High School

We appreciate your visit to William Manufacturers has decided to use a c Chart to monitor the number of defects per minivan produced by their manufacturing process The c Chart. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

William Manufacturers has decided to use a c-Chart to monitor the number of defects per minivan produced by their manufacturing process. The c-Chart should be constructed with an alpha risk of 9%. The operations manager randomly samples one minivan at six successively selected time periods and counts the number of defects in the minivan.

Sample Defects:
1: 12
2: 6
3: 7
4: 15
5: 14
6: 7

Steps:

**Step 1 of 7:**
What is the Center Line of the control chart? Round your answer to three decimal places.

**Step 2 of 7:**
What is the Upper Control Limit? Round your answer to three decimal places.

**Step 3 of 7:**
What is the Lower Control Limit? Round your answer to three decimal places.

**Step 4 of 7:**
At the next time period, 20 defects were detected on the randomly selected minivan. Determine if the process is "In Control" or "Out of Control".

**Step 5 of 7:**
At the next time period, 17 defects were detected on the randomly selected minivan. Determine if the process is "In Control" or "Out of Control".

**Step 6 of 7:**
At the next time period, 7 defects were detected on the randomly selected minivan. Determine if the process is "In Control" or "Out of Control".

**Step 7 of 7:**
You, acting as the operations 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 :

The c-Chart is used to monitor defects per minivan. The center line, upper control limit, lower control limit, and process control are determined. The probability of a Type I Error is calculated.


1. The Center Line of the control chart represents the average number of defects per minivan. It is calculated by finding the average of the sample defects: (12 + 6 + 7 + 15 + 14 + 7) / 6 = 61 / 6 ≈ 10.167.

2. The Upper Control Limit (UCL) is calculated using the formula: UCL = Center Line + 3 * √(Center Line) = 10.167 + 3 * √(10.167) ≈ 24.157.

3. The Lower Control Limit (LCL) is calculated using the formula: LCL = Center Line - 3 * √(Center Line) = 10.167 - 3 * √(10.167) ≈ -3.824. Since the LCL cannot be negative, it is set to zero.

4-6). To determine if the process is "In Control" or "Out of Control" at each time period, compare the number of defects detected to the control limits. If the number of defects is within the control limits, the process is "In Control"; otherwise, it is "Out of Control".

7. The probability of a Type I Error is the alpha risk (9%) specified in the problem. Therefore, the probability that the process is actually "In Control" when it is concluded as "Out of Control" is 0.09, or 9%. This represents the chance of incorrectly rejecting the null hypothesis and concluding that the process is "Out of Control" when it is actually "In Control".


Learn more about Control chart click here :brainly.com/question/18958241

#SPJ11

Thanks for taking the time to read William Manufacturers has decided to use a c Chart to monitor the number of defects per minivan produced by their manufacturing process The c Chart. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada