# Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decim

Do not include anything other than numbers in your responses. For example, do not include comma or dollar sign in your numbers. As a rule of thumb, keep 2 decimal places for larger numbers and 3 decimal places for smaller numbers less than 1.

1) The product we make is a type of glue. We are advertising that our glue dries very fast. To monitor the quality of the produced glue, we record the time it takes for the glue to dry for each batch of glue we make. The following table summarizes the data we collected during the last 4 days. In each day, we produced 3 batches of glue and recorded the time of each batch.  All values are in minutes. We know the standard deviation of the process is approximately 0.15 minutes.

Time for the glue to dry:

Sample Batch 1 Batch 2 Batch 3

1 6.9 7.13 7

2 6.72 7 7.44

3 6.91 7.34 7.48

4 7.31 6.86 7.14

Calculate the center line to control the average of the time it takes for the glue to dry:

Calculate the average of ranges to control the variability of the time it takes for the glue to dry:

Number of observation in each sample (n):

D4:

Upper Control Limit to control average of the time it takes for the glue to dry:

Lower Control Limit to control average of the time it takes for the glue to dry:

Is the average of the process in control?

Upper Control Limit to control variability of the time it takes for the glue to dry:

Lower Control Limit to control variability of the time it takes for the glue to dry:

Is the variability of the process in control?

An inspector inspects for scratches in the exterior paint of each of the automobiles being prepared for shipment to dealers. The result of his inspection of cars in 10 days is as follows:

Day Flaws

1 9

2 5

3 4

4 10

5 12

6 7

7 5

8 5

9 2

10 2

Sum 61

2) Construct a control chart for this process to control for number of flaws and indicate if the process was out of control at any time.

Which of the following charts is appropriate to control the number of flaws?

Based on your choice on the last question, “calculate” “one” of the followings,  P (for P chart), or C (for C chart):

If you chose P Chart, how much is standard deviation of p (sigma_p)? (Write 0, if you are not doing P chart)

Upper Control Limit:

Lower Control Limit:

Is the number of flaws in control?

3) Before shipping lawn mowers to dealers, an inspector attempts to start each mower and notes any that do not start on the first try. The inspector 100 mowers for 10 days. The results of his inspection are given below:

Day Number of defective mower

1 0

2 0

3 8

4 5

5 0

6 0

7 4

8 1

9 5

10 1

Sum 24

Which of the following charts is appropriate to control the proportion of defective items? (P Chart/ C Chart)

Based on your choice on the last question, “calculate” “one” of the followings: calculate P if P chart, or calculate C if C chart:

If you chose P Chart, how much is standard deviation of p (sigma_p)? (Write 0 if you are not doing P chart)

Upper Control Limit:

Lower Control Limit:

Is the proportion of defective products in control? (Yes/No)

4) Each of the processes listed is non-centered with respect to the specifications for that process. Compute the capability index and capability ratio for each process, and decide if the process is capable.

Process Average SD USL LSL

H 20 1.5 24.5 16.5

K 50 6 78 34

Capability index of Process H:

Based on capability index, is Process H capable? (Yes/No)

Capability ratio of Process H:

Based on capability ratio, is Process H capable? (Yes/No)

Capability index of Process K:

Based on capability index, is Process K capable? (Yes/No)

Capability ratio of Process K:

Based on capability ratio, is Process K capable? (Yes/No)

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