Sigma Magic Help Version 19

Accelerated Life Testing

Overview

Accelerated Life Testing (ALT) is a testing methodology used to estimate the reliability and lifespan of a product or material by subjecting it to stress conditions that are harsher than normal operating conditions. The goal is to simulate aging and failure more quickly than would happen under typical use. The purpose of ALT:

• Predict product life in a shorter time frame.
• Identify failure modes and weak points.
• Improve product design, quality, and warranty planning.

The test samples are exposed to elevated stress factors such as:

• Higher temperatures
• Increased voltage
• Higher vibration levels
• More intense humidity or pressure

These stresses accelerate wear and degradation mechanisms. Data from failures under stress is then extrapolated to normal conditions using models (e.g., Arrhenius equation for temperature).

This tool can be added to your active workbook by clicking on Stats and then selecting Acc Life Testing.

Inputs

Click on Analysis Setup to open the menu options for this tool.

Setup

A sample screenshot of the setup menu is shown below.

1	Data Type: Specify the type of failure data you are analyzing. The available options are: Option Description Complete Data Complete data refers to the data for which we have exact failure times. Left Censor Left-censored data refers to observations in a dataset where the failure time is known to be below a certain threshold, but the exact value is unknown. Right Censor Right censored data means that the test was stopped for whatever reason and the item/product had not failed by the time the test was stopped. Interval Censor Interval-censored data occurs when the exact value of an observation is unknown, but it is known to lie within a specific time or value interval.
2	Num Rows: Specify the number of rows of input data you would like to consider for analysis. This data will be used to reformat the worksheet.
3	Model: Specify the model to use for accelerated life testing. The available options are: Option Description Arrhenius Model Used for temperature related aging. It is based on chemical reaction rates. Ln(Life) = A + B / Temp Inverse Power Used for voltage, pressure, or mechanical stress. Ln(Life) = A - B * Ln(Stress) Eyring Model Used for multiple stresses like temperature, humidity, voltage. Ln(Life) = A + B / Temp + C Ln(Stress) Exponential Model Used to model product failure assuming constant failure rate. Ln(Life) = A + B * Stress
4	Distribution: Currently, only the Weibull distribution is available as the selection for the distribution to use for the fit. Note that the Weibull distribution is a very versatile distribution and depending on the values of its parameters can model both exponential and normal distributions.
5	Help Button: Click on this button to open the help file for this topic.
6	Cancel Button: Click on this button to discard any changes and close the dialog box.
7	Create Design: Click this button to save all the changes and format the worksheet template. You can also update the worksheet format any time, but remember that you may lose any data entered on this worksheet.
7	Analyze Design: Click on this button to save all changes and compute the outputs for this analysis. Review the results of your analysis and make changes to your inputs if required to update analysis results.

Data

You will see the following dialog box if you click the Data button. Here, you can specify the data required for this analysis.

1	Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and speed up the search for the right data for analysis. Enter a few characters in the search field, and the software will filter and display the filtered data in the Available Data box.
2	Available Data: The available data box contains the list of data available for analysis. The data listed in this list box can be selected for analysis. The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is crucial that you not only specify the column name but also the table name.
3	Add or View Data: Click on this button to add more data to your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens the Data Editor dialog box, where you can import more data into your workbook. You can also switch from the list view to a table view to see the individual data values for each column.
4	Failure Type: If your Data Type is set to Complete Data, then this list box is not enabled. If the Data Type is set to Left Censor or Right Censor then this list box can be used to specify the Failure Type. If the Data Type is set to Interval Censor, then this list box can be used to specify the Start Time of the Interval Censor. You can drag and drop the items from the Available Data or select the item in the Available Data and then click on the Arrow next to this list box. Note that you can double-click on any of the columns in this box to remove them from the box. The Failure Type data is a column containing the key words for Censored Data (default: Censor) and Failed Data (default: Failed). You should use the variable names specified in the Options tab. For example, if the first row contains Censor, then the corresponding row of data (Failure Time, Frequency, Temperature, etc.) refers to censored data. Similarly, if the first row contains Failed, then this row refers to failure data where we know the exact time of failure.
5	Failure Time: If your Data Type is set to Complete Data, Left Censor, or Right Censor, then this list box can be used to specify the Failure Time. If the Data Type is set to Interval Censor, then this list box can be used to specify the End Time of the Interval. You can drag and drop the items from the Available Data or select the item in the Available Data and then click on the Arrow next to this list box. Note that you can double-click on any of the columns in this box to remove them from the box. The Failure Time is the time of failure. It is an exact time for Complete Data but an approximate time of failure for censored data.
6	Frequency: You do not need to specify the Frequency column. If this column is not specified, the frequency is assumed to be 1. Frequency is the number of rows of data with the same failure condition. For example, if we are specifying complete data and we note that the failure time is 250 hours. Then a frequency of 2 implies, we had two failures at 250 hours.
6	Temperature: You can specify the column or columns that contain the stressor variables. The input to this list box depends on the model you are using for your accelerated life testing. The following options are available: Model Data to be entered Arrhenius Model Specify the column that contains the accelerated temperature. Inverse Power Specify the column that contains the accelerated stress values. Eyring Model Specify two columns the first for accelerated temperature, and the second for accelerated stress. Exponential Model Specify the column that contains accelerated temperature.
8	View Selection: Click on this button to view the data specified for this analysis. The data can be viewed in a tabular format or a graphical summary.

