Determine the tolerancesInstructor : In Step two we performed optimization experiments and used statistical analysis to obtain the transfer function for the effect of the X's of nut type and installation torque force upon the Y of nut removal time. The enabled us to optimize the vital X settings for our proposed solution.
Instructor : In this Step we will use the results of previous Step, to determine tolerances of the key operating parameters, or vital x's, necessary to achieve the project objectives and thus satisfy the customer C T Qs.
Instructor : In this final step of the Improve phase, we will define the basic purpose of Statistical Tolerancing,
Instructor : Define the basic principles of Statistical Tolerancing, and
Instructor : Apply Statistical Tolerancing to the Rockledge case.
Instructor : The basic purpose and concept which guide tolerancing are straightforward.
Instructor : The purpose is to establish the range of values for each vital X that will satisfy customer requirements.
Instructor : The concept is equally direct. If you know the relationship between X and Y and also the required specifications of Y,
Instructor : Then you can set the tolerance of the X factor.
Instructor : In the next few minutes, we will go through an exercise which will culminate in developing the tolerances for a specific task. we will begin by defining some basic terms, developing the transfer function, and then applying tolerancing techniques to develop a final description of the solution. The transfer function we're looking at involves the relationship between hours of exercise per week and pounds of weight lost per week. Given those two factors, which one do you think is the X and which one is the Y?
Instructor : So in previous step, where we determine variable relationships, we would produce a chart like that shown here, in order to provide a visual representation which quantifies the relationship between weight loss
Instructor : and hours of exercise per week.
Instructor : In order to determine how much exercise we need to achieve a specific weekly weight loss, we draw a horizontal line from the desired weight loss to the transfer function line,
Instructor : And then drop a vertical line from that intersection to the exercise scale.
Instructor : We can then read the required exercise time directly from the scale. So this tells us that we need to exercise two point two hours per week in order to lose two point five pounds per week.
Instructor : This is a simple example, but we can add additional parameters which will more accurately reflect the real world.
Instructor : We have decided that we would like to lose at least one pound per week, and preferably two. For health reasons, we would like to lose no more than three pounds per week. So how do we translate this to our statistical model?
Instructor : First, our Target is two pounds per week. So we draw the horizontal line from that value to the transfer function and then drop the vertical line down to the exercise scale where it intersects two hours per week.
Instructor : We then set our lower specification limit at one pound per week, which means we need to exercise at least one point four hours of exercise per week to meet the minimum goal.
Instructor : Finally, we set our upper specification limit at three pounds, which corresponds to exercising no more than two point six hours per week, or we may exceed our upper spec limit. So our preliminary statement is that we should exercise two hours per week, with a tolerance of plus or minus zero point six hours per week.
Instructor : Before we can finalize these limits, we need to take into account the variation of our measurement system. As it turns out, there is a one-quarter pound variation in our measurement system. So we need to modify our limits accordingly.
Instructor : First, we center a one quarter pound range over the L S L and the U S L at the pounds per week scale.
Instructor : We then use these variation ranges to adjust our lower specification limit upward to one point five hours of exercise and
Instructor : our upper specification limit down to two point five hours of exercise.
Instructor : So accounting for any variation due to our measurement system, our new tolerance around two hours per week is plus or minus zero point five hours of exercise.
Instructor : At this point, we look at the transfer function and can say that the part between to adjusted lower spec limit and the adjusted upper spec limit defines the acceptable range.
Instructor : In some cases there may also be measurement variation in the X. In that case, you would use the same technique to adjust the lower and upper specification limits for the X values after they had been set and adjusted for Y value measurement variation. The results, as you can see, are a further tightening of the tolerances for X. These adjustments will be critical in the next phase, Control.
Instructor : This is a graphical representation and simplification of the statistical tolerancing process. A detailed look at this process and its calculations will be covered in further training.
Instructor : Let's take a look at how this applies to the Rockledge case. The measurement variation for Y is less than one point five percent, as established in Step Three of Measure. The measurement of X, the torque force, also has very small variation. Therefore, establishing the tolerance around our target of 17,000 for this case is very straightforward.
Instructor : Since the variation associated with measurement is minimal, the team decided to take advantage of this situation and use the curve as an approximation of the acceptable solutions. First, we draw a line across the chart at thirty minutes, since that is our upper specification limit. The curve of the line under thirty minutes represents acceptable operating settings, because any torque setting based on the portion of the curve under the upper spec limit will provide acceptable results. Of course, we're going to try to optimize our solution to provide the maximum benefits possible, but there are cases where you may need to compromise the ideal solution with other considerations.
Instructor : So now we'll drop two lines down from where the thirty minute mark intersects the transfer function.
Instructor : This gives us a lower limit of fifteen thousand one hundred and sixty six foot pounds for the lower specification limit and eighteen thousand eight hundred and fifty three for the upper. Rounding the lower limit up and the upper limit down to three significant places gives us a lower limit of fifteen thousand two hundred and an upper limit of eighteen thousand eight hundred,
Instructor : The manufacturer adjusts the torque setting of the wrench at the factory and re-adjusts them at scheduled intervals. The setting is certified to be plus or minus five percent, which in this case is eight hundred and fifty.
Instructor : So a wrench set at seventeen thousand will be between sixteen thousand one hundred and fifty on the low side and seventeen thousand eight hundred and fifty on the high side. These are both well within our limits for keeping our nut removal times below our upper specification limit of thirty minutes.
Instructor : So we can rest assured that our torque wrenches will properly apply the correct force.
Instructor : Let's summarize this step
Instructor : Process tolerances are based upon specification flow-down from customer requirements
Instructor : You will need to adjust tolerances due to variation in both the process and product measurement systems, unless those variations are small enough to ignore.
Instructor : This is a very simplified overview of statistical tolerancing. There are times when trying to determine the tolerancing for multiple variables becomes extremely complex. Consult with your Master Black Belt for assistance with such situations.
Instructor : So here is where we are with the Rockledge case. We will make two changes in the Nut Installation process in order to affect our Nut Removal Time.
Instructor : Our first change is that the nuts used will be changed to the Torque Master type.
Instructor : Second, we will have them installed at a torque setting of seventeen thousand foot pounds
Instructor : The guaranteed tolerance from the factory is will be within our upper and lower specification limits. So we will not need to apply any control measures to this factor.
Instructor : Congratulations. You have finished this Step
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