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'''Lognormal Distribution General Example Complete Data RRX'''
#REDIRECT [[The Lognormal Distribution]]
 
From [[Appendix: Weibull References|Kececioglu [20, p. 347]]]. Fifteen identical units were tested to failure and following is a table of their times-to-failure:
 
 
<center><math>\text{Table }\text{ - Times-to-Failure Data}</math></center>
 
<center><math>\begin{matrix}
  \text{Data Point Index} & \text{Time-to-Failure, hr}  \\
  \text{1} & \text{62}\text{.5}  \\
  \text{2} & \text{91}\text{.9}  \\
  \text{3} & \text{100}\text{.3}  \\
  \text{4} & \text{117}\text{.4}  \\
  \text{5} & \text{141}\text{.1}  \\
  \text{6} & \text{146}\text{.8}  \\
  \text{7} & \text{172}\text{.7}  \\
  \text{8} & \text{192}\text{.5}  \\
  \text{9} & \text{201}\text{.6}  \\
  \text{10} & \text{235}\text{.8}  \\
  \text{11} & \text{249}\text{.2}  \\
  \text{12} & \text{297}\text{.5}  \\
  \text{13} & \text{318}\text{.3}  \\
  \text{14} & \text{410}\text{.6}  \\
  \text{15} & \text{550}\text{.5}  \\
\end{matrix}</math></center>
 
 
'''Solution'''
 
Published results (using probability plotting):
 
::<math>\begin{matrix}
  {{\widehat{\mu }}^{\prime }}=5.22575  \\
  {{\widehat{\sigma' }}}=0.62048.  \\
\end{matrix}</math>
 
 
Weibull++ computed parameters for rank regression on X are:
 
 
::<math>\begin{matrix}
  {{\widehat{\mu }}^{\prime }}=5.2303  \\
  {{\widehat{\sigma'}}}=0.6283.  \\
\end{matrix}</math>
 
 
The small differences are due to the precision errors when fitting a line manually, whereas in Weibull++ the line was fitted mathematically.

Latest revision as of 07:56, 14 August 2012

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