CPIM Practice Exam

If a process has a yield of 99.7% at each step, what is the probability of defect for the final good?

1. 0.3 percent

2. 1.195 percent

3. 3.988 percent

4. 98.81 percent

The correct answer is: 1.195 percent

To calculate the overall probability of defect in a process with a yield of 99.7% at each step, it is essential to understand how yields combine when there are multiple steps involved in the process. When a process step has a yield of 99.7%, this implies that 0.3% of the product is defective at each step. Therefore, if there are n steps in the process, the probability of producing a non-defective final product (yield) after all steps can be calculated as follows: Overall yield = (Yield at Step 1) × (Yield at Step 2) × … × (Yield at Step n) If we assume there are 4 steps in the process, the calculation would be: Overall yield = (0.997) × (0.997) × (0.997) × (0.997) = (0.997)^4 To find the probability of defect for the final good, one subtracts the overall yield from 1: Probability of defect = 1 - Overall yield Using the calculation for four steps: Overall yield = (0.997)^4 = 0.988^4 ≈ 0.9881 So, Probability of defect