Calculations for Normal Distribution

Failure Rate

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CDF

Reliability

Note: In GE Digital APM, there are two parameters: Mean, represented as µ, and Standard Deviation, represented as σ.

MLE

Where, is the failure time of component i, i=1,..., r or the censoring time 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 and , then the parameters for are estimated using the following equations:

In this case, and .