Template:Example: Lognormal General Example Complete Data RRX

Lognormal Distribution General Example Complete Data RRX

From Kececioglu [20, p. 347]. Fifteen identical units were tested to failure and following is a table of their times-to-failure:

[math]\displaystyle{ \text{Table 9}\text{.5 - Data of Example 11} }[/math] [math]\displaystyle{ \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]

Solution

Published results (using probability plotting):

[math]\displaystyle{ \begin{matrix} {{\widehat{\mu }}^{\prime }}=5.22575 \\ {{\widehat{\sigma }}_{{{T}'}}}=0.62048. \\ \end{matrix} }[/math]

Weibull++ computed parameters for rank regression on X are:

[math]\displaystyle{ \begin{matrix} {{\widehat{\mu }}^{\prime }}=5.2303 \\ {{\widehat{\sigma }}_{{{T}'}}}=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.