Quick visual check for normality in Six Sigma
Using graph paper, spreadsheets, or statistically based software, measurement data from randomly selected samples of parts can be quickly checked for normality as follows:
1. Randomly select a number of parts samples for measurement of the quality characteristic, which is the part attribute of interest to the six sigma effort. Thirty samples are considered statistically significant. However smaller numbers might be used for a quick 1^ at the distribution.
2. Rank the data in ascending order, from 1 to n.
3. Generate a normal curve score (NS) corresponding to each data point. Each ranked data point is subtracted by 0.5, then divided by the total number of points n so that it sits in the middle of a box 〇f
ranked points. Each data point probability is based on the rank 〇f point i, with i ranging from 1 to n. The normal score (NS) represents the position of that ranked point versus its equivalent value of the z distribution:
P(z) = (i — 0.5)/AI i = 0，1，. . .，AI (2.14)
NS=z of P(z)
N = total number of parts to be checked for normality
5. Plot each data point value on the Y axis against its normal score. If the data is normal, it should show as a straight line.
Example for 5 points: 67, 48, 76, 81, and 93
| Data | Rank (i) | P(z) = (i- 0.5)/n | z from P{z) |
| 67 | 2 | 0.3 | -0.52 |
| 48 | 1 | 0.1 | -1.28 |
| 76 | 3 | 0.5 | 0 |
| 81 | 4 | 0.7 | 0.52 |
| 93 | 5 | 0.9 | 1.28 |
A quick graphical check for normality is given in Figure 2.12. It can be visually determined that the data represents close to a straight line.
An even quicker method to determine normality is to use the same procedure but with seminormal graph paper. This would eliminate the z calculations in step 3 above.
