1. I.Introduction to Engineering Statistics A. The Engineering Method The heart of sound engineering practice is the engineering method systematic approach for problem solving constant interplay between the concrete and abstract Concrete: Actual engineering process Abstract: Mathematical models Example: Uniformity of layer of silicon grown into wafers

3. B. Probabilistic Models The engineering method requires: 1.data collection 2.data analysis Problem: Data always exhibit variability. Variability obscures our ability to make decisions.

4. Example: Thicknesses of a particular type of silicon wafer Target value: 244 μm. Consider a sample of five wafers from one batch. 245 250 250 247 248 All are larger than the target. Is there real evidence of a problem?

5. Engineers have always used abstract models to address concrete problems. For example, consider Ohm's Law V = IR where V is the voltage I is the current R is the resistance Note: This is a deterministic model. If we know I and R, we claim to know V exactly. Consider an EE lab with 20 students All set up circuits same current same resistance All measure the voltage.

6. How many different voltages do you think will be observed? A better approach uses a probabilistic model V = IR + ε where ε is a random error. In this case, ε is best viewed as an experimental error. C. Populations Models provide a basis for describing populations. Definition: Population A population is the set of all possible observations of interest to the problem at hand.

7. Examples of Populations: 1.The viscosity of a paint Let y i be the viscosity for the i th batch produced. Consider the following deterministic model: y i = μ where μ is the “typical” viscosity. Note: This model claims every batch has exactly the same viscosity, which is ludicrous. A better model y i = μ + ε i where ε is the random error associated with the i th batch.

8. 2. The thickness of the silicon layer on a wafer for an integrated circuit. Let y i be the thickness of the silicon layer on the i th wafer. Earlier, we proposed the deterministic model where the β’s are constants, t is the deposition time, T is the deposition temp, and A is the Argon flow rate. A better model is where ε i is the random error associated with the i th wafer.

9. D. Issues in Data Collection The Engineering Method requires data. Important issues in data collection: purpose of the study characteristic of interest measurement of the characteristic of interest presumed engineering model “parameters‘” of interest physical constraints Example: Battery Plate Process Problem: Plates with ``blisters'' causes premature failure of battery cells.

10. purpose: eliminate blisters on plates characteristic of interest: number of plates showing blisters in a test cell of 60 plates model where -- y: the number of blisters -- x 1 : plate porosity -- x 2 : concentration of an important electrolyte -- x 3 : load applied to the plates during charging -- β’s: constants relating the effect of the x's on the number of blisters -- ε: random error parameters of interest: the β's in the model constraints: can test only four cells at a time.

11. Important Concept: “Pairing Data” Purpose: to remove unwanted variability. Example: Comparing two temperature instruments used to control a chemical process. Problem: The true process temperature changes daily: an unwanted source of variability. Solution: Use both instruments on the same process, take measurements at same time. Note: the two measurements are paired. Perform the analysis on the differences between the two measurements. Result: we eliminate the day-to-day temperature variability due to the chemical process!

12. E. Methods for Collecting Data Three basic methods of collecting data are: retrospective studies observational studies designed experiments Retrospective studies use previously collected data. Primary advantage: cost since the data are already collected Disadvantages: 1.may not have the information required 2.often have problems with missing data 3. may not be able to document interesting phenomena.

13. Observational studies interact with the process only as much as is required to obtain relevant data. Usually we use observational studies to monitor processes. Observational studies usually use a sampling plan to collect their data. Some common sampling plans are: simple random sampling stratified random sampling systematic sampling Of these three, the most common is simple random sampling. See the text for details

14. Designed experiments intentionally disturb the process and then observe the results. Example: Consider the yield (concentration of desired product) from a distillation column. We call the yield our response. Factors which may influence the yield: reboil temperature column pressure flow rate into the column In a designed experiment, we manipulate the factors, allow the system to reach equilibrium, and then we observe the response.

15. Suppose we wish to conduct an experiment using a “high” and “low” level for each factor. For example: Reboil temp. 120 º - 150 º Pressure 2 - 3 atm. Flow rate 100 - 150 GPM What would seem a reasonable strategy? Use all possible combinations.

16. This is called a 2 3 factorial experiment,

17. Common reasons for conducting designed experiments are: to screen important factors to predict the behavior of an important characteristic to optimize a characteristic of interest to make products and processes robust to known sources of variability.

18. An Overview of Experimental Design In my experience, the absolute best way to teach the text's material through the section on the 2 k full factorial designs is through simple, hands on experiments planned, conducted, and analyzed in class. Two good experiments to conduct in class are the catapult, and the paper helicopter. A friend of mine has conducted experiments building cars out of legos, which also works. There are other examples which will work. The key is to make this material real to the student. Conducting an experiment that they plan, execute, and analyze together is very important.

19. Start the process as a 2 2 factorial. Have the students determine the two factors and their specific levels. In the course of planning the experiment discuss the concepts: experimental unit and experimental error, observational unit and observational error, (Be sure to explain the difference between the two!) randomization, (Emphasize that randomization does not eliminate systematic bias; rather, it fairly distributes any systematic bias over the entire experiment.) replication, and (Emphasize that replication allows the estimation of experimental error, which is the basis for formal statistical tests.) local control of error. Discuss all of these concepts within the specific context of your experiment.

20. G. Purpose of Engineering Statistics To learn how: to collect data to estimate models to reach decisions in the face of uncertainty due to variation.