Question

A cell 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 0.2 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

Answer 1

Given that 5000 phones are inspected every day for 10 days. Hence, the total number of observations is 5000 * 10 = 50000.

Defect percentage (p) is given as 0.2% = 0.002

Sample size (n) = 5000

Standard deviation = √ [p (1-p)/n] = √ [0.002 (1-0.002)/5000] = 0.00063

Upper control limit is the addition of Defective proportion and 3 times the standard deviation.

Upper control limit = p + 3*0.00063 = 0.002 + 0.00189 = 0.00389

Lower control limit is the deduction of Defective proportion and 3 times the standard deviation.

Lower control limit = p - 3*0.00047 = 0.002 - 0.00189 = -0.00011 ≈ 0

Control limit cannot be negative. Hence, lower control limit must be taken as 0.