Qusetion: In the context of Exercise, suppose that after five interruptions the process undergoes a major evaluation. Suppose also that inspections happen once every week. Let Y denote the number of weeks between successive major evaluations.
(a) The random variable Y is (choose one)
(i) binomial
(ii) hypergeometric
(iii) negative binomial
(iv) Poisson.
(b) Find the expected value and variance of Y.
Exercise: Average run length. To control the quality of a manufactured product, samples of the product are taken at specified inspection time periods and a quality characteristic is measured for each product. If the average measurement falls below a certain predetermined threshold, the process is declared out of control and is interrupted. The number of inspections between successive interruptions of the process is called a run length. The expected value of the random variable X = run length is called the average run length. Suppose the probability that an inspection will result in the process being interrupted is 0.01.
(a) The random variable X is (choose one)
(i) binomial
(ii) hypergeometric
(iii) negative binomial
(iv) Poisson.
(b) Give the sample space and PMF of X.
(c) What is the average run length?