One of the assumptions underlying the theory of control charting is that success

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 0.06. What is the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly? (Round your answer to three decimal places.) What is the probability that at least one of 45 successive points indicates a problem when in fact the process is operating correctly? (Round your answer to three decimal places.)

Explanation / Answer

Ans:

We can use Binomial distribution for above case,as trials are independent.

when n=10,p=0.06

P(atleast one)=1-P(none)=1-(1-0.06)^10=1-0.94^10=1-0.539=0.461

when n=45,p=0.06

P(atleast one)=1-P(nome)=1-(1-0.06)^45=1-0.94^45=1-0.062=0.938

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