Life Cycle Simulator for qualitative accelerated tests
Life Cycle Simulator for qualitative accelerated tests.
This computer program (named Life Cycle Simulator) is applied to optimization of
reliability development of high-reliability products with qualitative accelerated tests.
The typical situation of reliability development of an aircraft engine is considered. We
need to determine optimal:
- Necessary amounts of the tested products, time and cycles of tests
- Levels of the testing regimes
- Stopping criteria for the development
For example, we must make the development program for product Exam1. We open the
file Exam1.eng in the dialog “Engine-Open”.
Submenus “Development”, “Qualification”, “Manufacture”, “Use” of the menu
“Definitions” contains the information about the life cycle stages:
In this example we give the warranty to a customer on 20 products with the lifetime 5000
hours for each. We repair the failures of knots at own expense or pay the fixed payment (the
analysis of other cases of the warranty is possible):
Up to 12 components of a product (e.g., blades of the turbine, disks of the turbine,
bearings, toothed transfers etc.) with various failure modes (e.g., thermal fatigue, hightemperature strength, contact fatigue, wear, thermal aging, gas corrosion, erosion etc.) can be
analyzed. The list of components (named "Problem Name") is contained in the dialogue.
Information about the failure time distribution or degradation distribution (Normal,
Lognormal, Exponential, Weibull, Bernoulli, etc.) and the its parameters (named Param1,
Param2, Param3) are known by a model and/or by tests on samples (" Definitions-Use-UpdatesModify Level 0 ") - are entered by the user. The damages from failures of these parts in the use
are indicated in a column Loss.
In this example four parts of the product are critical (Problem Name = Part 1, …, Part 4).
They have the base performance by the beginning of development (Modify Level=0, Modify
Name=Base) with life time distribution for each part. Part 1 by base performance has Normal life
time distribution (column Distribution) with the expectation 12000 hours (column Param 0) and
the standard deviation 1500 hours (column Param 1). The damage from failure of the Parts 1 in
use is $120. And so on.
The failures of parts in the use are independent and do not mask one another in this example:
The actual parameters of life time distributions not agree with those found by calculated
(can be on one- two order below or above). This uncertainty of distribution parameters is
accepted on each a parameter. We take into account it by correction factors. The ranges (minmax) of correction factors are specified in the dialogue:
The ranges of correction factors show "the measure of our ignorance" and are caused by
many reasons. These reasons are present both in the use and in the test; therefore, they have
identical correction factors. It follows from principles of the theory of a similarity. For example,
the calculated life time expectations of Part 1 are 12000 hours in the use and 4000 hours in the
accelerated test (the acceleration factor is 3) and the correction factor is 0,5. The actual life time
expectations will are 6000 hours in the use and 2000 hours in the accelerated test.
The purposes of the development are the demonstrating and the improving of reliability.
The absence of failures satisfies the first purpose. Existence of failures, removal the cause of
failures and the new tests satisfy the second purpose. Therefore, the development is considered
fully, include possible removal the cause of failures (Modify Level 1, 2, ...) and new tests realized by the network graph with alternate paths and returns.
We indicate variants of improving of reliability on pages of the multipage dialogue "Use
Updates". The buttons "Next" and "Prev" look through pages of the dialogue. "Modify Lavel =
1,2,..." specifies a level of updating. The column "Modify Name" specifies a name of updating.
Thus, Part 1 by base performance had Normal life time distribution with the expectation
12000 hours (column Param 0) and the standard deviation 1500 hours (column Param 1). Part 1
by Modify 1-1 performance will have the expectation 15000 and the standard deviation 1875
hours. Part 1 by Modify 1-2 performance will have the expectation 18000 and the standard
deviation 2250 hours.
The improving of reliability results in increase of manufacture cost of a product. The
increasing of manufacture cost of a product on the levels of updating is indicated on pages of the
multipage dialogue "Manufacture".
The development requires many material and temporary resources. The temporary
resource is limited for a beginning of qualification or batch production. This information is
indicated on dialogues "Development Scenario", "Development Step" and "Development
The dialogue "Development Scenario" contains information about the Number of parallel
tests, the Stopping criteria for the development, the Limitation of development duration, the
Tempo of Testing and the Cost of Testing per hour:
The dialogue "Development Step" contains information about the Time and the Cost of
engine making for test and the Factor of increase the cost of last modification.
The dialogue "Development Updates" contains information about the Time and the Cost
of modification designing on the levels of updating.
The failures of parts in the test are independent and do not mask one another in this
We set up the ranges of high levels of up to 12 accelerating variables (e.g., use rate,
temperature, voltage, or pressure etc.) proceeding from practical ability and preservation of a
physical nature of failures:
We enter the mathematical models of influence of high levels accelerating variables on
life time distribution parameters (e.g., Arrhenius, Coffin-Manson, etc.):
In this example, we have taken the simplest functions. In practice, these functions can be
The commands “Compile”, “Link” (or “Make”) of the menu “Run” compile and link this
function in DLL-library:
The command “Calculate” of the menu “Run” begins search of the optimum test
In this case, the accelerated tests, as a method of control, have operating performance
with risks of the consumer and supplier. There is a most bad uncertainty of failure time of
components, which results in the largest risks of the consumer and supplier in the aggregate. It is
a new moment of the theory. The block of optimization finds this "the worst uncertainty" and
will realize a principle "of the best guaranteed outcome".
Existence of risks of the supplier and consumer on each component, the difference of
components and the difference of their sensitivity to high levels accelerating variables results in
many criterions of optimization. The life cycle cost, including cost of development, manufacture
and warranties costs is used for reduction of optimization multicriteria to one criterion.
We set up the reliability of an evaluation of life cycle cost (%) in the Optimization
dialogue - probability that life cycle cost will not exceed certain cost. The letter “E” in a field
"reliability of an evaluation" specifies that the expectation of cost is analyzed:
The MDI-windows show process and outcomes of search.
The outcomes of simulation and optimization are removed in the Exam1.txt file also.
Simulator is tool for creation of such program of the tests, which reduces the risk of the
consumer and the guarantee cost, reduces risk of the supplier and unreasonable rise in price of
General problem of any tests that demonstrate reliability - determination of number of
tested products and necessary stocks on a time and number of a test cycles is decided.
General problem of any accelerated tests - determination of high levels accelerating
variables for the identical accelerating factors for all parts of a product is decided.
This program optimizes the next parameters of qualitative accelerated tests also: the
number of parallel tests and "A Rule of a stop", attainment of which stops the development.
I think it is a new class of the reliability software as an envelope for quantitative
There is a Demo.
For example, the outcome of simulation of the life cycle without tests is:
The outcome of simulation of life cycle with tests in use conditions is:
The outcome of simulation of life cycle with accelerated test is: