Since the implementation of an SPC program in the foundry department in January 1990, the engineers had made one change in the foundry operations, which appear to have resulted in a 4% reduction in the scrap rate from the 1989 average rate of 28% (the standard deviation was 2%) The table summarizes the weekly scrap rate data for the first half of 1990. i123456789 10 11 12 13 X 26.4 25.3 31.8 27.1 28.5 20.2 19.3 22.7 20.4 19.5 21.7 24 22.6 (a) Construct a CUSUM chart to analyze the data and verify the engineer's claim regarding the scrap reduction. Please use h = 5 and k = 0.25. and K=ko=0.25*2=0.5, H=ho=5*2=10. A table like this may help with your calculation: i - X₁ X₁(HK) | C† N+ (μo-K) - X₁ Ci NIC or OC? 1 2 13 (b) What is the starting point that an out-of-control sample appears? (c) What is the magnitude of the mean shift?

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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Author:HOUGHTON MIFFLIN HARCOURT
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Chapter11: Data Analysis And Displays
Section: Chapter Questions
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Since the implementation of an SPC program in the foundry department in January 1990, the
engineers had made one change in the foundry operations, which appear to have resulted in a
4% reduction in the scrap rate from the 1989 average rate of 28% (the standard deviation was
2%)
The table summarizes the weekly scrap rate data for the first half of 1990.
i123456789 10 11 12 13
X 26.4 25.3 31.8 27.1 28.5 20.2 19.3 22.7 20.4 19.5 21.7 24 22.6
(a) Construct a CUSUM chart to analyze the data and verify the engineer's claim
regarding the scrap reduction. Please use h = 5 and k = 0.25. and
K=ko=0.25*2=0.5, H=ho=5*2=10.
A table like this may help with your calculation:
i
-
X₁ X₁(HK) | C†
N+
(μo-K) - X₁
Ci
NIC or OC?
1
2
13
(b) What is the starting point that an out-of-control sample appears?
(c) What is the magnitude of the mean shift?
Transcribed Image Text:Since the implementation of an SPC program in the foundry department in January 1990, the engineers had made one change in the foundry operations, which appear to have resulted in a 4% reduction in the scrap rate from the 1989 average rate of 28% (the standard deviation was 2%) The table summarizes the weekly scrap rate data for the first half of 1990. i123456789 10 11 12 13 X 26.4 25.3 31.8 27.1 28.5 20.2 19.3 22.7 20.4 19.5 21.7 24 22.6 (a) Construct a CUSUM chart to analyze the data and verify the engineer's claim regarding the scrap reduction. Please use h = 5 and k = 0.25. and K=ko=0.25*2=0.5, H=ho=5*2=10. A table like this may help with your calculation: i - X₁ X₁(HK) | C† N+ (μo-K) - X₁ Ci NIC or OC? 1 2 13 (b) What is the starting point that an out-of-control sample appears? (c) What is the magnitude of the mean shift?
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