An Important Experiment And Project In The First Measurement Course

One of the important components of a first measurement course in an engineering curriculum should be the coverage of the fundamental concepts in probability, uncertainty, and statistical analysis. An experiment and Project are designed and offered to better instill the significance of the above concepts and tools in engineering measurements, data analysis, and decision making process. The experiment calls for the establishment of the “Statistical” Spring Rate value (K) in each of the several sets of springs. Groups of students equal to the number of sets are formed to accurately measure and obtain the necessary data for each of the samples. These groups are then divided into smaller teams which conduct a comprehensive statistical analysis for each set and compare its tendencies with the rest. The teams then must justify their final decisions based on the statistical conclusions that they have drawn. The process for the establishment of six distinct samples is described. Design of the associated apparatus and their costs are presented. The parameters influencing the choice of the sample are discussed. The sample size and how its optimal selection may enable the coordinators to create fifteen (15) different combinations of the sets are described. The required number of measurements and the process for the establishment of K-values are briefly discussed. A comprehensive assessment of how the experiment and the project have improved the learning curve of the students is presented. Sufficient details are provided for creation of a variation of this exercise utilizing electronic components. This alternative features reduced cost and time for assembly and machining. The handout of the project and the experiment as well as a sample of the data required for conducting the analysis is included in the Appendices. I Introduction Laboratory experimentation is a critical final link for a thorough understanding and appreciation of scientific and engineering theories and principles. Every possible effort should be made not to deprive the future engineers or educators from this vital component of their education. It is therefore necessary to continue development of effective and efficient pedagogical methods and techniques for the engineering laboratory experience. The ability to perform Statistical Analyses and developing a solid understanding of the parameters influencing the reliability requirements/considerations in the engineering decision making process may prove critical for a functional design team. An integrated experiment and project are designed to better instill the significance of the above parameters. P ge 15153.2 The experiment and the project call for the establishment of the “Statistical” Spring Rate value (K) of each of the three (3) or four (4) samples of springs that (in a hypothetical scenario) are sent by different companies for winning a bid. Each sample is comprised of 25 springs. The springs are to be used in the design of 12 modules of the International Space Station (ISS). The modules are comprised of eight (8) identical subassemblies/panels. All 12 modules are to be transported to the station with only one trip of the Space Shuttle Atlantis. The cargo bay of the shuttle is not spacious enough to accommodate the transport of all 12 modules in their intended (fully expanded) mode. As a result, the eight (8) panels of each module need to be coupled with each other in a manner that transportation requirements may be met. The springs are to be used in the design of the mechanisms to satisfy the required modes/configurations of the modules during their: a) transport, b) expansion, and c) the final intended geometry. For full details of the scenario and the activity, refer to Appendix “A”. If there are to be four (4) groups of students [comprised of three (3) or four (4) members] for conducting the experiment, each group will collect data on only one of the sample sets. Each group will then share the results of their measurements with the other groups. In this process, each group has established an average “K” value for “each and all” of the 25 springs in one assigned set. Since five (5) measurements are required for “each” of the springs, each team then will have to conduct a total of 125 measurements. This will translate to a total of 500 measurements for the entire class. The completed and shared data for each of the four (4) sets will be used for the statistical analyses of all sets. Central tendencies of each set will be compared with the rest. Each group of four will then break down into two groups with only two members to address the requirements of the project component of the task. These teams of two students must each perform the required analysis and justify their final decisions and recommendations based on the (statistical) conclusions that they have drawn for the assessment of the quality of each set. II Objectives of the Experiment and the Project The following major objectives were set at the inception of the project: 1. To develop an experiment and project for a complete review and a better understanding of the statistical parameters that may heavily influence the engineering/design decision making process. 2. To create an opportunity for collaborative research and design efforts between undergraduate engineering student(s) and faculty. 3. To design, produce, test, and optimize a cost-effective, reproducible apparatus with outstanding features. 4. To make all information necessary for fabrication of the apparatus and conducting the experiment and the project available to engineering programs nationwide. Page 15153.3 It was therefore desirable to design an apparatus and experiment that would be feasible for replication in other educational institutions within a budget of $1,000 for materials and components. The package would include no less than four sets of distinct samples and require approximately 15 hours of machining and assembly time. IIIDesign of the Experiment and the Project 1. Pedagogy This project has been designed for sophomore level students. Pedagogical measures have been taken for its realistic effectiveness (nation-wide). Therefore, the framework of the project has been set at a level that sophomores may succeed in its implementation and developing deeper appreciation for some of the statistically based decision making processes. The students in the Mechanical Engineering, Civil Engineering, Bio-Medical Engineering, and Engineering Management at The College of New Jersey (TCNJ) are all required to take the first measurement course. In Chapter 4 of their “Theory and Design for Mechanical Measurements” text, Figliola and Beasley offer a concise coverage of the Probability and Statistics concepts and analytical tools that are most critical for engineering applications. This is followed by a detailed chapter in Uncertainty Analysis. All of Chapter 4 and the first four (4) articles of Chapter 5 (of the above text) are covered in the first measurement course at TCNJ. The premise for creation of the project is to further review and explore the potential applications of the following parameters and topics that may influence the engineering design and production decisions. In this process, the targeted audience may also develop additional appreciation for other considerations such as safety, reliability, expected life, quality control, production constraints, cost, etc. 1. Finite VS Infinite Statistics 7. Number of Measurements Required 2. Mean, Median, Mode, and True Mean 8. Probability Density Function 3. Variance and Standard Deviation 9. Central Tendencies 4. Histograms and Frequency Distribution 10. Probability Linked to Reliability 5. Normal Distribution, Chi-Squared, etc. 11. Measurements and Sources of Error 6. Confidence and Precision Intervals 12. [Introduction to] Uncertainty The author invited two rising junior engineering students for collaboration. The details of their involvement and contributions are provided in Appendix “C”. P ge 15153.4 2. Choosing of the Sample The choice of the Sample is quite important and it may be considerably influenced by the following factors; 1. Desired Sample Size [as this may be the single most important parameter in most Statistical Analyses] , 2. The Number of Students and Intended Groups in each section, 3. The Number of Sections in a given semester/academic year, 4. Time Limitations for Conducting the Measurements and Recording the Data, 5. Desire to Repeat the Experiment (and Project) in Future with Sufficient Modifications to avoid Repetition of Previously Used Data, 6. Cost [depending on the quality and the sample size(s)] , 7. Availability, Durability, and Aesthetics, 8. The Intended/Desired Spectral Density of the Sets/Data, 9. Degree of Difficulty in creating the Required Number of Different Sets [with different ranges and frequencies] , 10. Probability of obtaining the intended Spectral Density and the Ranges for the target Sets, 11. Degree of Difficulty, Feasibility, and Safety in Performing the Required Measurements, 12. The Number of Necessary Measurements for obtaining a relatively meaningful set(s) of statistics for the targeted parameter(s)] , 13. The Cost and the Complexity of the Design of the Associated Apparatus, 14. The Tools required for performing the necessary measurements, 15. Creation of (Numbered/Colored) Housing Units/Cradles to Prevent the Potential Mixing of Samples in one set with others, and 16. Ease of Maintenance and Storage for Continuous Reuse [in other sections and future] . In the previous iterations of this exercise, the following choices for the samples have been made. As shown in Table (1), for some, the groups of students had to physically take measurements of the provided samples and for others; the data for the different sets was provided. Table 1. The Choices and the Types of Samples in the Previous Iterations # Sample Type Specifications Size of the Samples Actual / Physical Simulated / Prem