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GROUP 7
Weibulls model andSystem Reliability
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The Weibull distribution is word wide used to model Life Data.
The distribution can handle increasing, decreasing or constant
failure-rates and can be created for data with and without
suspensions (non-failures).
It is flexible and fits to a wide range of data, including ormal
distributed data.
The Weibull distribution is one of the most commonl! used
distributions in "eliabilit!
It gains in popularit! for reliabilit! wor#, particularl! in the area of
mechanical engineering because of the man! shapes it attains for
$arious $alues of reliabilit!, due to its inherent $ersatilit!.
Weibull model
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Weibull analysis includes:
% &lotting the data and interpreting the plot
% 'ailure forecasting and prediction
% $aluating correcti$e action plans
% Test substantiation for new designs with
minimum cost
% aintenance planning and cost effecti$e replacement strategies
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% *pare parts forecasting
% Warrant! anal!sis and support cost predictions
% +ontrolling production processes
% +alibration of complex design s!stems, i.e., +D+, finite
anal!sis, etc.
% "ecommendations to management in response to ser$ice
problems
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Weibulls formulae:
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Data Requirements Plotting Procedures
Life data that is relevant tothe failure mode iscritical
Order data from lowest tohighest failure time
Individual Data Estimate ercentagefailing before each failuretime !median ran"s#
$otal Units %raw best line &t through
data oints lotted onWeibull aer
'umber of observedfailures
Estimate weibullarameters
(tem $ime to )ailure
Grouped Data
$otal Units
'umber of grous
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Failure types include:
% De$elopment, production and ser$ice
% echanical, electronic, materials, and human failures
% ature lightning stri#es, foreign ob/ect damage, human error,
woodpec#er holes in power poles
% 0ualit! control, design deficiencies, defecti$e material
% Warrant! claims
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Advantages
The primar! ad$antage of Weibull anal!sis is the abilit! to pro$ide
reasonabl! accurate failure anal!sis and failure forecasts with
extremel! small samples
nother ad$antage of Weibull anal!sis is that it pro$ides a simple and
useful graphical plot of the failure data.
The data plot is extremel! important to the engineer and to the
manager
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*+stem reliabilit+
s products become more complex (ha$e morecomponents), the chance that the! will not function
increases.
The method of arranging the components affects the
reliabilit! of the entire s!stem.
+omponents can be arranged in series, parallel, or a
combination.
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R* , R-R./// Rn
- . n
)or a series s+stems0 the reliabilit+ isthe roduct of the individual
comonents/
1s comonents are added to the series0the s+stem reliabilit+ decreases/
*eries *+stem
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Rs , - 2 !- 2 R-# !- 2 R.#/// !- 2 Rn#
-
.
n
When a comonent does not function0 the
roduct continues to function0 using anothercomonent0 until all arallel comonents do
not function/
Parallel s+stem
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*eries2Parallel *+stem
3onvert to e4uivalent series s+stem
1 5
3
3
%
R1 R5 R3R%
R3
1 5 36 %R1 R5 R%
R36, - !-2R3#!-2R3#
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% Reliabilit+ can be achieved b+overdesign/
% $he use of large factors of safet+ can
increase the reliabilit+ of a roduct/
% When an unreliable roduct can lead
to a fatalit+ or substantial &nancial
loss0 a fail2safe t+e of device should
be used/
% $he maintenance of the s+stem is an
%esign
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% $he second most imortant asect of
reliabilit+ is the roduction rocess/
% Emhasis should be laced on thosecomonents which are least reliable/
Production
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% $he third most imortant asect of reliabilit+
is the transortation/
1 Pac"aging
1 *himent
% Performance of the roduct b+ the customer is
the &nal evaluation/
% Good ac"aging techni4ues and shiment
evaluation are essential/%
$ransortation
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$81'9 OU
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