Problem 1 A metal fabricator produces connecting rods with an outer diameter tha
ID: 362027 • Letter: P
Question
Problem 1
A metal fabricator produces connecting rods with an outer diameter that has a 1 ± 0.02 inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.004 inches with a standard deviation of 0.003 inch.
a. Calculate the process capability index for this example. (Round your answer to 3 decimal places.)
b. Is the process capable of producing the desired quality? Explain
Problem 2
Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart for control. The samples and the number of defectives in each are shown in the following table:
SAMPLE
n
Number of Defective Items in the Sample
1
15
0
2
15
0
3
15
0
4
15
2
5
15
0
6
15
3
7
15
1
8
15
0
9
15
3
10
15
1
a. Determine the p, Sp, UCL and LCL for a p-chart of 95 percent confidence (1.96 standard deviations). (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal places. Round any negative LCL up to zero.)
b. What comments can you make about the process? Why?
b.1 Process is out of statistical control.
b.2 Process is in statistical control.
SAMPLE
n
Number of Defective Items in the Sample
1
15
0
2
15
0
3
15
0
4
15
2
5
15
0
6
15
3
7
15
1
8
15
0
9
15
3
10
15
1
a. Determine the p, Sp, UCL and LCL for a p-chart of 95 percent confidence (1.96 standard deviations). (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal places. Round any negative LCL up to zero.)
b. What comments can you make about the process? Why?
b.1 Process is out of statistical control.
b.2 Process is in statistical control.
Explanation / Answer
1) UCL = 1.02
LCL = 0.98
Mean = 1.004
SD = 0.003
a) As the mean is not centered, Cpk will be used
aCpk = Min ((UCL-Mean)/(3*SD), (Mean-LCL)/(3*SD))
= Min ((1.02-1.004)/(3*0.003), (1.004-0.98)/(3*0.003))
= Min (1.78, 2.67)
= 1.78
b) The process is capable as Cpk value is above 1.33
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