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, what is his risk (alpha) of concluding that service life is out of control when it is actually under control (Type I error)?

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

		0.0026
		0.0456
		0.3174
		0.6826
		0.9544

Answer 1

ANSWER Given that an designer engineer wants to construct a sample mean chast. given upper control limit = 520 hours lower control limit a 480 hours (UCL) (LOL) Mean = 500 hours "z UCL-mean - value for upper control limit = 520 - 500 lo LCL - mean Z value for control limit = lower 480 500 a ko at 480 asco - -2 - lies between 2 an. the probabi - Referring to the standard normal distribution table, the probability of " Ž lies b/w r2 and 2 is 0.9544.

. Hence, the risk of concluding that service life of Control when it is under Control - 1-0.95un. oiou56 is the answer