Statistical Process Control

Activity 2 (Teacher Copy)
Quality Assurance

Students will learn some basics of quality assurance in industry-in particular, as applied to the dimension of length of produced items. They will look for patterns in graphed data and determine appropriate actions for detected problem areas, and they will exercise coordinate graphing skills. Students will become familiar with tolerances provided for product dimensions and how upper and lower control limits are derived using these. Use with student copy and reference copy.

• To look for patterns in graphed data in order to determine problem areas and recommend appropriate courses of action.
• To make and interpret line graphs.
• To determine upper and lower control limits for a product dimension, given the nominal (ideal dimension) and tolerance.

Introduction

• What is a sample? (set of items randomly drawn from the total number produced) Why do quality assurance measures involve examining random samples of manufactured items? (Because it is not practical/possible to check all items, and because a mean found for a random sample has been shown to approximate the mean for the population [total set of items] from which it comes. Therefore, it is reasonable in quality assurance to spot-check samples of a company's product.)
• The middle horizontal line for each graph shows the ideal length of the coils, called the nominal. The upper line, marked UCL, is the upper control limit, and the lower line-LCL-is the lower control limit. What do you think these terms mean? (The upper and lower control limits designate the range within which coil length must fall-maximum and minimum lengths-to meet company standards.)
• Have students read over the sheet on their own and raise questions or points for discussion. Include the following question if students do not: Why is action called for in the case of "overcontrol," which shows that coils are consistently falling close to their ideal length? (Employees might be putting too much effort into producing coils that fall closer to their ideal length than is necessary for the coils to be acceptable [for example, by adjusting machines often],thereby resulting in excessive time expenditure which means extra cost for the company.)
• Before students begin the worksheet, ask if they know what symbol is used to represent the mean of a set of numbers (X bar). Then discuss the meaning of X double bar. See if a student can tell what it represents (mean of the means) and explain it in terms of its use on the graph shown in #1. (Ideally, a mean found for the coil length means represented by points on the graph should fall at the thick horizontal bar labeled X double bar, also called "X bar average." Note that X double bar could differ somewhat from the ideal length for a product ordered by a customer, because a company's machine might not be capable of being set at the ideal length. [The ideal length is termed the nominal and is the midpoint of the range of length that will be accepted by the customer for the desired product. This range-consisting of the nominal plus total "tolerance" (a term explained later in this activity)-is known as the customer's specifications, usually referred to as specs (pronounced "speks").])
• You might want to review/teach any necessary skills for constructing and interpreting line graphs (which students use beginning with #2 in this activity).

Part A [#'s 1 &; 2: patterns should also be circled/labeled on graphs.]

1)

• Coil samples A-I (other letter groupings, such as A-J, might be chosen) show a natural pattern, which calls for no action.
• F-L show a trend. Notify supervisor.
• L indicates out of control. Adjust machine.
• M-S (or some other combination starting with J, K, or L) show an unusual pattern. Notify supervisor.

1)

1. Moderately close tolerance would be okay for a pencil, because it does not have to fit into a particular, rather precise space in most cases. The tolerance for a 7 1/2" pencil might be ± 1/16". (You might want to work through with students what the upper-7 9/16"-and lower-7 7/16"-control limits would be for such a pencil.)
   
2. The tolerance would not have to be particularly close for the gate, because it can be adjusted with hinges, etc. (although it can depend on the type of gate/fence). An example of a gate width might be 36" with a 1" tolerance, for an acceptable range of 35-37".
3. Because each tongue must fit into the groove of an adjoining piece, tongue-and-groove flooring requires close tolerance. For example, tongue-and-groove hardwood flooring used for a gymnasium floor has very close tolerance, such as ± 1/64" (about half the thickness of a sheet of paper) for a width of 2 1/2". The length of each plank is about 2-3'. The small plank size is necessary to minimize the movement-expanding and contracting-that is caused by humidity changes.
   

• No. The lower control limit is 15/16", which is equivalent to 60/64", and 57/64" falls below that and thus outside of the acceptable range.
• The LCL is 3 7/8" and the UCL is 4 1/8" (the width is the smaller of two sides that comprise a rectangle); length-7 3/4" (LCL) and 8 1/4" (UCL).