Question

Shirts.com 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. Is the process in control?
Shirts Defect
1 4
2 6
3 3
4 1
5 5
6 6
7 4
8 6
a.) No, the process is not in control.
b.) Not enough information to determine this.
c.) Yes, the process is in control.

Answer 1

Answer: c.) Yes, the process is in control.

Explanation:

For the process to be in control, the number of defects have to be between the Upper Control Limit and the Lower Control limits of the c-chart which can be used to measure defects of irregularities per unit.;

UCL = C-bar + z*√(c-bar)

LCL = C-bar - z*√(c-bar)

C - Bar = $\frac{Number of Dfects}{Number of shirts}$

C - Bar = $\frac{4+6+3+1+5+6+4+6}{8}$

C - Bar = 4.375

z = 3 when using the 3 sigma control

UCL = C-bar + z*√(c-bar)

UCL = 4.375 + 3 * √(4.375)

UCL = 10.65

LCL = C-bar - z*√(c-bar)

LCL = 4.375 - 3 * √(4.375)

LCL = -1.9

LCL = 0 (Lower limit minimum should be 0 at least)

Defects are within the control limits. The process is in control.