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same focus that they traditionally have on timing,
resources and other issues.
The reliability logic flow diagram (reliability suc-
cess tree) of the case study is shown in Figure 1.
The base elements of the system, components A, B,
C, and manufacturing process MP, are all examples
taken from the authors' work on different systems.
The sub-system SS, and the overall system S, are
fictitious, and are incorporated here for clarity in
order to allow all of the real world examples to be
shown in the same case study. The organization of
this "system" allpws several aspects of PREDICT
to be demonstrated in this case study, including 1)
the development of the appropriate prior distribu-
tion for a product component, 2) the development
of the appropriate prior distribution for a manufac-
turing process, 3) the mechanism for dealing with
manufacturing "spills", 4) the development of sub-
system and system reliabilities at various times, 5)
how to process updates at the component and
manufacturing process level, and 6) how to perform
"what if' studies. Over the years many advancing
techniques in the area of reliability engineering
have surfaced. One of these techniques in the mili-
tary sphere of influence is Reliability Growth Test-
ing (RGT). Private industry has reviewed RGT as
part of the solution to their reliability concerns, but
many practical considerations have slowed its im-
plementation as discussed in detail in Kerscher et
al. (2000). This paper speaks directly to the need to
demonstrate the reliability requirement of a new
product with a specified confidence, but discusses a
somewhat different approach to achieving it. Rather
than conducting testing as a continuum and devel-
oping statistical confidence bands around the re-
sults, this approach starts with a reliability estimate
organized by combining all available information
and data sources available. The areas of large un-
certainty revealed are then reduced, by working to
fold in fresh, relevant information. Reducing the ar-
Figure 1. Case Study Reliahility Success Tree Diagram
eas of uncertainty results in driving the reliability
There is a definite need for an understanding
of the reliability perspective of a new product dur-
ing its development program. Identifying the un-
certainty in the reliability estimates, which typically
drives the unreliability, and doing it early enough in
the development cycle for corrective action to be
organized by the development team, has been found
to be a culturally acceptable way to approach the
reliability issue, and can therefore be a powerful
factor in the drive for high reliability. The informa-
tion combination and updating approach is a meth-
odology which is directly applicable to this prob-
The following notations are used:
Ri reliability characterization of a system, es-
timated at time step, i.
f(Ri) probability distribution function of Ri, repre-
senting the uncertainty in system reliability.
X failure rate for a component, subsystem or
system (e.g., failures per vehicle per scaled
unit of time) and scale parameter of the
s slope or shape parameter of the Weibull dis-
R(t) reliability from a two-parameter Weibull
r(n) gamma function, which is the fx("1) ex dx
from 0 to 1.
0 parameter of interest.
(a,b) two parameters of the beta distribution,
sometimes referred to as the pseudo suc-
cesses and pseudo failures, respectively.
p probability of success of a trial.
n number of tests.
(a, ij) two parameters of the gamma distribution,
sometimes referred to as the pseudo failures
and pseudo total transformed test time, re-
T total transformed test time (tip + t2p + ...)
3 OVERVIEW OF RELIABILITY UPDATING
The reliability of the product (including the manu-
facturing process) at any given point in time or at
any given step in the overall product / process de-
sign assurance program is what has been referred to
by the term reliability characterization. "Reliability
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Chen, Bin; Lin, Jung-Fu; Chen, Jiuhua; Zhang, Hengzhong & Zeng, Qiaoshi. Synchrotron-based high-pressure research in materials science, article, June 1, 2016; (digital.library.unt.edu/ark:/67531/metadc927600/m1/3/: accessed April 26, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.