Three parts are required to fully assemble an item. The times and probabilities

Question

Three parts are required to fully assemble an item. The times and probabilities to complete each part of the assembly are shown below. Worker B is a robot, and all parts always take exactly 5 minutes. Worker C has the most difficult task, and, as you can see, their times have the largest range. A worker can only work on one item at a time, and they cannot work on an item until the previous worker is finished. a. Complete the tables below to find the Expected Length of Time for each worker to complete their task. b. A customer orders three parts, and wants to know when they can be ready. Using the results from (a), calculate how long it's expected to take. c. Using the answer from (b), sketch a graph of what the times might look like if we took into account the variability in times only. d. The actual amount of time ranges from 22 to 44 minutes. Sketch what this graph might look like. e. Explain why the two graphs differ. Three parts are required to fully assemble an item. The times and probabilities to complete each part of the assembly are shown below. Worker B is a robot, and all parts always take exactly 5 minutes. Worker C has the most difficult task, and, as you can see, their times have the largest range. A worker can only work on one item at a time, and they cannot work on an item until the previous worker is finished. a. Complete the tables below to find the Expected Length of Time for each worker to complete their task. b. A customer orders three parts, and wants to know when they can be ready. Using the results from (a), calculate how long it's expected to take. c. Using the answer from (b), sketch a graph of what the times might look like if we took into account the variability in times only. d. The actual amount of time ranges from 22 to 44 minutes. Sketch what this graph might look like. e. Explain why the two graphs differ.

Explanation / Answer

a. Expected time for A = 0.5*4 + 0.5*6 = 5 mins

Expected time for B = 5 min

Expected time for C = 0.5*3+0.4*6+0.1*11 = 5 mins

b. Expected time to assemble all 3 parts = 5+5+5 = 15 mins

c. Considering variability of time, time could be as follows:

Expected time range is from 12 to 22 mins

The difference in the actual and expected situations could be due to time for movements of parts from A to B and then B to C and reduced efficiency of workers A and C when working for a long time

A B C Prob. Total time 4 5 3 0.5*1*0.5=0.25 12 4 5 6 0.2 15 4 5 11 0.05 20 6 5 3 0.25 14 6 5 6 0.2 17 6 5 11 0.05 22

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