Question

One of the assumptions underlying the theory of control charting is that successive plotted points are independent of one another. Each plotted point can signal either that a manufacturing process is operating correctly or that there is some sort of malfunction. Even when a process is running correctly, there is a small probability that a particular point will signal a problem with the process. Suppose that this probability is 0.07. What is the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly

Answer 1

P(at least 1 wrong in 10) =0.5160

Explanation:

Let A be the event that there is a problem in the proces. Then the probability of problem with the process is P ( A) = 0.07

Let B be the event that the process is without the problem. Then the probability of without problem is P ( B) = 0.93

Now we want to find the 10 successive points of event B. Since the events are independent we can find this as

P(B)+P(B)+P(B)+P(B)+P(B)+P(B)+P(B)+P(B)+P(B)+P(B)

or

P(B)^ 10= .93^10=0.48398

As we have to calculate at least 1 in 10 then we will subtract it from 1.

P(at least 1 wrong in 10) = = 1 - .93^10 =1- 0.48398=0.5160