Process 'A' is identified to have 4000 defects per million opportunities. In this context, what is the sigma level of process 'A'?1. 12. 23. 64. 4

1. Break Down the Problem

To determine the sigma level of process 'A', we first need to understand the relationship between defects per million opportunities (DPMO) and the sigma level.

2. Relevant Concepts

The formula to calculate the sigma level (Z) from DPMO is given by:

$Z = \Phi^{-1}\left(1 - \frac{\text{DPMO}}{1,000,000}\right)$

Where:

• $\Phi^{-1}$ is the inverse of the standard normal cumulative distribution function.

3. Analysis and Detail

• Given DPMO = 4000.
• Convert DPMO to the fraction of defects:

$\frac{DPMO}{1,000,000} = \frac{4000}{1,000,000} = 0.004$

Thus, we have:

$1 - \frac{DPMO}{1,000,000} = 1 - 0.004 = 0.996$

Now we need to find $\Phi^{-1}(0.996)$.

Using standard normal distribution tables or a calculator, we can find that:

$\Phi^{-1}(0.996) \approx 2.88$

However, in Six Sigma methodology, there is an adjustment made for the non-conformance rate. Therefore, we can approximate the sigma level as follows:

$\text{Sigma Level} = Z + 1.5 = 2.88 + 1.5 = 4.38$

4. Verify and Summarize

After calculating the sigma level, it's clear that the result rounds approximately to 4 (since the options given are 1, 2, 3, 6, and 4). This indicates that the process is performing at the four sigma level, which is a significant quality standard.

Final Answer

The sigma level of process 'A' is approximately 4.