Students have confused thoughts on what constitutes 3 sigma and 6 sigma quality.

Here is an explanation .. ( from the theoritical base..)

99.73% observations lying outside the +- 3 sigma limits amount to .27 units lying outside the 3 sigma control limits in 100, ie. 2.7 units in 1000, 27 units in 10,000, 270 units in 100,000 and 2700 units in a million. Clearly very bad quality !!

If you check up in the simulation link given below, for a sample mean of 50 mm and a standard deviation of 2 mm, you will find the 6 sigma limits of 50 +- 6 x 2 = 38 and 62, producing about 0.002 parts outside the 6 sigma limits. Considering the possibility of the shift in the process mean by a maximum of 1.5 sigma, ie 1.5 x 2 = 3, with the mean shifted to 53 with the same 6 sigma limits of 38 and 62, we find exactly 3.4 parts in a million going out of the 6 sigma limits.

Just keep this in mind : 6 sigma methodology works to "reduce variability in a process" and Lean systems work to "reduce waste in the process ".

Here is an explanation .. ( from the theoritical base..)

The process of taking mean (mhu) and +- 3 sigma on either side of the mean is 3 sigma quality, the spread is 6 sigma. (talking of population parameters). Cp and Cpk discussion in most of the textbooks is in the context of 3 sigma quality. Of course, the same can be extended to 6 sigma too.

99.73% observations lying outside the +- 3 sigma limits amount to .27 units lying outside the 3 sigma control limits in 100, ie. 2.7 units in 1000, 27 units in 10,000, 270 units in 100,000 and 2700 units in a million. Clearly very bad quality !!

The process of taking the mean (mhu) and +- 6 sigma on either side of the mean is 6 sigma quality, the spread is 12 sigma. Cpk =2.0 in case of six sigma..

If you check up in the simulation link given below, for a sample mean of 50 mm and a standard deviation of 2 mm, you will find the 6 sigma limits of 50 +- 6 x 2 = 38 and 62, producing about 0.002 parts outside the 6 sigma limits. Considering the possibility of the shift in the process mean by a maximum of 1.5 sigma, ie 1.5 x 2 = 3, with the mean shifted to 53 with the same 6 sigma limits of 38 and 62, we find exactly 3.4 parts in a million going out of the 6 sigma limits.

Pl feel free to play around with the Normal Distribution simulation spreadsheet and get the concepts clear. ( give diff values of mhu and sigma and find the probability of a range of values using the spreadsheet..) It will explain how 6 sigma is theoretically speaking only of 2 defects in a billion, (0.002 defects in a million opportunities) and by considering the 1.5 sigma shift in the mean to either side, ( ie 4.5 sigma to one side and 7.5 sigma to the other side and vice versa..) the defects are 3.4 per million, ie. 3.4 defects per million opportunities ( dpmo) ( information of how you compute 3.4 dpmo, most of the 6 sigma trainers do not tell you ..)

Just keep this in mind : 6 sigma methodology works to "reduce variability in a process" and Lean systems work to "reduce waste in the process ".

Just like you have many numerical computation packages and the theory behind Mathematics remaining the same, you can have many means ( DMAIC, green belt, black belt etc..proposed by Motorola being one) to reduce the variability in the process. You have to ensure that the 6 sigma control limits and the customer specification limits at the most match or are within the spec limits, ( given by Cp and Cpk metrics) though the theory behind 6 sigma and Normal Distribution remains the same.. These are based on Deming's basic quality improvement (PDCA) cycle !!!!

Good Luck ..!!

ge..

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