Determining the reliability of manufactured items often requires performing a life test and analyzing observed times to failure. Such data is frequently censored, in that some items being tested may not have failed when the test is ended. In addition, it may be necessary to accelerate failure times by changing the value of an influential variable such as temperature. For all of these reasons, special tools are needed to deal with this type of data.

STATGRAPHICS Centurion provides several special procedures for dealing with failures times:

1. Life tables - nonparametric methods for estimating the survivor function (the probability that an item will still be working at time t, as a function of t).

2. Distribution fitting with censored data - estimation of probability distributions when the data contains censored observations.

3. Weibull analysis - special techniques for fitting the very commonly used Weibull distribution.

4. Arrhenius plot - widely used plot for an accelerated life test when the accelerating variable is temperature.

5. Life data regression - estimation of a regression equation for life data with a specified parametric form for the error distribution.

6. Cox proportional hazards - estimation of a regression equation for life data without specifying a specific error distribution.

Life Tables

In analyzing life data, interest commonly centers on estimating the probability that a unit will still be operating at any given time. A common way of estimating this survival function, without making any assumption about functional form or error distribution, is to tabulate the data and calculate the survivor function directly from the observed failures. When censoring is present, the estimates are calculated using the Kaplan-Meier approach.

Distribution Fitting with Censored Data

If sufficient data is available, it may be possible to fit a specific distribution to the failure times. Maximum likelihood methods can be easily adapted to the presence of censored data. STATGRAPHICS Centurion will automatically fit up to 45 probability distributions for any sample of data and rank them according to goodness-of-fit.

Weibull Analysis

Experience has shown that failure data can often be well modeled by a Weibull distribution. A common method to check the fit of a Weibull distribution is through a Weibull plot. Uncensored failure times should fall approximately along a straight line.

In the STATGRAPHICS Weibull plot, you may add a histogram of censored failure times and confidence limits for failure percentiles.

Arrhenius Plot

When failures do not occur often enough under normal operating conditions, it is necessary to accelerate the failures by increasing the stress caused by one or more variables. A very common accelerant is temperature. By analyzing failure rates at high temperatures and fitting an Arrhenius model, it is often possible to extrapolate the data back to a normal operating temperature (usually expressed in Kelvin).

Life Data Regression

To describe the impact of external variables on failure times, regression models may be fit. Unfortunately, standard least squares techniques do not work well for two reasons: the data are often censored, and the failure time distribution is rarely Gaussian. For this reason, STATGRAPHICS provides a special procedure that will fit life data regression models with censoring, assuming either an exponential, extreme value, logistic, loglogistic, lognormal, normal or Weibull distribution.

Cox Proportional Hazards

The Cox proportional hazards procedure is an alternative method for fitting a life data regression without assuming any specific distributional form. Instead, it is assumed that the predictor variables affect the hazard function in a multiplicative manner. Like the parametric life data regression procedure, the predictor variables can be either quantitative or categorical.