Question

HCH Manufacturing has decided to use a p-Chart with 2-sigma control limits to monitor the proportion of defective steel bars produced by their production process. The quality control manager randomly samples 250 steel bars at 12 successively selected time periods and counts the number of defective steel bars in the sample.

Sample   Defects
1   7
2   10
3   14
4   8
5   9
6   11
7   9
8   9
9   14
10   11
11   7
12   8

Step 1 of 8:

What is the Center Line of the control chart? Round your answer to three decimal places.

Step 2 of 8:

What value of z should be used to construct the control chart?

Step 3 of 8:

What is the Upper Control Limit? Round your answer to three decimal places.

Step 4 of 8:

What is the Lower Control Limit? Round your answer to three decimal places.

Step 5 of 8:

At the next time period, 250 steel bars are sampled and 8 defective steel bars are detected.

( In Control or Out of Control)

Step 6 of 8:

At the next time period, 250 steel bars are sampled and 28 defective steel bars are detected.

( In Control or Out of Control)

Step 7 of 8:

At the next time period, 250 steel bars are sampled and 22 defective steel bars are detected.

( In Control or Out of Control)

Step 8 of 8:

You, acting as the quality control manager, have concluded that the process is "Out of Control". What is the probability that the process is really "In Control" and you have made a Type I Error? Round your answer to three decimal places.

Answer 1

Step 1 of 8:

Center Line of the control chart = = (7 + 10 + 14 + 8 + 9 + 11 + 9 + 9 + 14 + 11 + 7 + 8)/12 = 9.75

Step 2 of 8:

For 2-sigma control limits, z = 2

Step 3 of 8:

UCL = = 9.75 + 2 * = 15.995

Step 4 of 8:

LCL = = 9.75 - 2 * = 3.505

Step 5 of 8:

Since 8 defective steel bars lies between 3.505 and 15.995, the system is In Control.

Step 6 of 8:

Since 28 defective steel bars does not lies between 3.505 and 15.995, the system is Out of Control

Step 7 of 8:

Since 22 defective steel bars does not lies between 3.505 and 15.995, the system is Out of Control

Step 8 of 8:

For 2-sigma control limits, the Type I Error is, P(Z < -2) + P(Z > 2) = 0.02275 + 0.02275 = 0.0455