Question

In a factory producing parts of an automobile, the parts manufactured on the shop floor are required to go through three quality checks, each conducted after a specific part of the processing on the raw material is completed. Only parts that are not rejected at one stage are put through the subsequent stages of production and testing. If average rejection rates at these three testing machines during a month are 10%, 5% and 2% respectively, then what is the effective rejection rate for the whole plant?

Answer 1

Correct Answer: 3

Concept: This is a
successive percentage (probability) problem:

• Only non-rejected items proceed further
• Multiply survival rates, then subtract from 100%

Step 1: Convert rejection to survival rates.
\[ \text{Stage 1 survival} = 90% = 0.9 \] \[ \text{Stage 2 survival} = 95% = 0.95 \] \[ \text{Stage 3 survival} = 98% = 0.98 \]
Step 2: Find overall survival rate.
\[ \text{Overall survival} = 0.9 \times 0.95 \times 0.98 \] \[ = 0.8379 \]
Step 3: Find rejection rate.
\[ \text{Rejection} = 1 - 0.8379 = 0.1621 = 16.21% \]
Step 4: Option analysis.

• (A) 17%: Approximation $\times$
• (B) 15.25%: Incorrect $\times$
• (C) 16.21%: Correct \checkmark
• (D) 16.76%: Incorrect $\times$
• (E) 17.2%: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (C).