Perform the following experiment. Place 200 pennies in a container (as an alternative, some other item such as poker chips or marbles will do). Line up five Styrofoam cups. The first four cups represent work-in-process between five workstations in a production line. Cup number five represents the output from the entire line that can be shipped to customers. Now let the roll of a single die represent the output for any of the workstations on one production cycle. Roll the die and place the corresponding number of pennies in the first cup. This is the production output for workstation number one on the first cycle. Now roll the die again and, based on the number that comes up, transfer that number of pennies from the first cup to the second cup. If the number on the die is greater than the number of pennies in cup number one, then transfer the entire contents to cup number two. Continue this process until the die has been thrown and pennies transferred for all five workstations. This completes the first cycle. Now, repeat this process for 20 cycles. Then answer the following questions. (Note: This experiment is more interesting if five different people participate as operators of the individual workstations and a sixth person keeps track of the cycle count.)
a. What is the expected output for each workstation? (Hint: What is the expected outcome from a single throw of a fair [i.e., nonbiased] die?)
b. What is the expected total production output for 20 cycles?
c. From the experiment, how many units did you count in cup number five that could actually be shipped to customers? How do you explain any observed discrepancy between the number of observed and the number you expected in part b?
d. What are the implications of this experiment on process variability?
e. What assumptions did we make with this experiment and are these assumptions realistic? (Hint: Consider the concepts of line balancing and workstation capacity.)