Two decision rules are given here. Assume they apply to a normally distributed quality characteristic and the sample size is n = 5. (a) Rule 1: The control chart uses the three-sigma control limits. If one or more of the next seven samples yield values of the sample average that fall outside the control limits, conclude that the process is out of control. i) What is the probability that a sample average is outside the 3-sigma control limits? ii) What is the α-error probability for the control chart under Rule 1?
Two decision rules are given here. Assume they apply to a
(a) Rule 1: The control chart uses the three-sigma control limits. If one or more of the next seven samples yield values of the sample average that fall outside the control limits, conclude that the process is out of control.
i) What is the probability that a sample average is outside the 3-sigma control limits?
ii) What is the α-error probability for the control chart under Rule 1?
a) Rule 1: i) The probability that a sample average is outside the 3-sigma control limits can be calculated as follows:
UCL = µ + 3σ/√n
LCL = µ -3σ/√n
where µ is the mean of the population,
n is sample size,
and σ is standard deviation of population
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