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STANDARD DEVIATION & VARIATION For rapid assessment of process repeatability, the shot weights for a number of successive cycles are usually measured. These values serve as basis for calculating the standard deviation or variation (Fig. 1). Both parameters are often expressed as a per- centage of the mean shot weight. As a result, they can be better compared using empirical values. Variations are considered very satisfactory if they lie below 0.1% of the mean part weight. The disadvantage of this consid- eration is that the variation is calculated from only two values: the biggest and the smallest measured value. What takes place between them is not taken into consideration. This minor short- coming can be pardoned, since the short-term repeatability in which, for example, 50 cycles are considered, actually conceals far more—but more about that later. In the last decade, machine capability and process capa- bility studies have become increasingly widespread. A determined number of parts are taken under defined conditions, and a property that is important for their subsequent function is measured. This property may be, for example, a critical dimension. Presupposing a normal distribu- tion of samples, the previously mentioned standard deviation is determined. From this standard deviation and from the permitted tolerance for the property under consideration, machine capa- bility indexes are calculated. The machine capability index (c m ) indicates how often six times the standard deviation fits into the given tolerance band. In one case example (Fig. 2), six times the standard deviation for part length is illustrated with six vertically stacked double arrows in red. As can be seen, the arrows fit about 2.3 times between the lower and upper tolerance limits. A value of c m >1.67 is usually required. The lower machine capability index c m,l indicates how often three times the standard deviation fits between the target value and lower tolerance limit; while the upper index c m,u states how often it fits between the target value and upper tolerance limit. In the case example, three times the standard deviation is repre- sented as three vertically stacked double arrows in blue. As can be seen in Fig. 2, the arrows fit about three times between the lower tolerance limit and mean value, but only 1.59 times between the mean value and upper tolerance limit. C m,l and c m,u thus describe the position of the measurement values within the tolerances. The larger the index is, the farther the measurement values are from the corresponding tolerance limit. Since a small value is consequently a problem, the smaller of the two values c m,l and c m,u is desig- nated as a critical machine capability index c m,c . In the example in Fig. 2, c m,u would thus be the critical value. A value >1.67 is also usually required for this. While the scattering of the values with a c m of 2.3 meets the requirements, c m,u at 1.59 is too low—the part-length measurements lie close to the upper The repeatability of a process is not a constant parameter, and therefore cannot be reliably established by sampling parts at any one point in time. A graph of shot weights, along with the standard deviation and variation range of 50 successive cycles, are commonly used for a rapid assessment of process repeatability. Shot Weight, g Shot Count max – min = 0.149% σ = 0.03% 20.16 20.14 20.12 20.1 20.08 20.06 20.04 Standard Deviation Variation 0 10 20 30 40 50 σ max to min FIG 1 @plastechmag 47 Plastics Technology Process Control