Chapter 7: Life Stress Models (LSM) Module

The Life Stress Models (LSM) module performs quantitative accelerated life testing data analysis. It can also be used to analyze the reliability in multiple operational conditions. The results can be used to determine the reliability in target stress (or use stress) using several life-stress relationships, including Arrhenius, Eyring, Inverse Power Law, Temperature-Non-Thermal, Temperature-Humidity and General Log-Linear. The LSM module can analyze up to 8 different stress types.

7.1 LSM – Analysis List

On the main page, the user can access the Life Stress Models on the dashboard or by clicking on the main menu “LSM  My Analysis”. The dashboard also provides a graphical representation of the quantity of LSM performed in the user’s account in relation to other analyses’ types and how many items were created.

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7.2 LSM – Settings

In the LSM Settings submenu option, it is possible to customize the analysis parameters and the analysis type. It is also in these fields that the confidence bounds are configured as default for the Life Stress Models module. Although all settings can be changed individually in each analysis screen, this is where the defaults are established for a future analysis, adjusted for the user’s preferences. The LSM Settings are accessed on the Menu via LSM ->  Settings LSM.

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On the General Settings section, the user can change the mathematical precision, and the analysis unit. It allows up to 16 decimal places of precision.

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The Stress Settings section will allow the user to input which physical stress factor is the most common in his analyses. Important to point out: these factors must be measurable physical quantities, and they must also have their own unit depiction.

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Confidence Bounds section.

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Note: Although all settings can be changed individually on each analysis screen, this is where the defaults are established for a future analysis, adjusted for the user’s preferences.

7.3 LSM – Data tab

As the LSM module, the LSM chart is like the LDA chart, but now there are some new columns, and the purpose of those is to receive input regarding the stress condition of the analyzed asset.

As the Life Stress Models (LSM) module was developed to perform quantitative accelerated life testing data analysis, the Data tab includes new column(s) to specify stress. The module can analyze up to eight different stress type. The module includes two life distribution models, being Weibull and LogNormal, and several life stress models, being Arrhenius, Eyring, Inverse Power Law, Temperature-Non Thermal, Temperature-Humidity and General Log-Linear.

When creating a new analysis on the LSM module, the page will always open with a default setting including three columns: Time to Failure, Stress and Comments column.
 

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With the mouse placed outside the sheet, simply scroll down to the bottom of the page until there is a scroll bar visible, located right below the input data sheet, and use this bar to scroll right and left to see the whole sheet.

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Note: Using the platform with 1366 x 768 pixels or higher resolution and pressing F11 function, the R4All platform interface will be enlarged giving an even better usability.

When making an analysis with more than two stress types, it might be interesting to check how a specific combination of factors, or even how a singular factor, is affecting the item. The field right above the sheet was made for the purpose of furthering this process without having to re-edit the item or create new ones.

By clicking on the “X” mark beside the factor’s name, the respective column will be darkened, indicating that this factor is no longer being considered in the analysis. Just remember to hit “Calculate” to see the new results and have in mind that only the “General Log-Linear” model can represent on its mathematical formula more than two factors.

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Note: At least one stress column must be selected.

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The LSM Data Type tab allows the user to generate different spreadsheets to meet the needs of each user’s analysis, including two sections:

Section 1: Regular Reliability Data Type:

  • Exact Time – F: Only "Time to Failure", in which the exact failure time is known for all the entries.

  • Exact Time – F/G: Only "Time to Failure" in which the exact failure time is known for grouped entries.

  • Exact Time – F/S: “Time to Failure” and “Time to Suspension” (censored data) in which the exact failure and suspension time are known for all entries.

  • Exact Time – F/S/G: “Time to Failure” and “Time to Suspension” (censored data) in which the exact failure and suspension time are known for grouped entries.

  • Interval Time – F: Only "Time to Failure” in which the exact failure time may not be known for some samples.

  • Interval Time – F/G: Only "Time to Failure" in which the exact failure time may not be known for some samples for grouped entries.

  • Interval Time – F/S: “Time to Failure” and “Time to Suspension” (censored data) in which the exact failure and suspension time may not be known for some samples.

  • Interval Time – F/S/G: “Time to Failure” and “Time to Suspension” (censored data) in which the exact failure and suspension time may not be known for some samples for grouped entries.

Section 2: Stress Data Type:

  • Stress Columns: One Stress, Two Stress or Multiple Stress (up to 8 Stress).

  • Stress Type: Stress name and respective unit.

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The “Data Type” button label shows the Data Type the user defined. The example below shows a Data Type for Failures, Suspensions (censored data), Grouped data and 8 different stress factors. Clicking on this button, the user can edit the data type settings.

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Besides the Data Type button, the Data tab on LSM module includes other analysis configurations:

  • Distribution: Weibull and LogNormal.

  • Life Stress Model: Arrhenius, Eyring, Inverse Power Law (IPL), Temperature Humidity (T-H), Temperature-Non-Thermal (T-NT) and General Log Linear (GLL).

  • Distribution Guide button: To rank the life distribution.

  • Target Stress button: To input the value the user wants to extrapolate the reliability distribution.

  • Stress Transformation button: For GLL life stress model, the user will need to set the stress transformation for each stress factor.

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It is mandatory to enter a Target Stress value. It is the target stress in which the user desires to extrapolate the life distribution, to evaluate if the item can achieve a wanted reliability requirement.

To determine the distribution parameters for the model, the method used on the LSM module will always be the MLE (Maximum Likelihood Estimator).

