The mean time to expose a single panel in a circuit-board plant is 2 minutes with a standard deviation of 1.5 minutes. What is the natural coefficient of variation? If the times remain independent, what will be the mean and variance of a job of 60 panels? What will be the coefficient of variation of the job of 60? (Hint: The Central Limit Theorem for the Sum can be applied to this question.) Now suppose times to failure on the expose machine are exponentially distributed with a mean of 60 hours and the repair time is also exponentially distributed with a mean of 2 hours. What are the effective mean and CV of the process time for a job of 60 panels? (Hint: The mean and the standard deviation of an exponential distribution are the same.) Reconsider the expose machine of Problem 3 with mean time to expose a single panel of 2 minutes with a standard deviation of 1.5
The mean time to expose a single panel in a circuit-board plant is 2 minutes with a standard deviation of 1.5 minutes.
What is the natural coefficient of variation?
If the times remain independent, what will be the mean and variance of a job of 60 panels? What will be the coefficient of variation of the job of 60?
(Hint: The Central Limit Theorem for the Sum can be applied to this question.)
Now suppose times to failure on the expose machine are exponentially distributed with a mean of 60 hours and the repair time is also exponentially distributed with a mean of 2 hours. What are the effective mean and CV of the process time for a job of 60 panels?
(Hint: The mean and the standard deviation of an exponential distribution are the same.)
Reconsider the expose machine of Problem 3 with mean time to expose a single panel of 2 minutes with a standard deviation of 1.5 minutes and jobs of 60 panels. As before, failures occur after about 60 hours of run time, but now happen only between jobs (i.e., these failures do not preempt the job). Repair times are the same as before.
(a) Compute the effective mean and CV of the process time for the 60-panel job?
(Hint: We can first figure out the average number of jobs between outages.)
(b) How do these compare with the results in Problem 3?
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