Life of Incandescent Light Bulbs

This example uses time-to-failure data from a life test done on incandescent light bulbs. The observed times-to-failure are given in the next table.

Do the following:


 * 1) Plot the data on a Weibull probability plot and obtain the Weibull model parameters.
 * 2) Compute the B10 life of the bulbs.

The median ranks for the  the $${{j}^{th}}$$ failure out of N units is obtained by solving the cumulative binomial equation for $$Z$$. This however requires numerical solution. Tables of median ranks can be used in lieu of the solution.

Median Rank Tables

represents the rank, or unreliability estimate, for the failure[15; 16] in the following equation for the cumulative binomial:

$$P=\underset{k=j}{\overset{N}{\mathop \sum }}\,\left( \begin{matrix}  N  \\   k  \\ \end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}$$

where $$N$$ is the sample size and $$j$$ the order number. The median rank is obtained by solving this equation for $$Z$$ at $$P=0.50,$$

$$0.50=\underset{k=j}{\overset{N}{\mathop \sum }}\,\left( \begin{matrix}  N  \\   k  \\ \end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}$$