Question

1) Triangle Packaging Machinery wants to test the quality of its cereal bag filling machines. The firm’s quality analyst took 35 samples of size 7 each from a cereal-bag-filling machine. The results were overall mean = 57.75 pounds; average range = 1.78 pounds.

a) Determine the upper and lower control limits of the x-chart, where sigma = 3

b) Determine the upper and lower control limits of the R-chart, where sigma = 3

2) The results of an inspection of component samples taken over the past 10 days at Advance Auto Parts are as given below. The sample size is 100.

Day	1		2	3	4	5	6	7	8	9	10
Defective	7		6	6	9	5	6	0	8	9	1

a) Construct a 3-sigma p-chart using this information.

b) Using the control chart in part (a), and finding that the number of defectives on the next three days are 12, 5, and 13, is the process in control?

3) Telephone inquiries of hundred Discover Card’s customers are monitored daily at random. Incidents of incorrect information or other nonconformities (such as impoliteness to customers) are recorded. The data for last week follow:

Day	1	2	3	4	5
Number of Non-conformities	5	10	23	20	15

Construct a 3-standard deviation c-chart of nonconformities.

4) Oklahoma LED’s production process yields lightbulbs with an average life of 1,800 hours and s = 100 hours. The tolerance upper and lower specification limits are 2,400 hours and 1,600 hours, respectively. Is this process capable of producing lightbulbs to specification?

Answer 1

Answer 1:

D4, D3 and A2 are taken from the table of factors computing 3 sigma control limits, sample size=7

overall mean= Xbarbar= 57.75, overall range= Rbar= 1.78

a.

A2 (n=7)			0.419
control limits for X bar,
CL or Xbarbar			57.750
UCL=Xbarbar+ (A2)*Rbar			58.496
LCL=Xbarbar- (A2)*Rbar			57.004

b.

D4 (n=7)=			1.924
D3 (n=7)=			0.076
control limits for Range,
CL or R-bar			1.780
UCL=R-bar*D4			3.425
LCL=R-bar*D3			0.135