Suppose 100 observations of brass bushing parts are planned to be measured to de

Question

Suppose 100 observations of brass bushing parts are planned to be measured to design X-bar and R charts. Please design the sample size and sample frequency. Assume that the production rate is 30 parts per hour and you are required to catch a one-sigma mean shift within an hour. Show clearly how to use rational subgrouping concept to design the sample size and frequency for both X-bar and R charts. Use the data collected and construct both X-bar and R charts in Minitab. Observations shown below.
1.00100 1.00500 1.01500 1.02000 1.01000 1.01500 1.00000 1.01000 0.99900 1.01000 0.99600 1.00000 1.00400 0.99500 1.00600 0.98500 1.01000 1.00000 0.99500 1.00000 1.00000 0.99900 1.01400 1.00900 1.00500 1.02500 1.00400 1.00400 0.99900 1.00000 1.01400 1.00900 0.99400 1.00900 0.99900 1.00400 1.00900 0.98900 1.00300 1.00900 0.99600 0.99600 1.00000 1.00100 1.00100 1.00100 0.99500 1.00000 1.01000 0.99400 1.00000 1.00500 1.01500 1.00500 0.99000 1.00500 1.01500 1.00000 1.00500 0.99000 0.99700 1.00000 1.00200 1.00100 1.00600 1.00500 1.01000 1.01500 1.00000 1.00000 1.01500 0.99500 1.00500 1.01000 1.01000 1.00600 0.99900 1.00600 1.00500 1.00100 1.00700 0.99500 1.00700 0.99900 1.01000 0.99100 0.99600 1.00600 1.01900 1.00600 1.00500 1.00500 1.00100 1.00200 1.01700 0.99900 0.99300 1.00100 1.01600 0.99000
Suppose 100 observations of brass bushing parts are planned to be measured to design X-bar and R charts. Please design the sample size and sample frequency. Assume that the production rate is 30 parts per hour and you are required to catch a one-sigma mean shift within an hour. Show clearly how to use rational subgrouping concept to design the sample size and frequency for both X-bar and R charts. Use the data collected and construct both X-bar and R charts in Minitab. Observations shown below.
1.00100 1.00500 1.01500 1.02000 1.01000 1.01500 1.00000 1.01000 0.99900 1.01000 0.99600 1.00000 1.00400 0.99500 1.00600 0.98500 1.01000 1.00000 0.99500 1.00000 1.00000 0.99900 1.01400 1.00900 1.00500 1.02500 1.00400 1.00400 0.99900 1.00000 1.01400 1.00900 0.99400 1.00900 0.99900 1.00400 1.00900 0.98900 1.00300 1.00900 0.99600 0.99600 1.00000 1.00100 1.00100 1.00100 0.99500 1.00000 1.01000 0.99400 1.00000 1.00500 1.01500 1.00500 0.99000 1.00500 1.01500 1.00000 1.00500 0.99000 0.99700 1.00000 1.00200 1.00100 1.00600 1.00500 1.01000 1.01500 1.00000 1.00000 1.01500 0.99500 1.00500 1.01000 1.01000 1.00600 0.99900 1.00600 1.00500 1.00100 1.00700 0.99500 1.00700 0.99900 1.01000 0.99100 0.99600 1.00600 1.01900 1.00600 1.00500 1.00500 1.00100 1.00200 1.01700 0.99900 0.99300 1.00100 1.01600 0.99000
Suppose 100 observations of brass bushing parts are planned to be measured to design X-bar and R charts. Please design the sample size and sample frequency. Assume that the production rate is 30 parts per hour and you are required to catch a one-sigma mean shift within an hour. Show clearly how to use rational subgrouping concept to design the sample size and frequency for both X-bar and R charts. Use the data collected and construct both X-bar and R charts in Minitab. Observations shown below.
1.00100 1.00500 1.01500 1.02000 1.01000 1.01500 1.00000 1.01000 0.99900 1.01000 0.99600 1.00000 1.00400 0.99500 1.00600 0.98500 1.01000 1.00000 0.99500 1.00000 1.00000 0.99900 1.01400 1.00900 1.00500 1.02500 1.00400 1.00400 0.99900 1.00000 1.01400 1.00900 0.99400 1.00900 0.99900 1.00400 1.00900 0.98900 1.00300 1.00900 0.99600 0.99600 1.00000 1.00100 1.00100 1.00100 0.99500 1.00000 1.01000 0.99400 1.00000 1.00500 1.01500 1.00500 0.99000 1.00500 1.01500 1.00000 1.00500 0.99000 0.99700 1.00000 1.00200 1.00100 1.00600 1.00500 1.01000 1.01500 1.00000 1.00000 1.01500 0.99500 1.00500 1.01000 1.01000 1.00600 0.99900 1.00600 1.00500 1.00100 1.00700 0.99500 1.00700 0.99900 1.01000 0.99100 0.99600 1.00600 1.01900 1.00600 1.00500 1.00500 1.00100 1.00200 1.01700 0.99900 0.99300 1.00100 1.01600 0.99000

Explanation / Answer

install.packages("qcc")
library(qcc)
x=c(1.00100,
1.00500,
1.01500,
1.02000,
1.01000,
1.01500,
1.00000,
1.01000,
0.99900,
1.01000,
0.99600,
1.00000,
1.00400,
0.99500,
1.00600,
0.98500,
1.01000,
1.00000,
0.99500,
1.00000,
1.00000,
0.99900,
1.01400,
1.00900,
1.00500,
1.02500,
1.00400,
1.00400,
0.99900,
1.00000,
1.01400,
1.00900,
0.99400,
1.00900,
0.99900,
1.00400,
1.00900,
0.98900,
1.00300,
1.00900,
0.99600,
0.99600,
1.00000,
1.00100,
1.00100,
1.00100,
0.99500,
1.00000,
1.01000,
0.99400,
1.00000,
1.00500,
1.01500,
1.00500,
0.99000,
1.00500,
1.01500,
1.00000,
1.00500,
0.99000,
0.99700,
1.00000,
1.00200,
1.00100,
1.00600,
1.00500,
1.01000,
1.01500,
1.00000,
1.00000,
1.01500,
0.99500,
1.00500,
1.01000,
1.01000,
1.00600,
0.99900,
1.00600,
1.00500,
1.00100,
1.00700,
0.99500,
1.00700,
0.99900,
1.01000,
0.99100,
0.99600,
1.00600,
1.01900,
1.00600,
1.00500,
1.00500,
1.00100,
1.00200,
1.01700,
0.99900,
0.99300,
1.00100,
1.01600,
0.99000)
xx=cbind(x,x,x,x,x)
q=qcc(xx, type="R", nsigmas=1)

q1=qcc(xx, type="xbar", nsigmas=1)

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