Pembahasan Ujian PAI: A70 – No. 4 – Mei 2017

Data dicocokkan (fitted) terhadap distribusi Weibull menggunakan metode maximum likelihood.

• Persamaan 1
  \(1 – \exp \left[ { – {{\left( {\frac{{1000}}{\theta }} \right)}^\tau }} \right] = 0.5\)
  \({\left( {\frac{{1000}}{\theta }} \right)^\tau } = – \ln \left( {0.5} \right)\)
• Persamaan 2
  \(1 – \exp \left[ { – {{\left( {\frac{{2000}}{\theta }} \right)}^\tau }} \right] = 0.8\)
  \({\left( {\frac{{2000}}{\theta }} \right)^\tau } = – \ln \left( {0.2} \right)\)
• Dengan membagi persamaan (1) dan (2)
  \(\frac{{{{\left( {\frac{{1000}}{\theta }} \right)}^\tau }}}{{{{\left( {\frac{{2000}}{\theta }} \right)}^\tau }}} = \frac{{\ln \left( {0.5} \right)}}{{\ln \left( {0.2} \right)}}\)
  \({\left( {\frac{1}{2}} \right)^\tau } = 0.430677\)
  \(\tau = \frac{{\ln \left( {0.430677} \right)}}{{\ln \left( {0.5} \right)}} = 1.21532\)