Question

Consider the following production process. The process consists of 33 steps and operates at a cycle time of 1.11 min/unit. Their most error prone operation is step 19. If each worker checks the work of the previous steps and there are on average roughly 247 units of inventory between step 19 and the end of the process, equally distributed across the remainder of the process, what is the average information turnaround time for a defect made at step 19 (in minutes)? (report your answer to 2 decimal places)

Answer 1

The average information turnaround time for a defect made at step 19 is approximately 145.51 minutes.

Step-by-step explanation:

The average information turnaround time for a defect made at step 19 can be calculated by considering the average cycle time, the number of steps between step 19 and the end of the process, and the average inventory between step 19 and the end of the process.

Step 19 is the most error-prone operation, so if a defect occurs there, it would need to go through the remaining steps before reaching the end of the process. The average cycle time is given as 1.11 min/unit, and there are 33 steps in total. Therefore, the average time it takes for a unit to go from step 19 to the end of the process is 1.11 min/unit * 33 = 36.63 minutes.

The question mentions that there are on average roughly 247 units of inventory between step 19 and the end of the process, equally distributed across the remainder of the process. This means that there are 247 units spread out over 33 steps, resulting in an average of 7.48 units between each step. Since the step 19 is the most error-prone, we can assume that the defect occurs here and needs to go through all the remaining steps. Therefore, the average time it takes for one unit with a defect to reach the end of the process is 36.63 minutes + 7.48 minutes * 14 (number of steps after step 19) = 145.51 minutes.

The average information turnaround time for a defect made at step 19 is therefore approximately 145.51 minutes.