Question 40.2: Determining the Sigma Level of a Process A final assembly pl...
Determining the Sigma Level of a Process
A final assembly plant that makes dishwashers inspects for 23 features that are considered important for overall quality. During the previous month, 9056 dishwashers were produced. During inspection, 479 defects among the 23 features were found, and 226 dishwashers had one or more defect. Determine DPMO , DPM , and DUPM for these data and convert each to its corresponding sigma level.
Summarizing the data, N_u = 9056 , N_o = 23 , N_d = 479 , and N_{du} = 226 . Thus,
DPMO =1,000,000 \frac{479}{9056(23)} = 2300
The corresponding sigma level is about 4.3 from Table 40.3.
| Sigma Level | Defects per Million | Sigma Level | Defects per Million |
| 6.0 σ | 3.4 | 3.8 σ | 10,724 |
| 5.8 σ | 8.5 | 3.6 σ | 17,864 |
| 5.6 σ | 21 | 3.4 σ | 28,716 |
| 5.4 σ | 48 | 3.2 σ | 44,565 |
| 5.2 σ | 108 | 3.0 σ | 66,807 |
| 5.0 σ | 233 | 2.8 σ | 96,801 |
| 4.8 σ | 483 | 2.6 σ | 135,666 |
| 4.6 σ | 968 | 2.4 σ | 184,060 |
| 4.4 σ | 1,866 | 2.2 σ | 241,964 |
| 4.2 σ | 3,467 | 2.0 σ | 308,538 |
| 4.0 σ | 6,210 | 1.8 σ | 382,089 |
DPM =1,000,000 \frac{479}{9056} = 52,893
The corresponding sigma level is about 3.1.
DUPM =1,000,000 \frac{226}{9056} = 24,956
The corresponding sigma level is about 3.4.