Simple Process Capability?

May 19, 2003
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Manufacturing operations throughout the industry have ignored geometric bonus tolerances, caused by varying feature sizes, when assessing statistical process capability from variables data. Attribute gages, or hard gages, address the bonus tolerance physically but do not produce the variables data that is needed for statistical reporting. The problem thus far has been integrating the variable feature size with the geometric form, location or orientation deviation in a simple, effective method and reporting the process capability. A solution to this problem may be at hand.

Process capability assessments derived from variables data gaging devices -- electronic gages and coordinate measuring machines -- can be computed from the residual or remaining tolerance of a feature rather than the consumed tolerance. The residual tolerance (Rt) is equal to the sum of specified location or orientation tolerance plus the individual feature bonus tolerance less the individual measured form, location or orientation deviation.

The calculation is made by factoring the following tolerances:

T is the form, location or orienta-tion tolerance specified at its material condition.

Bt is the bonus tolerance, which is the difference between the feature's actual size and its material condition limit that relates to the tolerance modifier specified. The actual size is the orientation or location constrained within the actual mating envelope.

Ct is the consumed tolerance, the measured deviation for form, location or orientation.

The formula to do the calculation is:
Rt = T + Bt - Ct

The residual tolerance will equal the maximum available tolerance when the feature's bonus tolerance is maximized relative to its material condition modifier and is at its exact basic location. The material condition modifers include the maximum material condition (MMC), least material condition (LMC) and the regardless of feature size (RFS). Likewise, the residual tolerance will be zero when the feature's bonus tolerance is minimized relative to its material condition modifier or is at its worst location or orientation.

There are two process capability indices, Cp and Cpk. One measures the potential process containability, and the other measures the process containment within specification. Size and location are evaluated separately for process capability. It is important to evaluate each characteristic separately to monitor and maintain the process, but when the tolerance for the form, location or orientation is dynamic, meaning it is dependent on size, the traditional model doesn't fit. Designers that recognize the relationship and attempt to optimize the design by including the tolerance for location in the tolerance for size, for example, |O+|O0.0(M)|A|B|C|, are forced to recant the specification because the tools don't support a way to evaluate or control a specification with a tolerance band that is itself variable. The result of which, for the designer, is the undesired alternative to portion the tolerance between the individual parameters with respect to prevailing process limitations.

By computing the residual tolerance from the given value and the bonus, zero becomes the constant for computing the value for Cpk. The overall process capability ratio Cp, as it is computed today, disregards the potential bonus tolerance. To compare the full potential tolerance, the sum of the potential bonus and the specified tolerances must be compared to six standard deviation of the distribution. The charts and data demonstrate the differences in the current method of reporting the process capability indices and that of the residual tolerancing model.

Manufacturing operations will realize immediate benefits from evaluating process capabilities using residual tolerances. Tolerances of virtually all fastener clearance holes include a tolerance modifier that permits a bonus positional tolerance relative to size. By addressing the bonus tolerance given in the design, the capability indices immediately improve. Furthermore, process targets can be optimized relative to the variability of the individual parameters rather than being targeted to the center individually.

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