POWER LAW RANDOM NUMBERS

POWER LAW RANDOM NUMBERS (LET)

Let Subcommand

Generate random failure times from a non-homogeneous Poisson process (NHPP) following a power law model.

If you have internet access, you can see a discussion of the NHPP Power Law model by entering the command:
WEB HANDBOOK NHPP POWER LAW

The non-homogeneous Poisson process power law model is:

where M_t is the expected number of failures at time t. The random failure times are generated from the formula for the interarrival times (i.e., the CDF for the waiting time for the next failure given a failure at time T):

LET <y> = POWER LAW RANDUM NUMBERS FOR I = <start> <inc> <stop>
where <start> is the starting row for the random numbers;
              <inc> is the increment for the random numbers;
              <stop> is the stopping row for the random numbers;
and where <y> is a variable where the power law random numbers are saved.

Typically and are 1 and is set to the number of random numbers to generate. If and are not 1, then will still contain elements, but the empty rows will be set to 0.

The alpha and beta parameters are specified with LET commands before entering the POWER LAW RANDOM NUMBERS command as demonstrated in the examples below.

LET ALPHA = 2
LET BETA = 3
LET Y = POWER LAW RANDOM NUMBERS FOR I = 1 1 100


LET ALPHA = 1
LET BETA = 2
LET Y = POWER LAW RANDOM NUMBERS FOR I = 1 1 1000


LET ALPHA = 1
LET BETA = 2
LET Y = POWER LAW RANDOM NUMBERS FOR I = 2 5 100

None

None

RANDOM NUMBERS	= Generate random numbers from various probability distributions.
INTERARRIVAL TIME	= Compute the interarrival times of a variable.
DUANE PLOT	= Generate a Duane plot.

Reliability

1998/5

LET ALPHA = 2
LET BETA = 3
LET Y = POWER LAW RANDOM NUMBERS FOR I = 1 1 100
X1LABEL ALPHA = ^ALPHA, BETA = ^BETA
TITLE AUTOMATIC
DUANE PLOT Y