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: Sample Service Life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 What is the LCL and UCL of the R-chart?

Explanation / Answer

mean of group 1

495 +500 +505+ 500 /4 = 500

mean of group 2

525 +515+ 505+ 515 /4 = 515

mean of group 3

470 +480 +460+ 470 /4 = 470

hence Ucl = 515

LCL = 470

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