James R. Martin, Ph.D., CMA
Professor Emeritus, University of South Florida
2. a (c if 2 standard deviations are used to establish the limits.)
1. The grand mean is 11.69. The mean of the ranges is .54.
The values for the equation below are from Exhibit 3-9 and based on 6 items per sample.
The upper limit is 11.69 + (.483)(.54) = 11.95
The lower limit is 11.69 - (.483)(.54) = 11.429
2. The limits for the range are based on the following equations.
The upper limit is (2.004)(.54) = 1.08216
The lower limit is (0)(.54) = 0
3. Yes the process appears to be in control since all ten means are within the limits, although some of the individual observations are outside the limits.
The original grand mean is 129.6/12 = 10.8
The new grand mean is 120/12 = 10
Note that every point in the new set of data is below the original mean. Unless the truck is being used for a different purpose (e.g., city driving vs. highway, heavy loads vs. light loads), it appears that it might be time for a tune up. Another possibility is that a different type of gas is being used. A different driver who drives less economically could also cause different results.