Question

Shirts makes business dress shirts. The shirts could have defects in various ways including in the weave or color of the fabric, loose buttons, wrong dimensions, and uneven stitches. 8 shirts are randomly examined, with the following results. What is the LCL for a three-sigma control chart?

Shirts Defects
1 4
2 6
3 3
4 1
5 5
6 6
7 4
8 6

a. 2.00
b. 0.00
c. -1.90
d. 1.90

Answer 1

our correct option is b = 0.00 for 3 sigma (σ)

Step-by-step explanation:

Solution:

Let's tabulate the data given:

Shirts Defects

1 4

2 6

3 3

4 1

5 5

6 6

7 4

8 6

Now, as we can see from the above data,

Number of samples taken = Shirts randomly examined = 8

Now, we have to calculate (C bar), for this we have to divide the sum of defects and total number of samples.

Note: We denoting (C bar) as B. So,

B = Sum of defects/ Number of samples

Sum of defects = 4 + 6 + 3 + 1 + 5 + 6 + 4 + 6

Sum of defects = 35

(C bar) = B = 35/8

B = 4.37

Formula to find out LCL for 3 sigma (σ):

LCL = B -
`z√(B)`

where z value for 3 sigma = 3

LCL = 4.37 -(3
`√(4.37)`)

LCL = 4.37 - (3 x (2.092)

LCL = 4.37 - (6.276)

LCL = -1.901

So, now, when the LCL = negative, it is taken as 0.0

Hence, our correct option is b = 0.00 for 3 sigma (σ)