Chapter 1: Life Data Analysis (LDA) Module
The LDA Module is the mathematical representation of the components or items life given their historical failure data. The analysis and respective results (KPIs and plots) allow the user to determine the reliability or maintainability of the items, perform the optimal time for maintenance, forecast failures, provide information for any taking decision for improvements, etc. It can be accessed through “My LDA Analysis” on the Dashboard, or through the menu on LDA > My Analysis option.
1.1 LDA Analysis List
On the LDA Analysis List, all the created analyses will be displayed in a list. It is possible to configure the dashboard to be sorted by name, quantity of items and creation date.
Right above the analysis list, it’s also possible to see 4 buttons (shown in the image below). This is an explanation of their functions, following the order from left to right:

Configure the dashboard to show relevant information in the list, such as name, quantity of items or creation date.

Copy the dashboards list’s information so that the user can then paste it in another document of his choosing.

Download a spreadsheet containing the dashboards information.

Generate a .pdf archive of the dashboard at hand.
1.2 LDA Settings
In the Settings LDA submenu option, it is possible to customize the analysis parameters and the analysis type. It is also on these fields that the confidence bounds are configured as default for the Life Data Analysis 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 LDA Settings are accessed on the Menu via LDA > Settings LDA.
1.3 Confidence Bounds
1.4 LDA – Data tab
By clicking on the View button beside any of the analyses, or after creating and naming a new analysis, the Create/Edit LDA dashboard will open. The first screen of the analysis is the Data tab. Here, the user can input its historical failure data or any other type of continuous random variable of a given item.
The following example is of an analysis using a Data Type as Exact Time, in other words, with just times to failure and without suspensions and grouped data in it.
The Data spreadsheet is the first tab to open when this page is accessed. By default, it comes with two fields: Time to Failure and Comments. Also, there is no need to enter the values in any specific order, because the LDA module is already performed to sort the data internally before applying the reliability methods.
The Best Fit button will rank the best distributions for the spreadsheet data, by LKV Value when the chosen parameter estimation method is MLE, and by Rho Value when the chosen parameter estimation method is RRX or RRY. By applying the recommended distribution, it automatically runs the analysis for that modeling. The parameter estimation method used is set according to how it is on the LDA Settings; however, it can also be redefined by clicking on the blue button Analysis Method beside the Calculate option until the desired method is set.
Note: Mixed Weibull 2 and 3 population are not included in the Distribution Best Fit list.
The Data Type tab allows the user to generate different spreadsheets to meet the needs of each user analysis, including:

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.

X (Time) vs Y (Probability of Failure  %): With two data entries being Time on X axis and Probability of Failure on Y axis.
See below the Data Type screen:
When selected Suspension and Grouped options on this screen, the spreadsheet will be created on the Data tab including all necessary columns. For the perfect functioning of the analysis, the Status column must be labeled with a capital letter “F” and a suspension one with a capital letter “S”, any other type of label will be rejected, and the program will inform the user to enter either “F” or “S”.
Note: If the user types “f” or “s” in lowercase letter, the system with automatically adjusts it to capital letter.
The Suspension and Grouped options for the data type are not mandatory and can be selected separately, as they are neither codependent nor excluding. When Interval Time is selected, there will be another column, as for this option the time interval estimated by the user for the failure or suspension must be entered.
Important Note: using the Sort Data option will result in losing the previous entry sorting.
Notes:

Although all settings can be redefined on the LDA Settings menu as discussed before, note that inside the analysis most of the settings are manageable so that the user does not have to surf back and forth to apply new settings to his items all the time.

Note that the “Comment” column is optional and should be used to hold some information on the asset, such as name, criticality, serial number, location, tag, etc.

The Analysis Method button will determine if the rank regression parameter estimation is being applied upon the X axis (RRX), the Y axis (RRY) or we will apply the Maximum Likelihood Estimation (MLE). However, to apply it correctly, it is necessary to recalculate the data again.

For Mixed Weibull, the RRX and RRY methods will not be available. Instead, we will have another method called the NonLinear Regression (NLR) method.

