Product and Process Comparisons
7.2. Comparisons based on data from one process
7.2.5. What intervals contain a fixed percentage of the population values?
|Two-sided tolerance intervals using EXCEL||
One method for computing factors for two-sided
tolerance intervals using EXCEL makes use of the definition
where r is defined by:
and is the critical value of the chi-square distribution with N - 1 degrees of freedom that is exceeded with probability, .
Unfortunately, r can only be found by iteration from the integral
above which defines limits within which p percent of the
normal distribution lies.
An EXCEL calculation is illustrated below
for the same problem as on the previous
page except where N= 220 measurements are made of thickness.
We wish to find tolerance intervals that contain a proportion
p = 0.90 of the wafers with probability
The EXCEL commands for this calculation are shown below. The calculations are approximate and depend on the starting value for r, which is taken to be zero in this example. Calculations should be correct to three signficant digits.
|Basic definition of r in EXCEL||
|Iteration step in EXCEL||
Click on the green V (not shown here) or press the Enter key. Click
on TOOLS and then on GOALSEEK. A drop down menu appears. Then,
Click OK. The screen below will be displayed:
|Calculation in EXCEL of k factor||
Now calculate the k factor from the equation
The resulting value k2= 1.853 appears in cell D1.
|Calculation in Dataplot||
You can also perform this calculation using the following Dataplot macro.
. Initialize let r = 0 let n = 220 let c1 = 1/sqrt(n) . Compute R let function f = norcdf(c+r) - norcdf(c-r) - 0.9 let z = roots f wrt r for r = -4 4 let r = z(1) . Compute K2 let c2 = (n-1) let k2 = r*sqrt(c2/chsppf(0.01,c2)) . Print results print "R = ^r" print "K2 = ^k2"Dataplot generates the following output.
R = 1.644854 K2 = 1.849208