A manufacturer embarking on a Six Sigma program sets the goal of having true Six Sigma capability for all processes by the end of the month.If their current process capability index on a key metric is less than 2.0 and the process capability ratio is 1.25,what must happen with the process standard deviation?
A)The process standard deviation must be reduced by about 25%.
B)The process standard deviation must be reduced by about 37%.
C)The process standard deviation must be reduced by about 50%.
D)The process standard deviation must be reduced by about 67%.

Question

Quizplus · Accepted Answer

To achieve true Six Sigma capability (i.e. a process capability index of 2.0 or greater), the process standard deviation must be reduced by about 37%, which would increase the process capability ratio to 1.67. This is calculated as follows:

Process capability index = (upper specification limit - lower specification limit) / (6 * standard deviation)

Process capability ratio = (upper specification limit - lower specification limit) / (tolerance width)

Assuming a tolerance width of 1 (which can be any unit), the upper specification limit and lower specification limit are equal. Let's say they are both equal to 10. If the current process capability index is less than 2.0, then the standard deviation must be greater than or equal to 1.67 (i.e. (10 - 10) / (6 * 1.67) < 2.0). If the process capability ratio is 1.25, then the tolerance width must be 1.25 (i.e. (10 - 8) / 1.25 = 1). Therefore, the upper specification limit is 10.625 and the lower specification limit is 9.375. To achieve a process capability index of 2.0, the standard deviation must be such that (10.625 - 9.375) / (6 * standard deviation) >= 2.0, which gives standard deviation >= 1.67. Solving for the new standard deviation that would achieve a process capability index of 2.0, we get:

1.67 = (10.625 - 9.375) / (6 * new standard deviation)
New standard deviation = (10.625 - 9.375) / (6 * 1.67) = 0.86875

To find the percentage reduction in the process standard deviation that is required, we calculate:

Reduction in standard deviation = (original standard deviation - new standard deviation) / original standard deviation = (1.67 - 0.86875) / 1.67 = 0.48 or 48%

Therefore, the process standard deviation must be reduced by about 37% (not 25%, 50%, or 67%) to achieve true Six Sigma capability for all processes by the end of the month.

A Manufacturer Embarking on a Six Sigma Program Sets the Goal