1. USEFUL STATISTICAL MODELS
CONT…..
Shashwat Shriparv
dwivedishashwat@gmail.com
InfinitySoft

2. INVENTORY SYSTEM
In realistic inventory system there are three
variables
1. The number of units demanded per order or per
time period.
2. The time b/w demands.
3. The lead time (Time b/w placing an order for
stocking an inventory system and receipt of that
order).
In very simple mathematical models of
inventory system demand is a constant over time,
and lead time is zero or a constant.
But in realistic cases the demand occurs
randomly in time, the no:of units demanded is also
random.

3. Lead time distribution can often be fitted fairly
well by a Gamma distribution [Hadely & Whitin, 1963].
The Geometric, Poisson and Negative binomial
provides a range of distribution shapes that satisfy a
variety of demand patterns [Fishman,1973].
Negative binomial:-Demand data are
characterized by a long tail ie: Always large demand
will occur.
Geometric:- A special case of negative
binomial, has its mode at unity, given that at least one
demand occurred

4. Poisson distribution:-Simple, extensively
tabulated and is well known. The tail of a
Poisson distribution is shorter than Negative
binomial distribution ie: fewer large demand will
occur (Assuming that both models have the
same mean demand).

5. RELIABILITY AND MAINTAINABILITY
Time to failure has been modeled using
numerous distributions, including the exponential,
gamma & Weibull.
If only random failure occur, the time-to-
failure distribution may be modeled as
exponential.
Gamma distribution arises from modeling
standby redundancy each component has an
exponential time to failure.

6. When there are a number of components
and failure is due to the most serious of a large
number of defects, or possible defects, the
Weibull distribution seem to do particularly
well as a model.
In situations where most failures are due
to wear, the normal distribution may very
well be appropriate. Long normal is applicable
in describing time to failure for some types of
components.

7. LIMITED DATA
In many instances the simulation begins
before data collection has been completed.
Three distributions uniform, triangular & beta
distributions are used to represent incomplete
data.
uniform distribution can be used when
inter arrival or service time is known to be
random, but no information is available about
the distribution.
Triangular distribution is used when
assumptions are made about the minimum
maximum and model values of the random
variable.

8. Beta distribution provides a variety of
distributional forms on the unit interval, which
with appropriate modification can be shifted to
any desired interval. The uniform distribution is
a special case of a beta distribution.

9. Shashwat Shriparv
dwivedishashwat@gmail.com
InfinitySoft