A design engineer wants to construct a sample mean chart for controlling the ser

Question

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results:

If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control?

Sample Service Life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470

Explanation / Answer

There are 4 instances which has been out of control and the first one is the first instance of the sample 2 where the sample is out of control but if derive the mean of the instances in sample 2:

= (525+515+505+515)/4

= 515

The sample as a whole is in control

In sample 3 there are 3 instances which are out of control as they are below the lower control limit. The mean is:

= (470+480+460+470)/4

= 470

This sample as a whole is out of control.

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