Generalized Eyring-Lognormal

By setting = L(V,U) as given in Eqn. (15), the generalized Erying-lognormal model is given by:

where:

Generalized Eyring-Lognormal Reliability Function

The generalized Eyring-lognormal reliability function is given by:

Parameter Estimation

Substituting the generalized Eyring model into the lognormal log-likelihood equation yields:

where:

and:

Fe is the number of groups of exact times-to-failure data points.
Ni is the number of times-to-failure in the ith time-to-failure data group.
A, B, C, D are parameter to be estimated.
Vi is the temperature level of the ith group.
Ui is the non-thermal stress level of the ith group.
Ti is the exact failure time of the ith group.
S is the number of groups of suspension data points.
is the number of suspensions in the ith group of suspension data points.
is the running time of the ith suspension data group.
FIis the number of interval data groups.
is the number of intervals in the ith group of data intervals.
is the beginning of the ith interval.
is the ending of the ith interval.

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

Example

The following data set represents failure times (in hours) obtained from an electronics epoxy packaging accelerated life test performed to understand the synergy between temperature and humidity and estimate the B(10) life at the use conditions of T = 350K and H = 0.3. The data set is modeled using the lognormal distribution and the generalized Eyring model.

The probability plot at the use conditions is shown next.

The B(10) information is estimated to be 3004.63 hours, as shown next.

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