While efficiency in the production operation is important to profitability, ACME Valve is also known

for high quality finished products. Parts that do not meet specifications cannot be $$reworked$,$ so

any out of spec parts eat into the company$$s profitability both for the raw material cost and the

machine time to produce them. Drills can become dull after producing so many parts, typically

resulting in oversized holes. Machines can get out of calibration as well. For the parts in your

department the critical dimension is the diameter of the center hole and design specifications

require that tolerances be maintained within $\mathrm{.}005.$ To ensure that quality is maintained, one part

from each machine is sent to the Quality Control Lab each hour and carefully measured and its hole

diameter recorded into the QC database for each machine.

To better learn how the QC process is coordinated with the production areas, you are spending a

day in the Quality Control Lab. In looking at the data for one of the machines making aluminum

flanges, you notice some variation and possibly some trending in the data. The data points for this

machine over the last $24$ hours are shown in the control chart below

Page $5$

Hole ID $($in$.)-$ Machine #$2$

$2\mathrm{.}51$

$2\mathrm{.}505$

$2\mathrm{.}5$

$2\mathrm{.}495$

$2\mathrm{.}49$

$2\mathrm{.}485$

$123456789101112131415161718192021222324$

The individual observations are plotted by time $($i$.$e$.$ observations $1-24).$ The upper and lower

control limits based on required tolerances for the center hole diameter are shown by the

horizontal lines. Looking at this graph, answer the following questions:

a$)$ What if anything should be done at observation $6?$

b$)$ At what point $($which sample #$)$ should the QC Lab alert manufacturing that the process

may be out of control or nearly so$?$

c$)$ Did this process actually become out of control and if so how many parts potentially may

need to be scrapped?

d$)$ What could account for the sudden change between samples $23$ & $24.$