The Distribution Guide button will rank the best life distribution. To determine the best life stress model, it is necessary that the user has previous knowledge of the physical laws governing the stress factors being considered, as well as their number and correlation.

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When using a General Log-Linear life-stress model, a new button will appear under “Target Stress”: the “Stress Transformation” button. Its function is to select which transformation will be used for each of the factors considered in the analysis, and there can be three types of transformation:

Inverse: which sets an inverse transformation to reduce to an Arrhenius life stress model.

Logarithmic: which sets a logarithmic transformation to reduce to an Inverse Power Law life stress model.

None: no transformation will be applied.

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Important Note: When dealing with discrete random variable stress, always use the General Log-Linear model.

7.4 LSM – Plot tab

On the Plot tab, you can choose several reliability plots. There are eight available:

  • Target Stress Probability of Failure vs. Time

  • Stress Levels Probability of Failure vs. Time

  • Reliability vs. Time [R(t, stress)]

  • Probability of Failure vs. Time [F(t, stress)]

  • Probability Density Function (pdf) [f(t, stress)]

  • Failure Rate vs. Time [l(t, stress)]

  • Life vs. Stress

  • Acceleration Factor vs. Stress

Although the user can change from item to item on the Data tab, on the Plot tab, the user cannot do it. He must switch back to the Data tab so that the R4All platform will allow him to edit or create another item.

The Plot tab will redirect the user to the plot interface. Here, the user will be able to plot the reliability curves and life-stress curves of the current analysis item, and even change some features to visualize how they affect the analyzed asset.

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Important Note: The results and plots under a target stress condition will be valid only for this target stress. To analyze plots for other stress conditions, it is mandatory to input the new target stress and use the “Refresh” button to update the plot. However, it is important to have in mind that the results shown on the plot are bound to the target stress set on the Data tab, and that changing the target stress settings on other tabs will only alter the plots. Do new calculations on the Data tab to see how the target stress alters the scale parameter.

The Plot tab allows user to change the Scale and Confidence Bounds. As these features were already explained in the LDA module, see chapter 2.5 LDA – Plot tab for more details.

There are 8 types of plot in this module. See below for some information about each one of them:

  • Target Stress Probability Plot: analogous to the Prob. of Failure vs. Time plot of the LDA module, it displays the life-stress probability of failure curve linearized on a special scale paper, along with all the events registered on the Data tab. Changing the target stress will make this curve move on along the X-axis, depending on how much it impacts on the life of the asset.

  • Stress Levels Probability Plot: this plot will display the Target Stress Probability Plot and the probability of failure plots for each different stress levels available on the datasheet input.

  • Reliability vs. Time: displays how the reliability curve declines in function of time in the Target Stress condition.

  • Prob. of Failure vs. Time: displays how the probability of failure curve increases in function of time in the Target Stress condition.

  • Pdf vs. Time: displays the probability density function in the Target Stress condition.

  • Failure Rate vs. Time: displays the failure rate and how it behaves through time in the Target Stress condition.

  • Life vs. Stress: this plot shows the characteristic life (scale parameter) in function of the stress factor, showing how it decreases while the stress changes. The probability density functions and times to failure of the input data are plot along the curve, on their respective stress level and characteristic life points.

  • Accel. Factor vs. Time: displays how the acceleration factor increases in function of the stress.

The Life x Stress and Acceleration Factor x Time graphs are based on stress, so to vary one type of stress, the others will be kept constant. This is shown in the “Target stress settings” button. The Target Stress button will highlight in yellow to show that the stress is varying.

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It is possible to set which stress is varying by just clicking on the radio button and selecting which one should vary (the X-axis):

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7.5 LSM - Overlay Plot tab

The Overlay Plot tab allows users to see more than their item in the same plot.

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In some plots, it is mandatory that the items’ distribution be the same. It is because a Weibull distribution has a different scale than a LogNormal distribution. Note in the image above that the plotted curves are both using different life-stress models, but, because both use a Weibull distribution, it is possible to plot them both on the Target Stress Probability Plot.

This scale’s property must be respected on the following plots: Target Stress Probability, Stress Levels Probability, Life vs. Stress and Acceleration Factor vs. Stress.

The Overlay Plot also does not allow to change the target stress freely as on the Plot tab. The user will only be able to change the target stress of the current item which he is using on the tab.

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The Overlay Plot tab also allows the user to change the Scale and Confidence Bounds. As these features were already explained in the LDA module, see chapter 2.6 LDA – Overlay Plot tab for more details.

7.6 LSM – Report tab

On the Report tab, the user can visualize all the plotted graphs from the item previously selected on the Data tab. The setting for each plot type presented in the Report will follow the setting the user made on the Plot tab.

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7.7 LSM - Calculator

On the Report tab, the user can visualize all the plotted graphs from the item previously selected on the Data tab. The setting for each plot type presented in the Report will follow the setting the user made on the Plot tab.

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The LSM Calculator comes with similar functions to the LDA calculator; however, it adds the Target Stress input to all functions and a new function to calculate the Acceleration Factor.

In other words, the LSM Calculator is applied to determine how impactful a new set of conditions (stress) will be for the item’s life curve.

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Note: If the user changes the target stress in the calculator, this will not change the target stress already set on the Data tab, and this new value will not be saved. The calculator will always open with the Target stress set on the Data tab.

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Other functions of the LSM calculator are shared with the calculator of a classic LDA and can be reviewed in section 2.8 of Chapter 2: LDA Module.

The LSM calculator also allows the user to change the Confidence Bounds. As these features were already explained in the LDA module, see chapter 2.8 LDA Calculator for more details.