Options

You will see the following dialog box if you click the Options button.

1	Beta Estimate: Specify how you want to estimate the beta parameter for the Weibull distribution. There are two options available: Option Description Estimate from data Software will estimate the best value for the beta parameter based on your data set. Fixed Value You can override this estimation by specifying your own value.
2	Parameter: Specify the parameter value for the beta value. This option is disabled if the previous setting says "Estimate from data. Otherwise, enter a numeric value for the beta parameter. For example, if you want to force the distribution to an Exponential distribution, then you can set beta = 1. If you set beta = 3.6, the shape of the Weibull distribution is approximately symmetric and similar to a normal distribution.
3	Censor Variable: Specify the name of the variable that specifies that this row contains censored data. The default it Censor. However, it could contain any valid text such as Suspended, Censored, etc. This option is only enabled if we are working with Censored data. If you have Complete Data set or Interval Data set, then this textbox is not enabled.
4	Failed Variable: Specify the name of the variable that specifies that this row contains exact failure data. The default it Failed. However, it could contain any valid text that is different from the name of the variable used for Censor. This option is only enabled if we are working with Censored data. If you have Complete Data set or Interval Data set, then this textbox is not enabled.

Forecast

You will see the following dialog box if you click the Forecast button. You can use this tab to make predictions after developing the accelerated life model. For example, if you have done the accelerated life testing at a temperature of 100 degrees and 150 degrees and built a model. You now want to use this model to predict, what will be the lift at a Temperature of 50 degrees. You can enter that temperature in this tab so that the software can make the prediction at that temperature. If you have only one acceleration variable, only one text box is enabled. However, if you have two acceleration variable, then both the text boxes are enabled.

You can enter up to 5 different combination of Temp & Stress to make the predictions. Note that the model equations are also displayed in the session window which you can use to make predictions at other combinations of Temp & Stress.

Charts

You will see the following dialog box if you click the Charts button.

0	Pick Charts: Select the charts you would like to display for this analysis.
1	Title: The system will automatically pick a title for your chart. However, if you want to override that with your title, you can specify a title for your chart here. Note that this input is optional.
2	Sub Title: The system will automatically pick a subtitle for your chart. However, if you want to override that with your subtitle, specify a subtitle for your chart here. Note that this input is optional.
3	X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your label for the x-axis, you can specify a different label here. Note that this input is optional.
4	Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your label for the y-axis, you can specify a different label here. Note that this input is optional.
5	X Axis: The system will automatically pick a scale for the x-axis. However, if you would like to override that with your values for the x-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10 and 20, the minimum x-axis scale is set at 10, and the maximum x-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the x-axis increment is set at 2. Note that this input is optional.
6	Y Axis: The system will automatically pick a scale for the y-axis. However, if you would like to override that with your values for the y-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum y-axis scale is set at 10 and the maximum y-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the y-axis increment is set at 2. Note that this input is optional.
7	Horizontal Lines: You can specify the values here if you want to add a few extra horizontal reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15, two horizontal lines are plotted at Y = 12 and Y = 15, respectively. Note that this input is optional.
8	Vertical Lines: You can specify the values here if you want to add a few extra vertical reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5, two vertical lines are plotted at X = 2 and X = 5, respectively. Note that this input is optional.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. The software checks if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, they are shown as green-colored checkmarks. If the verification checks fail, they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange exclamation mark. Finally, any checks that are required to be performed by the user are shown as blue info icons.

1	Item: The left-hand side shows the major tabs and the items checked within each section
2	Status: The right-hand side shows the status of the checks.
3	Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

Worksheet

When a new worksheet is added to the workbook, you can enter the censor information and time to failure data in the worksheet input area. If you have specified any data to import in the Data tab, then the corresponding tables are read and imported onto this worksheet.

The data for analysis can be directly entered on the worksheet if requred. In this example, we have a table to specify the Failure Type, Failure Time, Frequency, and Temperature (Accelerated) columns. Once the data has been entered in the worksheet, you are now ready to perform the analysis and generate results.

Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. The outputs area contains a summary of the inputs, the assumptions check verifies if the sample size is sufficient for this analysis and if the solver was above to arrive at a solution for the given problem. The analysis results section contains the distribution of the parameters. The model equations depict the models that were fit for the data. If any predictions are to be generated, a survival table at the prediction points are also included.

The graphs section includes a probability plot of the data along with the fit. If there are multiple acceleration points, each of them is plotted as a separate group.

Notes

Here are a few pointers regarding this analysis:

• Since we are using the Maximum Likelihood Estimates to get the distribution parameters, it is possible that the model may not converge for all cases.
• If you have fewer samples than the one mentioned by the analysis, you will make larger Type I and Type II errors when you perform hypothesis tests.

Examples

The following examples are in the Examples folder.

• For the failure data given in the reference file, perform accelerated life testing and make prediction at temp = 50, 45, 35 (ALT 1.xlsx).

---

© Rapid Sigma Solutions LLP. All rights reserved.