Parts of six lectures (one practice, five for-credit) will be spent discussing some real-life, high-profile issues. Data from relevant studies will be presented for analysis, and guidance will be given to prompt you to form your own conclusions and to think through the statistical issues involved. Up to a week's notice will usually be given for these class participation sessions to allow you time to prepare in your groups.
Grading for the sessions will be on a zero/full credit basis. A question about the study will be asked at the beginning of the session, and each group will write their answer down on a piece of paper. This will then be checked by the instructor and the class discussion will begin. Each member of a group will receive full credit for that session if the group gets their written answer correct, or, if not, if at least one of the group makes some relevant remark in the ensuing discussion. If the group gets their written answer wrong and no-one in the group makes a useful contribution to the discussion, everyone in that group gets zero credit for that session. Also, if you fail to show up for the session without having made a prior arrangement with the instructor, you get zero, regardless of whether the rest of your group gets credit.
A practice session will be held in class on Wednesday, week 2. This practice session will not be for credit.
You should prepare for the practice session; it will be based on the "Harnswell Sewing Machine Company" situation outlined below.
Before class, read the material given below, and get together in your group to discuss the problem for 25-30 minutes. Use the questions listed under "Focus" to guide your discussion. Then, when you come to class you should be prepared to answer questions and participate in a class-discussion, using what you've already discussed in your group.
You can (and probably should) make notes on what you've discussed in your groups before class. You should bring these notes to the class-discussion. Do not turn anything in however (except for the answer to the question asked at the beginning of the session) - this is not a written assignment.
In class, after the beginning question, we'll discuss the questions listed under "Focus" and also anything else that comes up that you think is relevant or interesting in the context of the problem. To keep the class-discussion orderly and the grading fair, you must raise your hand before saying something. The instructor will ignore anything you say unless you've raised your hand first and been asked to speak. The instructor will do his best to allow the first person to raise their hand the opportunity to speak each time. If you keep your hand up, you will be given the opportunity to speak once the current speaker has finished making their point.
When you make a relevant observation, suggest a useful approach to answering a question, or raise an interesting question not previously considered, the instructor will make a note of which group you are in, and keep a tally of which groups have participated and which have not. Remember, you only need to get the beginning question correct, or, failing that, make one relevant remark to get full credit for your group. The instructor will decide what is relevant and what is not, and his decision is final - no arguments.
The Harnswell Sewing Machine Company is a manufacturer of industrial sewing machines that has been in business for almost 50 years. The company specializes in automated machines called pattern tackers that sew repetitive patterns on such mass produced products as shoes, garments, and seat belts. The company sells both machines and machine parts. The company's reputation in the industry is good, and it has been able to command a price premium because of this reputation.
A recent University of Oregon graduate has been hired as production manager, and they are struggling with a problem involving "cam rollers," a particular precision ground part. They vaguely recollect learning about Statistical Quality Control in one of their classes and wonder if the following could be applied to their problem:
In all production processes, we need to monitor the extent to which our products meet specifications. One enemy of product quality is "deviations from target specifications". Statistics can be used to provide on-line quality control procedures to monitor an on-going production process and address this problem. The general approach to on-line quality control is straightforward: We simply extract samples of a certain size from the ongoing production process. We then produce line charts of the means (averages) in those samples, and consider their closeness to target specifications. If a trend emerges in those lines, or if samples fall outside pre-specified limits, then we declare the process to be out of control and take action to find the cause of the problem. These types of charts are sometimes also referred to as Shewhart control charts (named after W. A. Shewhart who is generally credited as being the first to introduce these methods).
For example, an "X-bar chart" contains upper and lower control limits that indicate when the process is out of control. The method for constructing the upper and lower control limits is a straightforward application of the concept of the sampling distribution and the characteristics of the normal distribution. In particular, if the mean (and variance) of the process does not change (i.e. the process is "in control"), the central limit theorem tells us that successive sample means will be distributed normally around the population mean. Moreover, we also know that the distribution of sample means will have a standard deviation of SD (the standard deviation of individual data measurements) divided by the square root of n (the size of the samples). Thus, for example, approximately 68% of the sample means will fall within approximately plus/minus 1 * SD/Square Root(n) of the center line, approximately 95% of the sample means will fall within approximately plus/minus 2 * SD/Square Root(n) of the center line, etc. By setting the control limits a particular distance from the center line, we can thus assess the probability that an "in control" process will go outside these control limits. Then, by making this probability very small (which determines how far from the center line to put the control limits), any time the process does go outside the limits, chances are it has gone out of control.
The Oregon graduate samples five rollers from each production batch over a 30 day period, and measures the diameters to the nearest 0.000001 inch. They then produce the following "X-bar chart" from the data:
