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# Statistics Control charts, probabilities

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Consider the xbar chart for the piston-ring example as follows, let ring diameter be normally distributed, and the sample size is n = 5.

a) Find the two-sigma control limits for this chart.
b) Suppose it was suggested that the two-sigma limits be used instead of the typical three-sigma limits. What effect would this have on the occurrence of false alarms?
c) What effect would the use of two sigma limits have on the in-control ARL of the chart.
d) Discuss the meaning of your findings in parts (b) and (c).

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The expert examines statistics control charts for probabilities.

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1. Consider the xbar chart for the piston-ring example as follows, let ring diameter be normally distributed, and the sample size is n = 5.

a) Find the two-sigma control limits for this chart.
Solution: We divide UCL-average by 3 to get 1-sigma limit:
1-sigma limit = (74.0135-74)/3 = 0.0045
Average + 1-sigma limit = 74.0000 + 0.0045 = 74.0045
Average - 1-sigma limit = 74.0000 + 0.00045 = 73.9955
These lines can now be ...

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