Question

A paint booth operation runs 5 days per week. As the production supervisor, you track the number of errors produced by the paint booth by week. Errors can be of any type (over spray, inadequate coverage, etc.), may occur on one or more pieces of equipment, and the number and type of equipment painted varies greatly. Ten weeks of data were collected and the number of errors identified are found in the following table. Construct a control chart with 3-sigma control limits to determine if the process is in control. Week Number of errors 1 5 2 4 3 5 4 4 5 4 6 3 7 0 8 2 9 0 10 3 1. What are the CL, UCL, and LCL? 2. Draw the control chart and plot the 10-weeks of data? 3. Does the control chart suggest that the paint booth operation may be out-of-control? Explain. 4. After investigating, you determine that there is a special cause. The paint booth had become wore and was overhauled after Week 5. What, if anything, should you do to continue monitoring the paint booth operation? Please demonstrate what should be done.

Answer 1

Answer:

1. CL, UCL, and LCL:

Sample	1	2	3	4	5	6	7	8	9	10
Data	5	4	5	4	4	3	0	2	0	3

u bar = Non conformance or defects (mean)

n = Sample Size

CL = Average = u bar = (5+4+5+4+4+3+0+2+0+3)/10 = 3.00

UCL = u bar + 3√(u bar/n) = 4.64

LCL = u bar - 3√(u bar/n) = 1.36

2. Control chart for the 10-weeks of data:

Populate the data:

	1	2	3	4	5	6	7	8	9	10
CL	3.00	3.00	3.00	3.00	3.00	3.00	3.00	3.00	3.00	3.00
UCL	4.64	4.64	4.64	4.64	4.64	4.64	4.64	4.64	4.64	4.64
LCL	1.36	1.36	1.36	1.36	1.36	1.36	1.36	1.36	1.36	1.36
Data	5	4	5	4	4	3	0	2	0	3

Draw the U-chart:

3. The control chart suggests that the paint booth operation is out-of-control because the initial defects are going beyond the UCL.

4. The paint booth had become wore and was overhauled after Week 5:

After the overhaul of paint booth after week 5, the number of defects reduced significantly and in some cases had gone till “0”.

So the regular periodic preventive maintenance (overhaul) should be done of the paint booth so that the process is within the statistical process control.