Statistical Process Control

Activity 3 (Teacher Copy)
Collecting and Interpreting Data

Students will work in groups to measure coil samples, graph the means of the samples, and then look at their graphs to recommend any required action. Use with student copy and reference copy.

• To gather data by measuring sets of coils to the nearest tenth of a centimeter and recording their lengths, mean length, and longest and shortest lengths.
• To make a line graph.
• To interpret data presented in the form of a line graph.

Introduction

Students should work in groups of about four, and each student should be assigned a role within the group. For example, two measurers would measure the coils in the sample, a recorder writes the information found for each sample, and a calculator/grapher finds the sample mean using a calculator then graphs the means. A system for rotating these roles should be devised.

If possible, it is helpful during this activity to have an "extra hand" (e.g., another teacher, a teacher's aide, or a parent or student aide) so that she/he can distribute and collect coil samples while the teacher moves about the classroom to student groups. Each group should only have one sample at a time, getting one from the distributor when needed and returning each when finished (to prevent samples from becoming mixed). One of the designated student roles (probably one of the measurers) might include getting and returning the samples.

Samples should be pre-measured and means determined, with an answer key for your use. Students should be provided with a slip of paper that lists the sample numbers that they should measure/record/graph (e.g., 5-14-10-21-8...) and these should be done in the order in which t hey are listed on the sheet (or each group can be given a Reference Sheet R3 that already has the sample numbers marked in the "date" spaces across the bottom of the graph). Different groups of students should receive different predetermined sample orders that have been arranged so that the graph of their mean lengths shows two or so of the patterns found on Reference Sheet R2. If the sample a group needs at a particular time is being used, they may temporarily skip ahead to the next sample, as long as they maintain the given sample order on the graph. You might want to have students first write the sample numbers in the "date" spaces across the bottom of the graph before beginning.

1. & 2 A key (graph) should be made for each of the different sample combinations given to groups (perhaps give each combination a number or letter for easy reference). Each key should have "run rule" patterns circled and labeled, as well as any action to be taken.

3. Answers will vary. Some possible responses may be:
   • So that coil length can be monitored over time to look for patterns.
   • To see if some individual bad parts are being produced that might not show up when only looking at the mean.
   • Noting the average coil length for a group of coils gives a better sense of what coil lengths are being produced at that point in time than by looking at an individual coil length, which might not be typical of the overall set of coils being produced.
   • The extremes show the range of the coil lengths, indicating the variability in lengths of coils produced at a point in time.
   
   
4. Answers will vary. You might want to mention to students that a part that goes outside of the control limits is not always "bad." For example, a customer might set her/his UCL at 7.8 cm and the company might then set its UCL at 7.7 cm to be "safe" in monitoring ("controlling") quality according to the customer's specifications (in which case a 7.8 cm part goes above the company's UCL but is still a usable part for the customer).