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Explain why a Shewhart control chart is limited in its ability to detect smaller process shifts.

Scenario: Suppose you joined a start-up company to produce paper helicopters which are intended to be an educational toy. The name of the company is California Choppers. The company consists of 5 people (Peter, Meir, Jennifer, Sara, and Selina) who were responsible for the product development, and who are now responsible for production.

Each of the 5 production personnel works for an 8-hour shift with a production output of 20 helicopters. Each of them uses their own tools and measurement equipment, so they are concerned that the performance of helicopters produced on different shifts may vary.

Your role in the company is to provide expertise for quality assurance. As a first step, the team has asked you to institute an SPC process to understand performance variability of flight times when the helicopter is dropped from 5 feet.

The flight duration data was collected for one week (5 shifts) and is shown graphically as a Shewhart control chart. The data from shift 1 (samples 1 to 20) was used to set the control limits.

This data set appears to be under control, but upon close examination, it was found that there may be l process shifts from operator-to-operator. The data is provided on the next page.

Their team leader is convinced that they can control the production with a Shewhart control chart, but the rest of the team is not so sure. So they hired you as an SPC expert! Your first assignment is as follows:

  1. Explain why a Shewhart control chart is limited in its ability to detect smaller process shifts. You should use the data from the first five shifts to illustrate the points.
  2. Propose an alternate control chart approach, and explain why it’s an improvement.
  3. Graph the data using the alternative approach, showing the control limits.

Test-taking advice: This need not be a long document (max of 2 pages), but you need to be careful to articulate your ideas. I’d propose you format with an introductory paragraph, and then for each idea on why the Shewhart chart is limited- state the conjecture, and then explain why. Similarly, for the alternative approach, state your conjecture, and explain why it’s an improvement.

Shift 1 Shift 2 Shift 3 Shift 4 Shift 5
1 Peter 1.644 Meir 1.903 Jennifer 1.510 Sara 1.668 Selina 1.812
2 Peter 1.823 Meir 1.852 Jennifer 1.576 Sara 1.909 Selina 1.729
3 Peter 1.585 Meir 2.060 Jennifer 1.350 Sara 1.807 Selina 1.808
4 Peter 1.464 Meir 2.206 Jennifer 1.561 Sara 1.939 Selina 1.600
5 Peter 1.807 Meir 1.730 Jennifer 1.752 Sara 1.894 Selina 1.638
6 Peter 2.062 Meir 1.715 Jennifer 1.607 Sara 1.232 Selina 1.758
7 Peter 1.213 Meir 1.898 Jennifer 1.208 Sara 1.723 Selina 1.461
8 Peter 1.770 Meir 2.263 Jennifer 1.444 Sara 1.624 Selina 1.756
9 Peter 1.834 Meir 1.960 Jennifer 1.462 Sara 1.433 Selina 1.310
10 Peter 1.581 Meir 1.875 Jennifer 1.895 Sara 1.438 Selina 1.684
11 Peter 1.512 Meir 1.921 Jennifer 1.426 Sara 1.490 Selina 1.640
12 Peter 1.693 Meir 1.688 Jennifer 1.269 Sara 1.588 Selina 1.596
13 Peter 1.751 Meir 1.912 Jennifer 1.463 Sara 1.473 Selina 1.786
14 Peter 1.608 Meir 1.942 Jennifer 1.424 Sara 1.577 Selina 1.891
15 Peter 1.689 Meir 1.421 Jennifer 1.465 Sara 2.046 Selina 1.847
16 Peter 1.970 Meir 2.072 Jennifer 1.101 Sara 1.730 Selina 1.422
17 Peter 1.993 Meir 1.995 Jennifer 1.903 Sara 1.658 Selina 1.984
18 Peter 2.049 Meir 1.852 Jennifer 1.429 Sara 1.565 Selina 1.808
19 Peter 1.551 Meir 1.495 Jennifer 1.570 Sara 2.009 Selina 1.389
20 Peter 1.829 Meir 1.400 Jennifer 1.666 Sara 1.778 Selina 1.847

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