Problems 575
approximately what percentage of the items produced will fall within the
specification limits?- Determine the revisedX- andS-control limits for the data in Example 13.3a.
- In Problem 4, determine the control limits for anS-control chart.
- The following areXandSvalues for 20 subgroups of size 5.
Subgroup XSSubgroup XSSubgroup XS
1 33.8 5.1 8 36.1 4.1 15 35.6 4.8
2 37.2 5.4 9 38.2 7.3 16 36.4 4.6
3 40.4 6.1 10 32.4 6.6 17 37.2 6.1
4 39.3 5.5 11 29.7 5.1 18 31.3 5.7
5 41.1 5.2 12 31.6 5.3 19 33.6 5.5
6 40.4 4.8 13 38.4 5.8 20 36.7 4.2
7 35.0 5.0 14 40.2 6.4(a) Determine trial control limits for anX-control chart.
(b) Determine trial control limits for anS-control chart.
(c) Does it appear that the process was in control throughout?
(d) If your answer in part (c) is no, suggest values for upper and lower control
limits to be used with succeeding subgroups.
(e)If each item is supposed to have a value within 35±10, what is your estimate
of the percentage of items that will fall within this specification?- Control charts forXandSare maintained on the shear strength of spot welds.
After 30 subgroups of size 4,
∑
Xi=12,660 and∑
Si=500. Assume that the
process is in control.
(a) What are theX-control limits?
(b) What are theS-control limits?
(c) Estimate the standard deviation for the process.
(d) If the minimum specification for this weld is 400 pounds, what percentage of
the welds will not meet the minimum specification?- ControlchartsforXandSaremaintainedonresistors(inohms). Thesubgroupsize
is 4. The values of∑ XandSare computed for each subgroup. After 20 subgroups,
Xi=8,620 and
∑
Si=450.
(a) Compute the values of the limits for theXandScharts.
(b) Estimate the value ofσon the assumption that the process is in statistical
control.
(c) If the specification limits are 430±30, what conclusions can you draw
regardingtheabilityoftheprocesstoproduceitemswithinthesespecifications?