Question

Jim's Outfitters, Inc., makes custom fancy shirts for cowboys. The shirts could be flawed in various ways, including flaws in the weave or color of the fabric, loose buttons or decorations, wrong dimensions, and uneven stitches. Jim randomly examined 10 shirts, with the following results shown to the right. Shirt Defects 1 7

2 1
3 6
4 10
5 7
6 9
7 1
8 5
9 8
10 5
a. Assuming that 10 observations are adequate for these purposes, determine the three-sigma control limits for defects per shirt. The UCLo equals and the LCLc equals.(Enter your responses rounded to two decimal places. If your answer for LCLc is negative, enter this value as 0.)

Answer 1

To determine the three-sigma control limits for defects per shirt, calculate the mean and standard deviation of the given observations and use them to calculate the UCLo and LCLc. The UCLo is 14.21 and the LCLc is 0.

Step-by-step explanation:

To determine the three-sigma control limits for defects per shirt, we can use the given observations to calculate the mean and standard deviation. The mean is the average of the defects per shirt, while the standard deviation measures the variability of the defects per shirt. The UCLo is calculated as: UCLo = mean + (3 * standard deviation) and the LCLc is calculated as: LCLc = max(0, mean - (3 * standard deviation)).

Using the given observations:

1. The mean defects per shirt = (1 + 7 + 6 + 10 + 7 + 9 + 1 + 5 + 8 + 5) / 10 = 5.9 (rounded to one decimal place)
2. The standard deviation of defects per shirt = square root((1 - 5.9)^2 + (7 - 5.9)^2 + (6 - 5.9)^2 + (10 - 5.9)^2 + (7 - 5.9)^2 + (9 - 5.9)^2 + (1 - 5.9)^2 + (5 - 5.9)^2 + (8 - 5.9)^2 + (5 - 5.9)^2) / 10 = 2.77 (rounded to two decimal places)
3. The UCLo = 5.9 + (3 * 2.77) = 14.21 (rounded to two decimal places)
4. The LCLc = max(0, 5.9 - (3 * 2.77)) = max(0, -1.31) = 0 (since negative values are rounded to 0)

Therefore, the UCLo is 14.21 and the LCLc is 0.