T-H Exponential

The pdf for the Temperature Humidity relationship and the exponential distribution is given next.

By setting m = L(U,V) in Eqn. (1) the exponential pdf becomes:

(3)

T-H Exponential Statistical Properties Summary

Mean or MTTF

The mean, , or mean time to failure (MTTF) for the T-H exponential model is given by:

Substituting Eqn. (3) yields:

Median

The median, for the T-H exponential model is given by:

Mode

The mode, for the T-H exponential model is given by:

Standard Deviation

The standard deviation, , for the T-H exponential model is given by:

T-H Exponential Reliability Function

The T-H exponential reliability function is given by:

This function is the complement of the T-H exponential cumulative distribution function or:

and:

Conditional Reliability

The conditional reliability function for the T-H exponential model is given by:

Reliable Life

For the T-H exponential model, the reliable life, or the mission duration for a desired reliability goal tR is given by:

or:

Parameter Estimation

Maximum Likelihood Estimation Method

Substituting the T-H model into the exponential log-likelihood equation yields:

where:

and:

The solution (parameter estimates) will be found by solving for the parameters A, and b so that = 0, = 0 and = 0.

See Also:
Temperature-Humidity Relationship


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