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 SampleService Life (hours) 1495500505500 2525515505515 3470480460470 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

Answer 1

Sample number 3

Explanation:

From the given information:

Sample Service life(hours) Total Mean(X)

1 2 3 4

1 495 500 505 500 2000 500

2 525 515 505 515 2060 515

3 470 480 460 470 1880 470

Total =
`\text{addition \ of \ numbers \ of \ observations}`

Mean =
`\frac{\text{addition \ of \ numbers \ of \ observations}}{4}`

Thus;

`UCL = \mu+x = 500 + 20 = 520\\ \\ LCL= \mu -x = 500 -20 =480`

To plot on an X_Bar chart, we have:

Sample Mean (X) UCL LCL

1 500 520 480

5 515 520 480

6 470 520 480

The x-Bar chart is shown in the image attached below. From the image, we realize that the average service life for sample number 3 occurs to be out of the statistical control.