DUANE PLOT

DUANE PLOT

Graphics Command

Generates a Duane plot.

Given a set of failure times T, the Duane plot is a plot of Ti/i (where i is the index from 1 to N) versus Ti on a log-log scale. This is a plot of the cumulative mean time between failures against the failure time.

The Duane plot is used to assess whether or not cumulative failure times can be adequately modeled with a Non-Homogeneous Poisson Process (NHPP) - 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

Duane plots are generally preceeded by one or more of the following plots to check for trends in the repair rates:

1. Plot cumulative failures versus system age. If the plot look linear, there is no obvious improvement or degradation trend. A bending downward indicates improvement while a bending upward indicates a degradation.

2. Plot the interarrival times between new failures. If these trend upward, there is improvement. If these trend downward, there is degradation.

3. Plot the reciprocals of the interarrival times. If these trend upward, there is improvement. If these trend downward, there is degradation.

If the trend plots do in fact indicate a trend, then the Duane plot should be generated. If the Duane plot shows a linear pattern, then this indicates that the NHPP Power Law model is consistent with the data.

You do not need to specify XLOGON or YLOG ON as Dataplot does this automatically. Dataplot also resets the original values for these switches after the Duane plot is completed.

A line is fit to the plotted data. Various parameters from the fit are saved as internal parameters. Specifically,

DPA0 - intercept term of the fitted line
DPA1 - slope of the fitted line
DPCC - correlation coefficent of the fitted line
SDDPA0 - standard deviation of the intercept term
SDDPA1 - standard deviation of the slope term
DPRESSD - residual standard deviation of the fitted line
DPRESDF - degrees of freedom of the fitted line


These can be used to assess the linearity of the Duane plot and can also be used to label the Duane plot (see the program example below).

DUANE PLOT <y>             <SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable containing failure times;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

DUANE PLOT Y1
DUANE PLOT Y1 SUBSET TAG > 1

None

None

LINES	= Sets the type for plot lines.
CHARACTERS	= Sets the type for plot characters.
TAIL AREA PLOT	= Generates a tail area plot.
KAPLAN MEIER PLOT	= Generates a Kaplan Meier plot.
HAZARD PLOT	= Generates a hazard plot.
PROBABILITY PLOT	= Generates a probability plot.
PLOT	= Generates a data or function plot.
POWER LAW RANDOM NUMBERS	= Generate a sequence of random failure times that follow a NHPP power law model.

Reliability

1998/5

SKIP 25
READ HAHN.DAT MILES TAG
Y1LABEL CUMULATIVE MEAN TIME BETWEEN FAILURE
X1LABEL FAILURE TIME
CHARACTER X BLANK
LINE BLANK SOLID
DUANE PLOT MILES SUBSET TAG = 1
JUSTIFCATION CENTER
MOVE 50 7
TEXT SLOPE OF FITTED LINE = ^DPA1
MOVE 50 4
TEXT INTERCEPT OF FITTED LINE = ^DPA0