A process is normally distributed and in control, with known mean and variance, and the usual three-sigma limits are used on the x control chart, so that the probability of a single point plotting outside the control limits when the process is in control is 0.0027. Suppose that this chart is being used in phase I and the averages from a set of m samples or subgroups from this process are plotted on this chart. What is the probability that at least one of the averages will plot outside the control limits when m = 5? Repeat these calculations for the cases where m = 10, m = 20, m = 30, and m = 50. Discuss the results that you have obtained
Answer to relevant QuestionsReconsider the situation in Exercise 5.32. Suppose that the process mean and variance were unknown and had to be estimated from the data available from the m subgroups. What complications would this introduce in the ...The fill volume of soft-drink beverage bottles is an important quality characteristic. The colume is measured (approximately) by placing a gauge over the crown and comparing the height of the liquid in the neck of the bottle ...Samples of n = 6 items each are taken from a process at regular intervals. A quality characteristic is measured, and x and R values are calculated for each sample. After 50 samples, we have Assume that the quality ...Control charts for x and R are maintained for an important quality characteristic. The sample size is n= 7; x and R are computed for each sample. After 35 samples we have found that (a) Set up x and R charts using these ...Samples f n= 5 units are taken from a process every hour. The x and R values for a particular quality characteristic are determined. After 25 sample have been collected, we calculate x =20 and R = 4.56. (a) What are the ...
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