The one parameter distributions (Weibull 1P, Normal 1P and Lognormal 1P) can be applied on occasions where the user wants to edit the shape parameter to previously known values (based on previous experience dealing with similar items). The Weibull 1P can be also applied to calculate dataset with no failures (with just censored data). In this case, the user must input the shape parameter and the Confidence Level. Examples of the one parameter distributions can be seen on the case studies chapters 11.8 and 11.9.
See some other examples of Data Types and how their interfaces are:
Important Note: When changing data types, some columns will be altered, thus if a column is removed, such as the Qty. or the Status columns by altering the data type to have no suspensions and no grouped data, the values stored on its cells will be removed as well, and cannot be retrieved, so it is strongly recommended to choose a data type before starting to edit the sheet.
1.5 LDA – Plot tab
On the Plot tab, the user can choose several reliability plots. There are seven available:

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

Reliability vs. Time [R(t)]

Probability of Failure vs. Time (unreliability curve) [%]

Probability Density Function (pdf) [f(t)]

Failure Rate vs. Time [l(t)]

Histogram of the Probability Density Function

Reliability – Contour Plot

Optimum Interval Time

Optimum Inspection Interval Time
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.
Before editing the axis scales, it is important to check if the Auto Scale boxes are marked. If they are, it means that the R4All platform is selecting a scale that allows the user to visualize the entire curve generated in the modeling. By unmarking the boxes, the scale fields will open. After any changes, the plot must be refreshed to apply the new setting.
The Confidence Bounds button comes with information on how they were calculated: method/confidence level (%)/sides/bound on. So, for the example above, the method is Fisher Matrix, the confidence level is 90%, twosided bounds and the bounds on Y. The acronyms are formed by the initial letters of the selected settings.
For Exponential life distribution, the Contour Plot is not available as the Exponential distribution has just one parameter.
Important Note: All the changes the user makes in the plot settings, including Confidence Bounds and Scales will be saved for the correspondent plot. In other words, the user can perform a different setting for a different plot type.
1.6 LDA – Overlay Plot tab
The Overlay Plot tab allows users to see more than one item on the same plot.
By selecting the ITEM 2 in the Test 1 Analysis, its Data spreadsheet will open, as shown in the example above. After calculating it using its Best Fit, it is available for an Overlay Plot containing any information from all the items, or any selected item (it is also possible to select just one item to be plotted).
On the Overlay Plot tab, it is possible to visualize all the different graphs:

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

Reliability vs. Time [R(t)]

Probability of Failure vs. Time (unreliability curve) [%]

Probability Density Function (pdf) [f(t)]

Failure Rate vs. Time

Histogram of the Probability Density Function

Reliability – Contour Plot
However, if one of those items is molded with a different distribution, the Overlay Plot will suppress the Probability of Failure plot in the distribution scale (first plot of the plot type list), the Contour plot, and the Histogram, as those require items with the same reliability life distribution.
See below some details on how the user can choose one or more items to be plotted on the Overlay Plot tab.
Important Note: Although the Overlay Plot tab allows the user to add more than one item in the plot, all the setting he applies for each plot type will be saved in the item the user is. The selected item can be seen at the top of the page, as the image bellow shows.
1.7 LDA – 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.
Those graphs are all plotted on the Plot tab after the calculation of the data, but on this tab it is possible to see all of them and compare in a more directly way. Each plot also presents the confidence bounds settings at the bottom.
1.8 LDA – Calculator
The LDA Calculator is available at the top of the page beside the item selection menu. It can be used after the data have been calculated. The user can access the calculator in the Data Plot and Repot tab. The calculator will not be available on the Overlay Plot tab.
In the result box, for this specific case, where the function selected is the Reliability function R(t), the LDA Calculator returns what the reliability of the item after working for a given time is. It also shows the confidence bounds value for this time and, in this case, the user is also able to reconfigure how the bounds are calculated and which bound he wants to see. The precision refers to how many decimal places will be considered for the results.
While exporting the calculator results history, the calculator stays locked and can only operate again after the opened document is closed.
As all the reliability functions have a range input, the LDA Calculator will inform the user if the entered value is valid for the given operation, as in the example below:
The function for the BX% Life needs a percentage parameter, so it only accepts values between 0 and 100. Therefore, it is important to check if the entered value is inside the function’s domain.
The functions are placed side by side with their inverted functions, and some may need a new input due to their parameters, like the Conditional Reliability Function R(t/T), which also asks for the working time performed by the item without presenting any failures.
The Mean Function is the only one which requires no parameters, because it is the average value of the modeling distribution.
The function λ(t) returns the failure rate for a specific time value.
The Parameter Bounds will show the values estimated for the current model parameters with their upper and lower bounds, based on the bounds configuration which can be altered at any time inside the calculator on the Confidence Bounds button.
Note that F(T) (cumulative probability of failure) and F(t/T) (conditional cumulative probability of failure) are placed beside R(T) and R(t/T), which are their complementary functions.
T(R) is a function which returns the time for a desired reliability value.
Optimum Replacement Interval is applied to plan preventive maintenances, as it returns the interval between preventive actions. It can be applied for items presenting increasing failure rates over time and with an unplanned replacement cost higher than the scheduled replacement cost. It can be used to minimize the shortterm cost per unit time or to minimize the longterm cost per time.
The LDA calculator also provides an option to calculate the Optimum Inspection Interval, based on costs of maintenance interventions, inspection intervention and failure detection probability.