Referring to Exercise 1.8 in Chapter 1, we see that the sample of 4 deviations (observation - specification) during the second hour for a critical crank-bore diameter is

\[\begin{array}{llll}-6 & 1 & -4 & -3\end{array}\]

ten-thousandths of an inch. For these 4 deviations

(a) calculate the sample mean $\bar{x}$

(b) calculate the sample standard deviation $s$

(c) On average, is the hole too large or too small?

Data From Exercise 1.8

Data From Table 1.4

Transcribed Image Text:

1.8 A Canadian manufacturer identified a critical diameter on a crank bore that needed to be maintained within a close tolerance for the product to be successful. Sam- ples of size 4 were taken every hour. The values of the differences (measurement-specification), in ten- thousandths of an inch, are given in Table 1.4. (a) Calculate the central line for an X-bar chart for the 24 hourly sample means. The centerline is =(4.25 -3.00 1.50 +3.25)/24. (b) Is the average of all the numbers in the table, 4 for each hour, the same as the average of the 24 hourly averages? Should it be? (c) A computer calculation gives the control limits LCL = -4.48 UCL = 7.88 Construct the X-bar chart. Identify hours where the process was out of control.