surveyselect in SAS is shown in Figure 4 for selection of five random samples from a set of 10.
Simulations can be used in software, such as JMP, to evaluate or
model the outputs of a process as a function of randomness in the
factors and noise in the model. Once a model is created of output
(y) as a function of inputs (xs) using Fit Model and the Prediction
Profiler and Simulator selected, factor levels can be selected. For
each factor, they can either by fixed at a specific value, given a
random value with a specified distribution and parameters, given
a value based on an expression that allows the user to create
their own distributions, or using a multivariate normal when
correlated factors exist. For the response, if only the response
from the model needs to be evaluated, then no noise needs to be
added to the response. Other options for the response are either
adding normal random or multivariate random noise. A setup to
generate 500 runs using a response y with 2 factors x1 and x2
and random noise from a normal distribution for each factor and
random noise in the response is shown in Figure 5.
Using the simulated table output, a normal distribution of the
response can be fit using the distribution platform. Specifications
can be entered and capability calculated to determine a defect rate
as shown in Figure 6.
The expected process mean is 421.5 with a standard deviation
of 73.8. For a lower specification of 200 and an upper specification
of 600, a capability Cpk of 0.81 is calculated with a defect rate of
0.9 %. This is only an initial estimate and needs to be confirmed
with additional process data.
The procedures to generate TRNGs often measure a random
physical occurrence, such as radioactive decay or atmospheric
noise, although the use of dice or coin flipping is still used. Lava-rand used a technique of running a hash function against images
from a number of lava lamps.
Random numbers have been shown to be valuable in sampling,
simulations, modeling, data encryption, gambling and even musical composition. Either computational or physical methods are
used depending on the application. A battery of statistical tests for
randomness is recommended for evaluation.
Note: SAS version 9. 3 and JMP version 11. 2.0 were used to
generate data in figures.
Mark Anawis is a Principal Scientist and ASQ Six Sigma Black Belt
at Abbott. He may be reached at
Figure 6: Specifications can be entered and capability calculated to
determine a defect rate.