Quality Control

Process Performence and Quality
Control Chart for Variable

Webster Chemical Company produces mastics and caulking for the constrtuction industry. The Product is blended in large mixers and then pumped into tubes and capped.


Webster is concrerned whether the filling process for tubes of caulking is in statistical control. The process should be center on 8 ounces per tube. SEveral samples of 8 tubes are taken and each tube is weighed in ounces.



Sample Tube Number Avg Range
1 2 3 4 5 6 7 8
1 7.98 8.34 8.02 7.94 8.44 7.68 7.81 8.11 8.04
2 8.23 8.12 7.98 8.41 8.31 8.18 7.99 8.06 8.16
3 7.89 7.77 7.91 8.04 8 7.89 7.93 8.09 7.94
4 8.24 8.18 7.83 8.05 7.9 8.16 7.97 8.07 8.05
5 7.87 8.13 7.92 7.99 8.1 7.81 8.14 7.88 7.98
6 8.13 8.14 8.11 8.13 8.14 8.12 8.13 8.14 8.13
Avgs 8.05

Assuming that taking only 6 samples is sufficient, is the process in statistical control?
Conclusion on process variability

UCLR =
LCLR =

Conclusion on process average
UCLX =
LCLX =


p-Chart for Attributes

A sticky scale brings Webster's attention to whether caulking tubes are being properly capped. If a significant proportion of the tubes aren't being sealed, Webster is placing their customers in a messy situation. Tubes are packaged in large boxes of 144. Several boxes are inspected and the following number of leaking tubes are faund:




Sample Tubes Sample Tubes Sample Tubes
1 3 8 6 15 5
2 5 9 4 16 0
3 3 10 9 17 2
4 4 11 2 18 6
5 2 12 6 19 2
6 4 13 5 20 1
7 2 14 1 Total =

Calculate the p-chart three-sigma control limits to assess whether the capping process is in statistical control.

UCL =
LCL =

c-chart for Attributes

At Webster Chemical, lumps in the caulking compound could cause difficulties in dispemsing a smooth bead from the tube. Even when the process is in control, there will still be an average of 4 lumps per tube of caulk. Testing for the presence of lumps destroys the product, so Webster takes random samples. The following are results of the study :




Tube # Lumps Tube # Lumps Tube # Lumps
1 6 5 6 9 5
2 5 6 4 10 0
3 0 7 1 11 9
4 4 8 6 12 2

Determine the c-chart two-sigma upper and lower control limits for this for this process

c = σc =

UCLXc = LCLc =

Process Capability Analysis
Webster Chemical nominal weight for filling tubes of caulk is 8.00 ounces + 0.60 ounces. The target process capability ratio is 1.33. The current distrubution of the filling process is centered on 8.054 ounces with a standart deviation of 0.192 ounces. Compute the process capability ratio and process capability index to assess whether the filling process and set properly.




Process capability Ratio
Cp =

Process capability Ratio
Cpk =