Chapter 14: Q6CQQ (page 654)

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.
What is the value of\(\bar R\)? In general, how is a value of\(\bar R\)obtained?

Expert verified

The value of\(\bar R\)is equal to 67.0 feet.

The value of\(\bar R\)is obtained by taking the mean of the ranges of each of the subgroups, and its formula is given as follows:

\(\bar R = \frac{{{R_1} + {R_2} + ....{R_N}}}{N}\),

where

\({R_i}\)represents the ith sample range, and

N represents the total number of samples.

Step by step solution

The R chart is plotted for the measurement of errors (in feet) obtained when the aircraft altimetersare tested in a pressure chamber.

The individual sample size is equal to 100.

By observing the R control chart, the value of\[\bar R\]is written on the left side of the chart adjacent to the central line.

Thus, the value of\[{\bf{\bar R}}\]is equal to 67.00 feet.

The general formula for computing the value of\[{\bf{\bar R}}\]is as follows:

\(\bar R = \frac{{{R_1} + {R_2} + .... + {R_N}}}{N}\),

where\({R_i}\)is the ith sample range, (i=1,2,…,N) and Nis the total number of samples.

First,obtain the range for each of the subgroupsand then take a sum of these ranges which is divided by the total number of samples.

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