Acell phone manufacturer inspects the video display on each color phone to verify that the screen can display all colors with the brilliance their customers have come to expect. each phone is turned on, run through a self-test procedure, and classified as either acceptable or unacceptable based on test performance. based on historical data, the manufacturer produces 0.1 percent defective displays. if they inspect 5000 phones each day for the next 10 days, what are the upper and lower control limits for their control chart if their sample mean mirrors their historical process average?

The answer is 0.002341 and 0.000000

Explanation

From the question stated we recall the following:

Let us find the lower and upper and control limits for their chart control if their mean sample mirrors their historical process average?

Now,

The number of sample size n =5000

The number of sample k =10

The total number of observations = n x k = 5000 x 10 = 50000

The proportion defective displays p = 0.1% which is =0.001

The standard deviation, Sp = √p (1-p)/n = √0.001 x (1-0.001)/5000 =0.000447

The Upper control limit is UCL = p+3 x Sp =0.001+3 x 0.000447 =0.002341

The Lower control limit is UCL = p -3 x Sp = 0.001 - 3 x 0.000447 = -0.000341 which is 0

Therefore the LCL is 0 which is seen as negative