Paul F. Jackson
Quite Involved in Discussions
The % of tolerance method of predicting process capability with the variable "bonus" tolerance does not yield good predictions because the variability of the inputs (bonus tolerance due to feature size) and (feature position deviation) can either be moderated or amplified in the computed variable (% of tolerance). A feature with a large bonus and a large position deviation can have the same value for (% of tolerance) as one that has a small bonus and small position deviation.
The problem is that the variability of the inputs is not always reflected in the variability of the resultant (% of tolerance). I'm think that I have stated this before in other threads but all of the methods that use the variables (bonus tolerance due to feature size) & (feature position deviation) to produce a surrogate variable with a constant USL have similar problems (Glen Gruner's "Adjusted TP", My own "Residual Tolerance", Marty Ambrose's "% of Tolerance").
If one were to plot the distribution "position deviation" on a graph starting with the boundary "zero" and the specified USL @ MMC (I call it the minimum variable limit) and then plot the distribution for feature size on the same graph with its LSL or USL (depending on what size of a hole or shaft produces the minimum bonus) beginning at the positions USL @ MMC you would see two distributions that intersect. The area under that intersection is the probability of a deviation with a variable position tolerance.
If both distributions were normal the Cpu for position would be ((USL[tp]+MEAN[bonus]-MEAN[tp devation])/(3*sqrt(variance[bonus]+variance[tp deviation]))). Unfortunately both distributions are not usually normal but even so the prediction yielded by this equation is typically very close to the predicted results one would get from an attribute gauge (Hard gage). The current practice of ignoring the bonus in a Cpu equation almost never correlates with the attribute prediction. If one were to figure the area under the intersecting curves with a monte-carlo analysis the error could be minimized.
Andy Nutt is correct that it is critical to monitor and control the individual X and Y in a process rather than the computed tp deviation. One can't tell if a mean-shift in X or Y will reduce the tp deviation unless they are the variables being monitored. It is not good however to try to measure the capability of the process by putting upper and lower specs on those coordinate variables.
With variable tolerances processes can be optimized by moving the means of the tp coordinates on target and targeting feature size so that its Cpu equals that of the Cpu for tp deviation.
That's all I have to say for now.
The problem is that the variability of the inputs is not always reflected in the variability of the resultant (% of tolerance). I'm think that I have stated this before in other threads but all of the methods that use the variables (bonus tolerance due to feature size) & (feature position deviation) to produce a surrogate variable with a constant USL have similar problems (Glen Gruner's "Adjusted TP", My own "Residual Tolerance", Marty Ambrose's "% of Tolerance").
If one were to plot the distribution "position deviation" on a graph starting with the boundary "zero" and the specified USL @ MMC (I call it the minimum variable limit) and then plot the distribution for feature size on the same graph with its LSL or USL (depending on what size of a hole or shaft produces the minimum bonus) beginning at the positions USL @ MMC you would see two distributions that intersect. The area under that intersection is the probability of a deviation with a variable position tolerance.
If both distributions were normal the Cpu for position would be ((USL[tp]+MEAN[bonus]-MEAN[tp devation])/(3*sqrt(variance[bonus]+variance[tp deviation]))). Unfortunately both distributions are not usually normal but even so the prediction yielded by this equation is typically very close to the predicted results one would get from an attribute gauge (Hard gage). The current practice of ignoring the bonus in a Cpu equation almost never correlates with the attribute prediction. If one were to figure the area under the intersecting curves with a monte-carlo analysis the error could be minimized.
Andy Nutt is correct that it is critical to monitor and control the individual X and Y in a process rather than the computed tp deviation. One can't tell if a mean-shift in X or Y will reduce the tp deviation unless they are the variables being monitored. It is not good however to try to measure the capability of the process by putting upper and lower specs on those coordinate variables.
With variable tolerances processes can be optimized by moving the means of the tp coordinates on target and targeting feature size so that its Cpu equals that of the Cpu for tp deviation.
That's all I have to say for now.
