Improving the Undergraduate Statistical Education of Engineers

Peter Nelson and Ted Wallenius

We believe that it is appropriate to think of providing statistical training for engineers as a process. The product (the students) should be produced to satisfy the customer (industry and government), and changes in the process are most effective if everyone involved in the process (statistics and engineering faculties and professionals) works together to establish goals and effect process changes. Thus, in order to most effectively modify the process, one must start by initiating discussions between statistics faculty and engineering faculty and by consulting with the customer to ascertain the exact nature of the product in which they are interested.

We have already initiated such discussions at Clemson University (CU), and we were fortunate enough to have Dr. Ronald D. Snee of DuPont Corporation to help us with the initial discussions of the project. Dr. Snee is internationally known for his research in and application of statistical methods to problems in engineering and technology.

Based on our initial discussions, we believe that an introductory course in statistics for engineers must be considered in conjunction with the entire engineering curriculum. No matter how good an introductory course in statistics is, if students are not asked to use this material in any subsequent courses, they will soon forget it and most probably question why they were required to take the course in the first place. Thus, we propose to enlarge our area of concern from just an introductory course in statistics to how the concepts from this course can be utilized, reinforced, and enhanced in subsequent engineering courses. This is in line with the 1986 ABET resolution, which also said "Such [concepts] should be infused throughout the engineering curricula along with some formal course work in these applied statistics areas" and "These [concepts] should be an integral part of all laboratory experiences." All of this necessitates a true collaborative effort between engineers and statisticians, and our goal is to introduce statistics into the various engineering curricula in such a way that engineering faculties will be eager to have their students participate.

Our approach will be to start by introducing statistical techniques into the engineering labs. We are suggesting engineering labs as the initial point of attack because laboratories are the setting where students perform experiments and collect data. Actually, this is not a new idea. It was suggested by Hunter (1968), but to our knowledge has never been implemented. The help of the engineers will be necessary in order to familiarize the statisticians with the many different experiments. Statistics and engineering faculty members will work together in order to determine where statistical techniques can be used and which techniques are appropriate.

Introducing Statistics Into Engineering Labs

At the core of our effort is the development of revised laboratory experiences that highlight the benefits to be gained by appropriate utilization of statistical techniques. In the spirit of continuous improvement and of designing quality into a product rather than trying to address problems with changes at the manufacturing stage, one can conceive of not being satisfied with simply dealing with variability in existing experiments, but eventually designing new experiments that better emphasize the engineering issues. As a start, however, it seems reasonable to first bring the statisticians up to speed relative to understanding the experiments as they are currently being conducted. We will illustrate our approach by means of a particular chemical engineering experiment.

Heat Exchanger Experiment

Chemical engineering students at CU have a laboratory exercise involving a heat exchanger where data are collected in order to estimate various heat transfer coefficients. A description of the present heat exchanger experiment is given in Appendix 1. As an aside, the statisticians reading this descriptions found it to be insufficient for a complete understanding of the experiment, and additional explanation by an engineer was needed before the relevant statistical issues became clear. This is not surprising since the process of statistical consulting (that is actually what is taking place) proceeds in this fashion, and progress is achieved only through collaboration.

One of the purposes of the experiment is to calculate (actually to obtain an estimate of) the outside film coefficient h_o using Wilson's method. From physical principles, the overall heat transfer coefficient U_o is related to h_o by the equation

   1/{U_o A_o} = 1/{h_o A_o} + {Delta r}/{kA_{lm}}  
                        + 1/{a{{U_b}^0.8}A_i}                        (1)


A_o = outside tube area
Delta r = thickness of the tube
k = thermal conductivity of the tube
A_{lm} = logarithmic mean of the inside and outside heat transfer areas
U_b = flow rate of the water inside the tube
A_i = inside tube heat transfer area
a = constant.

If the outside flow rate is held constant, then h_o is constant and equation (1) indicates that 1/{U_o A_o} is linearly related to 1/{{U_b}^0.8}. By measuring U_o for various inside flow rates one can estimate this linear function, and the intercept of the estimated line, which corresponds to an infinite inside flow rate, can be used to obtain an estimate of h_o. The write-up advocates taking some replicate measurements, but no concern is expressed about the precision of the estimate of h_o. Since students are aware that their estimates differ, this is an ideal opportunity to introduce statistical issues.

Some of the statistical issues that could be considered with this experiment include the following. The replicate observations could be used to check the assumption of linearity, confidence limits could be attached to the estimated intercept, and experimental design considerations could be discussed. If the relationship is truly linear, then the optimal design would consist of half of the runs at the lowest possible flow rate and the other half at the highest physically possible flow rate. Comparing the width of the confidence interval for the intercept obtained with this optimal design and the width obtained with the design recommended in the write-up would reveal the importance of selecting the appropriate experimental conditions. Further, a nonlinear regression model could be used to assess the suitability of the constant 0.8.

An Introductory Engineering Statistics Course

We believe that the content of an introductory course in statistics for engineers should be determined by the types of problems that engineers are most likely to encounter. Further, we believe that these topics should be introduced as they are encountered in actual problems rather than in an order determined for mathematical convenience. One might say that we are in favor of an introductory engineering statistics course being driven by problems rather than by techniques.

The information obtained from studying engineering experiments is one source of appropriate topics for an introductory course. As a second means for deciding on the appropriate material for an introductory course, we plan to obtain information from several companies that employ large numbers of engineers and do much of their own training in statistics. (We are consulting the customer.) Specifically, we plan to contact General Electric, General Motors, Allied-Signal, Kodak, Westinghouse, DuPont, Milliken, Florida Power & Light, Motorola, Xerox, and Corning. Milliken, Motorola, and Xerox are all winners of the Malcolm Baldrige National Quality Award, and Florida Power & Light has been awarded the Deming Prize.

A course in statistics for engineers is currently being taught at CU, and of necessity, it will continue to be taught while we are working on its improvement. The type of introductory course we are proposing will evolve as we gain information from industry and the engineering labs. The effectiveness of the course will increase as statistical content is added to the engineering labs and students are required to use statistical methods in their engineering curricula.

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