Calculations for LogNormal Distribution

Where, У_i is the failure time or censoring time.

Failure Rate

PDF

CDF

Reliability

MLE

Where, is the failure time (in t-space) of component i, i=1,..., r or the censoring time (in t-space) of component i, i=r+1,..., n. If there is no censoring (complete data), r = n and the last term in the Likelihood function disappears. The terms and are the standard normal probability density and standard normal cumulative distribution.

Least Square

Let us denote : n = total cases, r = uncensored cases, and n - r = k = censored cases

If ,, then the parameters for are estimated using the following equations:

In this case, and .

Note: You can obtain У by minimizing R-squared of least square line fit.