Statistical Process Control

Unit Overview
Measuring and Means
Quality Assurance
Data Collection
Credits




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Statistical Process Control

Activity 2 (Student Copy)
Quality Assurance

Materials


Part A

 1) The graph below shows the plotted means for samples of coils over a period of time. The thickest horizontal line (center) shows where the average of the means should ideally fall, and the other two thick horizontal lines represent the upper and lower control limits. Use your "Run Rule Overview" (Reference Sheet R2) to name any situations that you detect and any action called for. (Note that the tolerance is unrealistic in that the actual range allowed for coil length would not be nearly as broad as that shown. Also, it would probably be uncommon to find such an irregular pattern of data as that shown on the graph. However, practice in the basic concepts and needed skills for the task of monitoring quality assurance in this manner can be gained through this exercise.)

Click for the image

On the graph, circle any situations that you identified and write the "run rule" term that names it (out of control, run, unusual pattern, etc.) by the circle. Then complete the following information.

"Run Rule"
Situation Noted		 Action Required
(if any)


2) Using a ruler or other straightedge, graph the following samples below (letters name samples and numbers give mean lengths in centimeters): A-5.2, B-5.3, C-5.1, D-5.2, E-5.1, F-5.3, G-5.3, H-5.5, I-5.1, J-5.2, K-5.0, L-5.3, M-4.9, N-5.1, O-5.3, P-5.2.


Click for the image

Do you see any situations that compare to those found on your "Run Rule Overview" sheet? If so, circle and label them on the graph; also list them below (name them and tell any necessary action to be taken).


Part B

1) An ideal length, or nominal, is set for manufactured items, and a margin of error, or tolerance, is allowed, which results in upper and lower control limits. How "close" the tolerance is-close tolerance means a narrow margin of deviation from the specification-depends on the type of item. Tell how close you think the tolerance would need to be for each of the following items (in general terms, such as "very close," etc.), and explain why.

  1. pencil

  2. width of a gate to be attached to a fence by hinges

  3. tongue-and-groove hardwood flooring (tongue on one end of each piece fits into groove on other end of an adjacent piece)

2) A "four by eight" (4 x 8) piece of Styrofoam with square edges (i.e., not tongue-and-groove) made by the Dow Chemical Company is 4 x 8 x 1" (the last dimension is thickness). The company allows a tolerance of ± 1/16" for any thickness that is less than 2". Therefore, the thickness of the 4 x 8 x 1" Styrofoam must fall between 15/16" and 1 1/16" (the lower and upper control limits).

  • Does Styrofoam with a thickness of 57/64" thickness fall within the accepted range? Explain.

  • What are the lower and upper control limits (UCL and LCL) for the width with a tolerance of ± 1/8"?

    for the width with a tolerance of ± 1/4"?

<3>Give the upper and lower control limits for each of the following items.

Item Basic Dimension Tolerance LCL UCL
metal washer 1" (diameter) ± 32/1000"

metal
washer		 60/1000" (thickness) ± 10/1000"
catheter 55 cm (length) ± 3 cm
hypodermic
needle		 15 cm (length) ± 3 mm

  • Which of the previous items would you consider to have close or fairly close tolerance?

  • Do you think a tolerance of ± 1/64" is always closer (in terms of calling for a more precise measurement for an item) than a tolerance of 1/8"? Explain.


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Area 10 Mathematics and Technology Professional Development Center
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Last updated on 1/30/1999
Comments: egalindo@indiana.edu
http://www.indiana.edu/~atmat/units/spc/proc_s2.htm