Management
CHAPTER 16: THE MANAGEMENT AND CONTROL OF QUALITY
EXERCISES
16-42 Interpretation of Six-Sigma quality expectations (ppm) (30 minutes)
Sigma One-Tailed Two-Tailed Errors (Defects) Level Area1 Area Per Million 1 0.158655254 0.317310508 317,310.51 2 0.022750132 0.045500264 45,500.26 3 0.001349898 0.002699796 2,699.80 4 3.16712E-05 6.33425E-05 63.34 5 2.86652E-07 5.73303E-07 0.57 6 9.86588E-10 1.97318E-09 0.00
1Excel formula: = 1 - NORMSDIST(n), where n = sigma level (1, 2,...)
The preceding data indicate suggest a common misconception regarding the quality level assumed under Six Sigma. Only when a defect is defined as any deviation from the targeted level of the attribute (i.e., only when the “tolerance” is zero) will the above approach represent the maximum number of defects per million opportunities for error. Note, for example, that the expected number of errors (defects) under Six Sigma is approximately 2 per billion (when any deviation from target is considered a defect).
In actual practice, based on initial experience by Motorola, the application of Six Sigma allows some variation (drift) around the target value. That is, there is an assumption that no process can be maintained in perfect control (i.e., no “drift” at all). Thus, in practice, a drift of 1.5 standard deviations around the target value is “allowed.” Any deviation beyond this allowable “drift” would be considered a defect or out-of-control process.
What this means is that a revised formula is needed to calculate the defects per million as the Six Sigma methodology is applied in practice. According to Pyxdek (http://www.qualitydigest.com/may01/html/ sixsigma.html) the Excel formula (under the assumption of an allowable drift of 1.5 sigma) is: 1000000*(1-NORMSDIST(Z-1.5)), where 1.5 = allowable drift (in standard
EXERCISES
16-42 Interpretation of Six-Sigma quality expectations (ppm) (30 minutes)
Sigma One-Tailed Two-Tailed Errors (Defects) Level Area1 Area Per Million 1 0.158655254 0.317310508 317,310.51 2 0.022750132 0.045500264 45,500.26 3 0.001349898 0.002699796 2,699.80 4 3.16712E-05 6.33425E-05 63.34 5 2.86652E-07 5.73303E-07 0.57 6 9.86588E-10 1.97318E-09 0.00
1Excel formula: = 1 - NORMSDIST(n), where n = sigma level (1, 2,...)
The preceding data indicate suggest a common misconception regarding the quality level assumed under Six Sigma. Only when a defect is defined as any deviation from the targeted level of the attribute (i.e., only when the “tolerance” is zero) will the above approach represent the maximum number of defects per million opportunities for error. Note, for example, that the expected number of errors (defects) under Six Sigma is approximately 2 per billion (when any deviation from target is considered a defect).
In actual practice, based on initial experience by Motorola, the application of Six Sigma allows some variation (drift) around the target value. That is, there is an assumption that no process can be maintained in perfect control (i.e., no “drift” at all). Thus, in practice, a drift of 1.5 standard deviations around the target value is “allowed.” Any deviation beyond this allowable “drift” would be considered a defect or out-of-control process.
What this means is that a revised formula is needed to calculate the defects per million as the Six Sigma methodology is applied in practice. According to Pyxdek (http://www.qualitydigest.com/may01/html/ sixsigma.html) the Excel formula (under the assumption of an allowable drift of 1.5 sigma) is: 1000000*(1-NORMSDIST(Z-1.5)), where 1.5 = allowable drift (in standard