# Regression table - estimated regression equation for Accelerated Life Testing

The table estimates the best fitting model for failure times. The accelerated life testing model takes the form of:

Prediction = intercept + coefficient(predictor) + scale (quantile function), or

Yp = β0 + β1(x) + σΦ-1(p)

Where:
• Prediction (Yp): log failure time (Weibull, exponential, lognormal, and loglogistic) and failure time for extreme value, normal and logistic distributions.
• Intercept (β0): log failure time or failure time (depending on distribution) when the transformed accelerating variable and the percentile of the quantile function are 0.
• Coefficient ( β1): regression coefficient associated with x.
• Predictor (x): transformed accelerating variable.
• Scale (σ): scale parameter. For the Weibull distribution scale = 1.0/shape.
• Quantile function (Φ-1(p)): The pth quantile of the standardized life distribution .

Verify that the model assumptions, such as the distribution, equal shape (for the Weibull distribution and the exponential distribution), equal scale (for other distributions), and the transformation, are appropriate for your data. Use probability plots to check the assumptions of the model. These diagnostic plots assess the appropriateness of the model at accelerated levels of temperature. However, engineering knowledge is the only way to verify that the model is appropriate at design temperatures.

Because of the uncertainty in the prediction of failure time at design conditions, evaluate the model periodically as more information, such as field data, becomes available.

## Example output

Response Variable Start: StartTime End: EndTime Frequency: Count Censoring Censoring Information Count Right censored value 95 Interval censored value 58 Estimation Method: Maximum Likelihood Distribution: Weibull Relationship with accelerating variable(s): Arrhenius
Regression Table Standard 95.0% Normal CI Predictor Coef Error Z P Lower Upper Intercept -17.0990 4.13633 -4.13 0.000 -25.2061 -8.99195 Temp 0.755405 0.157076 4.81 0.000 0.447542 1.06327 Shape 0.996225 0.136187 0.762071 1.30232 Log-Likelihood = -191.130

## Interpretation

For the electronic device data, the table provides estimates of the best-fitting model, assuming a Weibull distribution with an Arrhenius transformation. The estimated model is:

log(Yp) = −17.0990 + 0.755405 x + (1.0/0.996225) * Φ-1(p)

Where:
• Yp: failure time for the electronic devices
• x: [11604.83/(Temp + 273.16)] (Arrhenius transformation)
• Φ-1(p): the quantile function (for more information, go to Methods and formulas for equations and click "Quantile function".)
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