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Home :: Contents (2267) :: Operations Management (61) :: Quality Control

Quality Control (4 problems)


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Problem #1: Acceptance Sampling

Suppose a quality control specification on a particular part allows at most 1% defectives. The company uses a sampling plan wherein 400 parts are examined, and if 8 or more are found to be defective, the lot is rejected. Construct a well-labeled power curve vs. p for this sampling plan. What is the exact a-level for the test when p = 0.01?

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Problem #2: Acceptance Sampling

Suppose a quality control specification on a particular part allows at most 1% defectives. The company uses a sampling plan wherein 400 parts are examined, and if 8 or more are found to be defective, the lot is rejected. Construct a well-labeled power curve vs. p for this sampling plan. What is the exact powe of the test when pi = 0.01?

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Problem #3: Xbar and Range Charts

Kitty Products caters to the growing market for cat supplies, with a full line of products, ranging from litter to toys to flea powder. One of its newer products, a tube of fluid that prevents hair balls in long-haired cats, is produced by an automated machine that is set to fill each tube with 63.5 grams of paste.

To keep this filling process under control, four tubes are pulled randomly from the assembly line every 4 hours. After several days, the data shown in the following table resulted.

Set control limits for this process and graph the sample data for both the x- and R-charts

Sample

Sample

Sample

1
 63.5
 2.0
 10
 63.5
 1.3
 18
 63.6
 1.8
2
 63.6
 1.0
 11
 63.3
 1.8
 19
 63.8
 1.3
3
 63.7
 1.7
 12
 63.2
 1.0
 20
 63.5
 1.6
4
 63.9
 0.9
 13
 63.6
 1.8
 21
 63.9
 1.0
5
 63.4
 1.2
 14
 63.3
 1.5
 22
 63.2
 1.8
6
 63.0
 1.6
 15
 63.4
 1.7
 23
 63.3
 1.7
7
 63.2
 1.8
 16
 63.4
 1.4
 24
 64.0
 2.0
8
 63.3
 1.3
 17
 63.5
 1.1
 25
 63.4
 1.5
9
 63.7
 1.6
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Problem #4: Xbar and Range Charts

A company makes ball bearings for high quality engine components that demand very close tolerances. The company randomly selects 10 ball bearings every hour. Past experience shows the mean diameter to be .37mm with an average range of .04mm (Average R = .04).

a. Set up the X-bar control chart.

b. Set up an R-bar chart.

A new customer is interested in buying your companies ball bearings. They have three potential uses, each with its own tolerances. They are:

1. Mean = .37mm, tolerance = ± .03mm

2. Mean = .40mm, tolerance = ± .035mm

3. Mean = .38mm, tolerance = ± .02mm

Prepare a memo to the marketing department on how to respond to this potential new customer.

A member of the marketing team suggested that if necessary the process control limits be reduced to + or - 2 standard deviations, so that the control limits are within the tolerance limits set by the prospective buyer. Address this issue in your memo.

Another marketing person has suggested that we increase the sampling to 40 ball bearings every hour, and thus catch process errors faster. How would you address this suggestion?

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