In order to establish control charts for an extraction job, 30 samples of five measurements of the extracted ores are taken, and the results are \(\overline{\bar{x}}=25.96\) tons and \(\bar{s}=1.5\) tons. Using the method of Exercise 15.5, construct an \(\bar{x}\) chart for \(n=5\) and on it plot the following means obtained in 25 successive samples: 24.15    25 .16    27.86    26.89    27.85    28.96    32.45    19.95    22.15    23.96    25.18  25.15    24.19    29.86    25.81    22.45    26.95    28.42    27.35    24 .12    21 .36    28 .45    27 .61    23 .95    24.81. Discuss the results.

Data From Exercise 15.5

Transcribed Image Text:

15.5 If the sample standard deviations instead of the sam- ple ranges are used to estimate , the control limits for the resulting chart are given by A 5, where 5 is the mean of the sample standard deviations obtained from given data, and A can be found in Table 8W. Note that in connection with problems of quality con- trol the sample standard deviation is defined using the divisor n instead of n-1. The corresponding R chart is replaced by a chart, having the central line c25 and the lower and upper control limits B3 5 and B4 5, where c2, B3 and B4 can be obtained from Table 8W. (a) Construct an x chart and a chart for these sam- ples of size 3 which had x equal to 25, 28, 26, 29, 30, 32, 22, 24, 27, 26, 29, 20, 25, 24, 27, 28, 24, 23, 27, 28 and s equal to 1, 2, 3, 5, 4, 2, 1, 3, 1, 4, 4, 3, 2, 1, 5, 4, 1, 3, 2, 2. (b) Would it be reasonable to use these control limits for subsequent data? Why?