yield & ppm chart with & without shift
Pop a question, “Why should one aim for six sigma?”. And pat will be the reply, “When you control the process variation to the extent of +/- 6σ within the tolerance limits, the rejection levels would be restricted to 3.4 parts per million (ppm)!”.
But try to verify the claim and you will experience the first limitation – that the Normal Distribution probability tables are available in books up to +/- 3σ. Secondly, if you try to compute the rejection probability using MS-Excel, it comes to 0.002 ppm. So how did the figure of 3.4 ppm crop up??
The answer lies with the phenomenon of shifting of the population mean (µ) on either side to the extent of +/- 1.5σ. Proponents of 6σ methodology claim that the mean(µ) of a stable process (a stable process is the one which is under statistical control) shifts by 1.5σ over a long period.
Hence, they proposed that the process variation be controlled to the extent of +/- 6σ spread within the tolerance band. After doing so even if the process mean shifts by 1.5σ, the rejection levels would be restricted to 3.4 ppm.
We have hence prepared Normal probability tables without and with 1.5σ shift. Also, we have prepared the tables up to 6σ against 3σ which are covered in the appendices of Statistics books.
