Weibull++ Degradation Analysis Folio

Degradation analysis is a technique that uses the performance measurements (degradation measurements) of a product over time to predict the point at which each unit in the sample is expected to fail. This analysis is useful for tests performed on products with very high reliability, where it is not possible to test the products to failure under normal operating conditions.

The Weibull++ degradation analysis folio extrapolates the times at which the amount or level of degradation is serious enough that the unit is considered to be failed. In addition, the folio automatically performs life data analysis on the extrapolated failure times. This allows you to obtain the life characteristics of the product.

The ReliaWiki resources portal has more information on degradation analysis at: http://www.ReliaWiki.org/index.php/Degradation_Data_Analysis.

This topic discusses the following:

Degradation folio data sheet
Control panel settings.

Degradation Folio Data Sheet

To add a Weibull++ degradation analysis folio to a project, choose Insert > Folios > Weibull++ Degradation or right-click the Specialized Folios folder in the current project explorer and choose Add Weibull++ Degradation on the shortcut menu.

The following example shows a degradation analysis of two automobile tires, A and B.

The data sheet contains the following information:

The Inspection Time column indicates the time at which the degradation of the unit was measured. Time may also be measured as the amount of usage the unit accumulates or as the factor that degrades the unit. For example, in the data sheet, the inspection time is in mileage because of its direct relation to the wear on the tires. The level of degradation may be measured either continuously or at predetermined intervals of time.
The Degradation column indicates the degradation measurement of a unit. In this example, the degradation is obtained by directly measuring the depth of the tire tread. In some cases, measuring the level of degradation is not possible without invasive techniques or destroying the specimen. In those situations, the degradation may be measured through a performance indicator, such as the luminosity of a bulb or resistance of a dielectric.

The Unit ID column indicates the unit being measured. The software extrapolates the point of failure for each unique unit based on its degradation measurements.

Control Panel Settings

The Weibull++ degradation folio control panel allows you to configure the analysis settings for the data sheet and view/access the results. It consists of multiple pages, each containing options for performing particular tasks. This topic focuses on the Main page of the Weibull++ degradation folio control panel, which contains the tools you will need to analyze the data set. For more information about control panels in general, see Control Panels.

The Main page includes the following settings:

The Degradation Model area allows you select the mathematical model to use for extrapolating the times at which the critical degradation level would be reached for each unique unit ID in the data sheet. The following is a list of all available models and their corresponding equations. The variable x represents the failure time, y represents the critical degradation, and variables a, b and c are the model parameters to be solved for in the extrapolation.

Linear: y = a*x+b
Exponential: y = b*exp(a*x)
Power: y = b*(x^a)
Logarithmic: y = a*ln(x)+b
Gompertz: y = a*b^(c^x)
Lloyd-Lipow: y = a-b/x

Tip: If you are not certain which degradation model would provide the best fit for your data, you can use the Degradation Model Wizard to guide you through the selection process.

The Critical Degradation field is for defining the level of degradation that is considered a failure. For example, you might wish to define failure as the time when the depth of the tire tread is less than 2 millimeters.
The Suspend After option allows you to define a censoring time past which no failure times are extrapolated. In practice, there is usually a rather narrow band in which the censoring time has any practical meaning. If the censoring time is relatively low, no failure times will be extrapolated, which defeats the purpose of the degradation analysis. On the other hand, a relatively high censoring time would occur after all of the theoretical failure times, thus rendering the censored data meaningless. Nevertheless, certain situations may arise in which it is beneficial to censor the degradation data. For example, if your product has a maximum warranty life of 10,000 hours, then you may want to treat all failures beyond that time as suspensions.

The Life Data Model area contains the settings for performing life data analysis on the failure times that were extrapolated via the degradation analysis. These settings have no effect on the degradation analysis calculations; they affect only the life data analysis calculations. The settings in this area are identical to the settings on the control panel of a Weibull++ standard folio, except for the following option:
- The Use extrapolated intervals option allows you to extrapolate the failure/suspension times as interval censored data. The intervals are calculated as bounds around the extrapolated data points.

What's Changed? In previous versions of Weibull++, you used the Associate Specialized Folio tool to transfer the extrapolated data points to a standard folio data sheet in order to perform life data analysis. In the Synthesis version, you can conveniently perform life data analysis calculations within the degradation analysis folio.

When you click the Calculate icon on the control panel, the software extrapolates the points at which the degradation measurements will reach the point of critical degradation. It then performs a separate life data analysis on the extrapolated points based on the settings you have specified in the Life Data Model area.

The Degradation Results area displays the parameters of the chosen degradation model and the extrapolated failure/suspension times. Click the Degradation Results (...) button to open the Results window, which allows you to view, edit and print the calculations.
The Life Data Results area displays the parameters of the life data model. Click the Life Data Results (...) button to open the Results window.

Note: If the distribution and parameters are associated with a published model, then the model's name will appear as a link at the bottom of the Life Data Results area. Click the link to view the model's properties. For details on how to publish the results as a model, see Publishing Models.

Folio Tools

The folio tools are arranged on the left side of the Main page of the control panel. Use these tools to manage data and experiment with the results of your analysis.

Calculate extrapolates the points at which the degradation measurements will reach the point of critical degradation (i.e., the times at which the degradation is serious enough that the unit is considered to be failed). The software then performs life data analysis calculations on the extrapolated data points. This tool is also available by choosing Degradation > Analysis > Calculate.

Plot creates a new sheet in the folio that provides a choice of applicable plot types. This includes the degradation vs. time plot in addition to the life data analysis plots. This tool is also available by choosing Degradation > Analysis > Plot.

QCP opens the Weibull++ Quick Calculation Pad, which allows you to calculate life data analysis metrics, identical to the calculations you can perform in a Weibull++ standard folio. This tool is also available by choosing Degradation > Analysis > QCP.

Degradation Model Wizard opens the Degradation Model Wizard, which helps you select the degradation model that best fits your data. This tool is also available by choosing Degradation > Analysis > Model Wizard.

Distribution Wizard opens the Distribution Wizard, which helps you select the distribution that best fits the data set based on the chosen parameter estimation method (i.e., RRX or RRY). In the degradation folio, the ranking in the Distribution Wizard is based on the life data model. This tool is also available by choosing Degradation > Analysis > Distribution Wizard.

Change Units opens the Change Units window, which allows you to change the units for the time values in the current data sheet.