Читать книгу Statistical Quality Control - Bhisham C. Gupta - Страница 47

The Six Sigma standard of quality has its basis in normal distribution theory (see Figure 2.4). We assume that the quality characteristic of interest – say, the diameter of a metal shaft – is normally distributed. The corresponding engineering specifications are assumed to be symmetric, and the process is centered at the specification target value.

For a centered process, 6σ quality is achieved when the lower and upper specifications map to ± six standard deviations from the mean, as shown in Figure 2.5. The centered process would produce approximately 2.0 defects per billion opportunities.

We then assume that no matter how well our process currently meets specifications, in the long run, the output will drift based on factors such as machine wear, incoming material variation, supplier changes, and operator variability. The assumption in Six Sigma is that even a well‐behaved process will drift from the target, perhaps by as much as 1.5 standard deviations. By applying this 1.5 sigma shift to a centered process, the rationale is that companies can gain a more realistic view of the quality level their customers will experience over the long term.

After adding a 1.5 sigma shift to a centered process, as shown in Figure 2.6, we then use a normal distribution table to calculate the fraction of parts that fall outside the specification limits. Thus the 6σ defect rate is equal to 3.4 DPMO after the shift in the mean. Table 2.1 lists the DPMO rates for various sigma levels for centered and shifted processes.

Figure 2.5 For a normally distributed characteristic, centered at specification target, 6σ quality is achieved when the lower and upper specifications map to ±6σ.

Figure 2.6 Applying the 1.5σ shift to a centered 6σ process.

Table 2.1 Defects per million opportunities (DPMO) for various sigma levels; centered and 1.5σ shifted processes.

	DPMO
Sigma	Centered Process	1.5 sigma shift
6.0	0.00	3.4
5.0	0.57	232.6
4.0	63.34	6209.7
3.0	2699.80	66,811
2.0	45,500.26	308,770
1.0	317,310.51	697,672