Uses of sampling in Quality
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Why sample?
 Samples give us information about a Population.
 For us, the population could be manufactured items,
internet orders from Amazon, Skype calls, customers in a
checkout line at a store, etc.
 In SPC (Statistical Quality Control) we are generally
interested in some quality related characteristic, qualitative
(audio-visual digital quality of Skype calls) or quantitative
(waiting times of customers in a checkout line) of some
element of the sample(s).
 We would like to make an inference about the quality
characteristic of the population based upon the
information from the sample(s).
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Random sampling
 Random sampling gives us a way to study population
characteristics without systematic bias.
 Random sampling is not arbitrary sampling, there are
systematic ways to do it.
 Random sampling is not representative, i.e. it does not
give an exact reflection of the population.
 For example, if the proportion of Skype calls made last
year with poor visual quality was p, then the
proportion of poor quality calls in a random sample
will almost never exactly equal p.
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What does random sampling mean?
 Suppose the population, which we will denote as P,
has N elements and we wish to randomly select a
sample of size n.
 There are a number of ways to accomplish this, but
every possible sample of size n must be equally likely.
This is called simple random sampling.
 The number of samples of size n which can be
randomly drawn from a population of size N is
N
N!
 
 n  n ! N  n  !
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Binomial coefficients
 The previous formula, often is termed “N choose n”, gives
us the number of possible samples of size n that one could
possibly draw from a population of size N.
 We say that we have a method for simple random sampling
if each possible sample is equally likely to be drawn.
 That means that every possible sample has equal
probability of being drawn, which is equal to
N!
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n! N  n !
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How to do it?
 Random number tables. Use a random number table
to give a random number to each item in the
population, then order the random numbers from
smallest to largest and choose the first n in order of
magnitude. This assumes no two values are equal.
 Random number generators. Excel or any standard
package will do this.
 Statistical software programs. There are a number of
programs which will do various forms of
randomization for Statistical studies.
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Two views on sampling and Quality.
 One can assure good Quality through intensive
sampling if everything in the population is sampled
and measured. This is generally not done due to
excessive cost. In some situations it may be impossible
to do, for example, if one needs to do destructive
testing.
 The modern approach is to assure Quality by
concentrating on improving the Process itself, then to
use sampling to audit or monitor the Process.
 This is the basis of SPC.
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Sampling with and without replacement.
 If we randomly sample n distinct items from a Population
of N items, this is simple random sampling without
replacement. This is what is typically done in SPC.
 If each time we randomly sample one item at a time return
it, randomly sample another, etc., this is sampling with
replacement. From a theoretical standpoint, this mimics
sampling from an infinite (or hypothetically infinite)
population.
 A hypothetically infinite population could be all future
production of a type of part, or it might be all future
transactions of a certain type.
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Simple vs. stratified random sampling
 Simple random sampling describes how to select one
random sample.
 When monitoring a process, one will sample the
process periodically.
 So really the population will be divided into
subpopulations from which we select random samples.
This is also called stratified random sampling.
 For example: take random samples from each day’s
production; sample the dropped calls on Skype by day;
sample the late shipments from Amazon by week, etc.
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Sampling and SPC
 In SPC we usually collect samples periodically to
monitor a process.
 The samples are collected in a relatively homogeneous
set of conditions over time/space. This will allow us to
separate “signal” from “noise”.
 The monitoring of the process is done to check to see
if the process is stable over time/space.
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