Template:Nominal idealized growth curve: Difference between revisions

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===Nominal Idealized Growth Curve===
#REDIRECT [[Reliability_Growth_Planning#Nominal_Idealized_Growth_Curve]]
<br>
During developmental testing, management should expect that certain levels of reliability will be attained at various points in the program in order to have assurance that reliability growth is progressing at a sufficient rate to meet the product reliability requirement. The idealized curve portrays an overall characteristic pattern, which is used to determine and evaluate intermediate levels of reliability and construct the program planned growth curve. Note that growth profiles on previously developed, similar systems provide significant insight into the reliability growth process and are valuable in the construction of idealized growth curves.
The nominal idealized growth curve portrays a general profile for reliability growth throughout system testing. The idealized curve has the baseline value  <math>{{\lambda }_{I}}</math>  until an initialization time,  <math>{{t}_{0}},</math>  when reliability growth occurs. From that time and until the end of testing, which can be one or, most commonly, multiple test phases, the idealized curve increases steadily according to a learning curve pattern until it reaches the final reliability requirement,  <math>{{M}_{F}}</math> . The slope of this curve on a log-log plot is the growth rate of the Crow Extended model [13].
 
{{nominal failure intensity function}}
 
{{initialization time rga}}
 
{{nominal time to real goal}}
 
{{growth rate for nominal idealized curve}}
 
====Lambda - Beta Parameter Relationship====
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Under the Crow-AMSAA (NHPP) model, the time to first failure is a Weibull random variable. The MTTF of a Weibull distributed random variable with parameters  <math>\beta </math>  and  <math>\eta </math>  is:
 
 
::<math>MTTF=\eta \cdot \Gamma \left( 1+\frac{1}{\beta } \right)</math>
 
 
The parameter lambda is defined as:
 
 
::<math>\lambda =\frac{1}{{{\eta }^{\beta }}}</math>
 
 
Using Eqn. (lambda eta relationship), the MTTF relationship shown in Eqn. (Weibull MTTF) becomes:
 
 
::<math>MTB{{F}_{B}}=\frac{\Gamma \left( 1+\tfrac{1}{\beta } \right)}{{{\lambda }^{\left( \tfrac{1}{\beta } \right)}}}</math>
 
 
Or, in terms of failure intensity:
 
 
::<math>{{\lambda }_{B}}=\frac{{{\lambda }^{\left( \tfrac{1}{\beta } \right)}}}{\Gamma \left( 1+\tfrac{1}{\beta } \right)}</math>

Latest revision as of 01:45, 27 August 2012

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