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.

Answer 2

The Process is in Control when the Upper Control Limit is above Zero atleast and Lower Control Limit should be Zero. Hence option is C is correct.

Upper Control Limit and Lower Control Limit

To Answer the given question, we need to find the value of UCL and LCL. The Formula for the UCL and LCL are as follows:

• UCL = C-bar + z*√(c-bar)

• LCL = C-bar - z*√(c-bar)

Where C- Bar is average of total numbers of defect shirts, hence value = 4.375, and z is sigma value control thus value will be 3.

Solving these equation will give result UCL as 10.65, and LCL as -1.9. Therefore, correct option is C. Yes, the process is in control.

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