Q. 2 Let X be a continuous random variable (quality characteristic of interest in aprocess) with mean u and standard deviation o (i.e. variance o) and isnormally distributed, i.e. X N (4,0'). Let x,,x,.x, be a random sample ofsize n from the process. Using this information, provide computations for thefollowing process scenarios. Using 25 phase I in-control samples of size n=2,we got =0.0296, R = 1.3167, S = 0.9311. For X , R and S charts, providethe following.i. 3-sigma control limitsIf the process variance remains stable at o but mean shifts to newlevel 4, = 4, + 8o,. Using the probability limits at false alarm rate of0.005 for X chart, evaluate the power at 8=-0.25 and 0.75 and findii.their corresponding ARL, values. Also interpret your results.

X is a continuous random variable. The answer can be given using the normal distribution.

Q. 2 process) with mean u and standard deviation o (i.e. variance o) and is normally distributed, i.e. X N (u,0o'). Let x,,x,.x, be a random sample of size n from the process. Using this information, provide computations for the following process scenarios. Using 25 phase I in-control samples of size n=2, we got F=0.0296, R 1.3167, 5 0.9311. ForX , R and S charts, provide the following. i. 3-sigma control limits Let X be a continuous random variable (quality characteristic of interest in a ii. If the process variance remains stable at o, but mean shifts to new level 4, = 4, + 8o,. Using the probability limits at false alarm rate of 0.005 for X chart, evaluate the power at 8= -0.25 and 0.75 and find their corresponding ARL, values. Also interpret your results.

Q. 2 process) with mean u and standard deviation o (i.e. variance o) and is normally distributed, i.e. X N (u,0o'). Let x,,x,.x, be a random sample of size n from the process. Using this information, provide computations for the following process scenarios. Using 25 phase I in-control samples of size n=2, we got F=0.0296, R 1.3167, 5 0.9311. ForX , R and S charts, provide the following. i. 3-sigma control limits Let X be a continuous random variable (quality characteristic of interest in a ii. If the process variance remains stable at o, but mean shifts to new level 4, = 4, + 8o,. Using the probability limits at false alarm rate of 0.005 for X chart, evaluate the power at 8= -0.25 and 0.75 and find their corresponding ARL, values. Also interpret your results.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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Question

Q. 2 Let X be a continuous random variable (quality characteristic of interest in a
process) with mean u and standard deviation o (i.e. variance o) and is
normally distributed, i.e. X N (4,0'). Let x,,x,.x, be a random sample of
size n from the process. Using this information, provide computations for the
following process scenarios. Using 25 phase I in-control samples of size n=2,
we got =0.0296, R = 1.3167, S = 0.9311. For X , R and S charts, provide
the following.
i. 3-sigma control limits
If the process variance remains stable at o but mean shifts to new
level 4, = 4, + 8o,. Using the probability limits at false alarm rate of
0.005 for X chart, evaluate the power at 8=-0.25 and 0.75 and find
ii.
their corresponding ARL, values. Also interpret your results.

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