Quality Progress - December 2016 - 64


STATISTICS ROUNDTABLE

SEGMENTATION ANALYSIS OF BLEED SYSTEMS

An earlier Statistics Roundtable column1 dealt with a system
that bleeds off air pressure from an aircraft engine to operate a
compressor or generator. Lifetime data were available on bleed
systems from 2,256 engines in military aircraft operating from
various bases. Sidebar Figure 1 shows a single Weibull distribution probability plot for the 19 failures that occurred.
The slope of the plot seems to change at about 600 hours,
indicating that a simple Weibull distribution does not provide an
adequate representation. Further study revealed that 10 of the 19
failures occurred at base D, one of the bases at which the planes
were stationed, even though base D involved only 202 engines.

REFERENCE
1.	Necip Doganaksoy, Gerald J. Hahn and William Q. Meeker, "Divide and Conquer in Reliability Analyses," Quality Progress, November 2009, pp. 46-48.

Separate Weibull probability
plots for bleed systems
lifetimes / SIDEBAR FIGURE 2

99
90

99
90

50

50

Percentage failing

Percentage failing

Weibull probability
plot of bleed systems
lifetimes / SIDEBAR FIGURE 1

Moreover, there was physical justification (salty air) for the
higher failure rate at base D. Thus, separate Weibull analyses and
probability plots were performed for the system lifetimes at base
D and for those at all other bases (see Sidebar Figure 2). The data
in each of these plots scatter around straight lines, suggesting
that separate Weibull distributions provide adequate representations and justifying the segmentation analysis.
				-N.D., G.J.H. and W.Q.M.

10
3
1
0.1

Base D
Other bases

10
3
1
0.1

0.01

0.01
10

100
1,000 10,000
Time to failure (hours)

10

100
1,000 10,000
Time to failure (hours)

to obtain the necessary information to

failure distribution of the first subpopula-

conduct such in-depth analyses and to

tion. More advanced mixture models can

consider mixture model analysis only as a

be used to accommodate multiple subpop-

last resort.

ulations and multiple failure modes.7 QP

Other models. A less-complicated
mixture is presented by the "limited
failure population model,"6 assuming two
subpopulations. The first subpopulation,
is made up of an unknown proportion p
of the population, consisting of units that
fail according to some statistical distribution, such as the Weibull. The second
subpopulation consists of units that, for all
practical purposes, will not fail.
This model typically requires estimation of only three parameters: p and the,
presumably, two parameters of the time to

64 QP * www.qualityprogress.com

REFERENCES
1.	Andy Barnett, "Expert Answers," Quality Progress, May
2016, pp. 8-9.
2.	Necip Doganaksoy, Gerald J. Hahn and William Q. Meeker,
"Divide and Conquer in Reliability Analyses," Quality Progress, November 2009, pp. 46-48.
3.	Necip Doganaksoy, Gerald J. Hahn and William Q. Meeker,
"Product Life Data Analysis: A Case Study," Quality Progress, June 2000, pp. 115-121.
4.	Doganaksoy, Hahn and Meeker, "Divide and Conquer in
Reliability Analyses," see reference 2.
5.	Necip Doganaksoy, William Q. Meeker and Gerald J. Hahn,
"Reliability Analysis by Failure Mode," Quality Progress,
June 2002, pp. 47-52.
6.	William Q. Meeker and Luis A. Escobar, Statistical Methods
for Reliability Data, John Wiley & Sons, 1998, section 11.5.
7.	Victor Chan and William Q. Meeker, "A Failure-Time Model
for Infant Mortality and Wearout Failure Modes," IEEE
Transactions on Reliability, Vol. 48, No. 2, December 1999,
pp. 377-387.

NECIP DOGANAKSOY is an associate
professor at Siena College School of
Business in Loudonville, NY, following
a 26-year career in the industry,
mostly at General Electric (GE). He has
a doctorate in administrative and engineering systems from Union College
in Schenectady, NY. Doganaksoy is a
fellow of ASQ and the American Statistical Association.
GERALD J. HAHN is a retired manager
of statistics at the GE Global Research
Center in Schenectady. He has a
doctorate in statistics and operations
research from Rensselaer Polytechnic
Institute in Troy, NY. Hahn is a fellow
of ASQ and the American Statistical
Association.
WILLIAM Q. MEEKER is professor of
statistics, and distinguished professor
of liberal arts and sciences at Iowa
State University in Ames. He has a
doctorate in administrative and engineering systems from Union College.
Meeker is a fellow of ASQ and the
American Statistical Association.


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