Question

The inner-diameter of piston rings follows a normal distribution with mean 75mm and variance = 9. The sample size is 5.

(1) If L=2, what is Type I error rate when the process is under in-control?

(2) If we set the control limits to UCL=78.354 and LCL=71.646, what is Type I error rate?

Answer 1

1)

For L = 2 standard deviations,

Type I error rate is the probability that the mean error rate is outside the control limit. The probability is obtained as follows,

The probability is obtained from the z distribution table for z = 2 and z = -2

2)

the control limits are,

The probability is obtained by calculating the z score,

The probability is obtained from the z distribution table for z = 2.4999 and z = -2.4999