Question

In a manufacturing system, four different types of products (P, Q, R and S) are produced. The batch size of each product is \(2 \times 10^{7}\). The numbers of defective units are 60, 71, 80 and 55, for P, Q, R and S, respectively. Which one of the following statements is TRUE?

• A. All products conform to six sigma standard.
• B. Only product S conforms to six sigma standard.
• C. Except R, all other products conform to six sigma standard.
• D. Products P and S conform to six sigma standard.

Hint:

Six Sigma requires extremely low defect rates—less than 3.4 defects per million.

Answer 1

The Correct Option is D

Six Sigma quality requires defects per million opportunities (DPMO) to be: \[ \text{DPMO} < 3.4 \] Batch size for each product: \[ 2 \times 10^{7} \] Compute DPMO for each: P: \[ \text{DPMO}_P = \frac{60}{2\times 10^7} \times 10^6 = 3 \] Q: \[ \text{DPMO}_Q = \frac{71}{2\times 10^7} \times 10^6 = 3.55 \] R: \[ 80 \Rightarrow \text{DPMO}_R = 4 \] S: \[ 55 \Rightarrow \text{DPMO}_S = 2.75 \] Interpretation: 
- Products P and S have DPMO < 3.4 → satisfy Six Sigma.
- Q and R exceed the limit. 
Hence, the correct statement is that only P and S meet Six Sigma quality. 
Final Answer: Products P and S conform to six sigma standard.