Answering questions

The mean time to expose a single panel in a circuit-board plant is 2 minutes with a standard deviation of 1.5 minutes.

  • (a) What is the natural coefficient of variation?
  • (b) 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?
  • (c) 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?

Reconsider the expose machine of Problem (1) 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. Compute the effective mean and CV of the process times for the 60-panel jobs. How do these compare with the results in Problem 1?

Frequently, natural process times are made up of several distinct stages. For instance, a manual task can be thought of as being comprised of individual motions (or “therbligs” as Gilbreth termed them). Suppose a manual task takes a single operator an average of 1 hour to perform. Alternatively, the task could be separated into 10 distinct 6-minute subtasks performed by separate operators. Suppose that the subtask times are independent (i.e., uncorrelated), and assume that the coefficient of variation is 0.75 for both the single large task and the small subtasks. Such an assumption will be valid if the relative shapes of the process time distributions for both large and small tasks are the same. (Recall that the variances of independent random variables are additive.)

  • (a) What is the coefficient of variation for the 10 subtasks taken together?
  • (b) Write an expression relating the SCV of the original tasks to the SCV of the combined task.
  • (c) What are the issues that must be considered before dividing a task into smaller subtasks? Why not divide it into as many as possible? Give several pros and cons.
  • (d) One of the principles of JIT is to standardize production. How does this explain some of the success of JIT in terms of variability reduction?