Threshold Parameter
The use of a threshold parameter is supported when the Weibull, exponential, or Rayleigh distribution is selected for life data analysis (LDA). You use this parameter, which is known as γ (gamma), only if you know there is some failure-free period. Earlier probability plots that display curvature can indicate that such a period exists. Also known as a location parameter or minimum life parameter, the threshold parameter shifts the plot from the beginning point where it was originally recorded to a new value so that it assumes a more linear form.
When you select a distribution/model combination that supports the threshold parameter, in the Weibull panes for parameter entry, γ is listed under
Calculation results. As described more fully in
Fixed Parameter Values,
Fixed? indicates whether the value is calculated or specified. When this checkbox is cleared for γ (default), the value is calculated. When this checkbox is selected, a field becomes available for specifying the value to use.
• A positive γ indicates an initial failure-free period where failure is either impossible or highly improbable. When γ is positive, this value is added to each x-axis value in the data set prior to running calculations. This shifts the interval from 0 to time t0, which indicates a failure-free period at the beginning of the unit life cycle where the probability of failure is negligible.
• A negative γ indicates the infant mortality of a component or the loss of some life (reliability) prior to the start of service. Examples of this case include products that experience loss of life with prolonged storage, such as rubber, ball bearings, and certain chemicals. Other examples are products exhibiting a manufacturing or assembly defect or a burn-in failure. When γ is negative, this value is subtracted from each x-axis value in the data set prior to running calculations. This shift is used to straighten plots of data values when the data shows a pronounced curve compared to the failure distribution line.
Because a threshold parameter makes the analysis more complicated, its use requires a larger sample size. Without prior knowledge, you should not use a threshold parameter for a data set with fewer than 20 failures. With prior knowledge, you might find it acceptable to use a threshold parameter with as few as 8 to 10 failures.
Prior to using a threshold parameter, ensure that the following three criteria are met:
• The probability plot shows concave curvature.
• A physical explanation exists for why failures cannot occur before t0.
• A larger sample size (at least 20 failures) is available. If prior knowledge from earlier analyses indicates that a threshold parameter is appropriate, a smaller sample size (8 to 10 failures) might be acceptable.
When you use a threshold parameter, the x-axis values and the characteristic value are no longer in the real time domain. To convert back to the real-time domain, you must remove the threshold parameter. For more information, see
Using a Threshold Parameter for a Data Set.