Question

I need help with my test review question please

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: Service life in hours Sample 1 Sample 2 Sample 3 Sample 4 Observation 1 495 500 505 500 Observation 2 500 456 490 Observation 3 505 456 485 474 Observation 4 500 490 474 504 490 if he uses a LCL of 481 hours and an UCL of 503, on what sample(s) (if any) does service life appear to be out of control? Hint: you don't have to calculate the UCL or LC. Sample 1 Sample 2 Sample 3 Sample 4 Sample 2 and 3

Answer 1

X-bar of Sample 1 = (495+500+505+500)/4 = 500

X-bar of Sample 2 = (500+490+456+490)/4 = 484

X-bar of Sample 3 = (505+456+485+474)/4 = 480

X-bar of Sample 4 = (500+490+474+504)/4 = 492

Given that,

UCL = 503

LCL = 481

From X-bar values we can see that X-bar value of sample 3 is not in the control limit.

Hence,

We can conclude that Sample 3 is out of control as per given UCL & LCL.