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The binomial distribution is a discrete
probability distribution. It shows the probability
of getting 'd' successes in a sample of
'n' taken from an 'infinite' population
where the probability of a success is 'p'.
(note the similarity to the
normal distribution)
The binomial distribution would be appropriate
if items taken from a process were inspected.
If the proportion of defective items is
'p' then the binomial distribution gives
the probability of finding 'd' defectives
in a sample of 'n':
Discrete distributions are used when the
characteristic being investigated is represented
by an integer value. For example the score
on a playing dice can only be 1, 2, 3, 4,
5 or 6.
A discrete distribution could be used to
show the probability of getting a particular
score on a single throw of the dice. If
only one dice was involved the distribution
would be uniform; there is an equal chance
of any score. If two die were thrown the
score could range from 2 to 12, with the
highest probability being a score of 7.
Discrete distribution theory is used in
sampling inspection where the problem is
reversed. A representative sample is taken
from a large batch. The batch will be accepted
unless the number of defects found in the
sample make it highly probable that the
proportion of defective items in the large
batch is greater than a specified agreed
maximum. This is known as the 'Limiting
Quality Level' (LQL).
| Hypergeometric
Distribution |
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The Hypergeometric distribution is used
when a fairly small sample is taken from
a reasonably small population without replacement.
This is the method most often used in sampling
inspection.
The equation is cumbersome. For reasonably
large samples both the numerator and denominator
become so large that even computers have
problems dealing with them; even though
the final answer is small.
The Poisson distribution is a discrete
distribution used when the sample is unbounded.
It is often used to find the probability
of a given number of events occurring in
a given time.
The symbol 'l'
represents the average number of occurrences.
This is often used in reliability
engineering in the form:
This is the probability of zero faults,
or the probability of the device not failing,
in time 't'. Note that definition of 'l'
has changed to the average number of occurrences
per unit time. Hence 'lt'
is the average number of the faults in the
time period of interest.
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