Question

A control chart for nonconformities is to be constructed with c=2.0, LCL=0, and UCL such that the probability of a point plotting outside control limits when c-2.0 is only 0.005

(a) Find the UCL
(b) What is the type error probability if the process is assumed to be out of control only when two consecutive points fall outside the control limits?

Answer 1

To find the UCL, we need to find the z-score that corresponds to the probability of a point plotting outside control limits. For part b, we need to find the probability that two consecutive points fall outside the control limits.

Step-by-step explanation:

To find the UCL, we need to find the z-score that corresponds to the probability of a point plotting outside control limits. Since the probability is 0.005 and we want to find the z-score for the right tail, we can use a standard normal distribution table or calculator. The z-score is approximately 2.575. The UCL can be calculated using the formula UCL = c + 2 * (Standard Deviation).For part b, to calculate the type error probability, we need to find the probability that two consecutive points fall outside the control limits. This is the probability of both points being outside the limits, which is equal to the probability of a single point outside the limits squared. So the type error probability is 0.005 * 0.005 = 0.000025.