Template:Example: Standard Actuarial Example: Difference between revisions

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'''Standard Actuarial Example'''
#REDIRECT [[Non-Parametric_Life_Data_Analysis]]
 
Find reliability estimates for the data in the [[Simple-Actuarial Example Data|Simple-Actuarial Example]] using the standard actuarial method.
 
 
'''Solution'''
 
The solution to this example is similar to that of [[Simple-Actuarial Example Data|Simple-Actuarial Example]], with the exception of the inclusion of the  <math>n_{i}^{\prime }</math>  term, which is used in equation for the standard actuarial method. Applying this equation to the data, we can generate the following table:
 
<center><math>\begin{matrix}
  Start & End & Number of & Number of & Adjusted & {} & {}  \\
  Time & Time & Failures, {{r}_{i}} & Suspensions, {{s}_{i}} & Units, n_{i}^{\prime } & 1-\tfrac{{{r}_{j}}}{n_{j}^{\prime }} & \prod\mathop{}_{}^{}1-\tfrac{{{r}_{j}}}{n_{j}^{\prime }}  \\
  0 & 50 & 2 & 4 & 53 & 0.962 & 0.962  \\
  50 & 100 & 0 & 5 & 46.5 & 1.000 & 0.962  \\
  100 & 150 & 2 & 2 & 43 & 0.953 & 0.918  \\
  150 & 200 & 3 & 5 & 37.5 & 0.920 & 0.844  \\
  200 & 250 & 2 & 1 & 31.5 & 0.937 & 0.791  \\
  250 & 300 & 1 & 2 & 28 & 0.964 & 0.762  \\
  300 & 350 & 2 & 1 & 25.5 & 0.922 & 0.702  \\
  350 & 400 & 3 & 3 & 21.5 & 0.860 & 0.604  \\
  400 & 450 & 3 & 4 & 15 & 0.800 & 0.484  \\
  450 & 500 & 1 & 2 & 9 & 0.889 & 0.430  \\
  500 & 550 & 2 & 1 & 6.5 & 0.692 & 0.298  \\
  550 & 600 & 1 & 0 & 4 & 0.750 & 0.223  \\
  600 & 650 & 2 & 1 & 2.5 & 0.200 & 0.045  \\
\end{matrix}</math></center>
 
 
As can be determined from the preceding table, the reliability estimates for the failure times are:
 
<center><math>\begin{matrix}
  Failure Period & Reliability  \\
  End Time & Estimate  \\
  50 & 96.2%  \\
  150 & 91.8%  \\
  200 & 84.4%  \\
  250 & 79.1%  \\
  300 & 76.2%  \\
  350 & 70.2%  \\
  400 & 60.4%  \\
  450 & 48.4%  \\
  500 & 43.0%  \\
  550 & 29.8%  \\
  600 & 22.3%  \\
  650 & 4.5%  \\
\end{matrix}</math></center>

Latest revision as of 08:10, 10 August 2012

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