terms of total uncertainty. Topics include R-square, partial correlation coefficients, hypotheses testing and analysis of variance.
8. Logistic Regression—This wildly applicable and powerful analysis technique is rarely taught outside of specialized courses because it is relatively new and it requires statistical software. Since it is important in weapon system analysis, including the detection of reliability changes with time and in understanding the effects of controllable variables, it is being presented in this course. The technique is simpler to use than neural networks and often provides better solutions.
9. Test for Normality—Many analysis techniques assume that the data are normally distributed. Impact data provides such an example. You will learn to test the assumption of normality.

## Scheduling:

REGISTRATION:  There is no obligation or payment required to enter the Registration for an actively scheduled course.   We understand that you may need approvals but please register as early as possible or contact us so we know of your interest in this course offering.

SCHEDULING:  If this course is not on the current schedule of open enrollment courses and you are interested in attending this or another course as an open enrollment, please contact us at (410)956-8805 or ati@aticourses.com. Please indicate the course name, number of students who wish to participate. and a preferred time frame. ATI typically schedules open enrollment courses with a 3-5 month lead-time.   To express your interest in an open enrollment course not on our current schedule, please email us at ati@aticourses.com.

For on-site pricing, you can use the request an on-site quote form, call us at (410)956-8805, or email us at ati@aticourses.com.

## Instructors:

• Dr. Alan D. Stuart,

Associate Professor Emeritus of Acoustics, Penn State, has over forty years experience in the field of sound and vibration. He has degrees in mechanical engineering, electrical engineering, and engineering acoustics. For over thirty years he has taught courses on the Fundamentals of Acoustics, Structural Acoustics, Applied Acoustics, Noise Control Engineering, and Sonar Engineering on both the graduate and undergraduate levels as well as at government and industrial organizations throughout the country.

Contact this instructor (please mention course name in the subject line)