SHORT- AND LONG-TERM SIX SIGMA CAPABILITY

SHORT- AND LONG- TERM SIX SIGMA CAPABILITY

The six sigma approach also differentiates between short- and long-term process variation. Just as in the past, the short-term standard deviation has been estimated from within- subgroup variation, usually from R , and the long-term standard deviation incorporates both the short-term variation and any additional variation in the process introduced by the small, undetected shifts in the process average that occur over time. Although no exact relationship between these two types of variation applies to every kind of process, the six sigma philosophy ties them together with this general equation (Harry and Lawson, 1992, pp. 6 “8).

ƒ _LT = c ƒ _ST

As c is affected by shifts in the process average, it is related to the k factor, which quantifies how far the process average is from the middle of the tolerance.

If a process has a C _p of 2.00 and is centered at the middle of the tolerance, then there is a distance of 6 ƒ _ST from the average to the USL. When the process average shifts up by 1.5 ƒ _ST , it has moved off target by 25 percent of one-half the tolerance (1.5/6.0 = .25). For this k factor of .25, c is calculated as 1.33.

C = 1/(1 - .25) = 1/.75 = 1.33

The long-term standard deviation for this process would then be estimated from ƒ _ST , as:

= c ƒ _ST = 1.33 ƒ _ST

The value 1.33 is quite commonly adopted as the relationship between short- and long-term process variation (Koons, 1992). This factor implies that long-term variation is approximately 33 percent greater than short-term variation. Other authors are more conservative and assume a c factor between 1.40 and 1.60, which translates to a k factor ranging from .286 to .375 (Harry and Lawson, 1992, pp. 6 “12, 7-6). For a c factor of 1.50, k is .333.

1.50 = 1/(1 - k)

1 - k = 1/1.50

k = 1 - (1/1.50) = .333

This assumption expects up to a 33.3 percent shift in the process average. With six sigma capability, there is 6 ƒ _ST from M to the specification limit, a distance that equals one-half the tolerance. A k factor of .333 represents a maximum shift in the process average of 2.0 ƒ _ST , a number derived by multiplying one-half the tolerance, or 6 ƒ _ST , by .333.