Confidence Level and P Value

About Confidence Level and P-Value

In a Distribution Analysis, the Confidence Level and the P-Value are used to determine whether the data passes the Goodness of Fit test.

The Confidence Level indicates the percentage of uncertainty of the Goodness of Fit method. This percentage is usually determined by experience or an industry standard and limits how closely the data must fit the model in order for it to pass the Goodness of Fit test. The higher the Confidence Level, the farther apart your confidence bounds will be, and the easier it will be for your data to pass the Goodness of Fit test. The lower the Confidence Level and the closer together the bounds are, the harder it will be for your data to pass the Goodness of Fit test. If the data does pass, however, the data will be a very close fit to the model.

Note: When you enter a Confidence Level, you must specify a value that is greater than one (1) but less than one hundred (100).

About Data Censoring in a Reliability Distribution Analysis

Reliability Distribution Analysis supports the functionality of censoring, which accounts for the period of time from the last failure date to the analysis end date. You can censor or ignore datapoints in a Reliability Distribution Analysis to estimate the probability of when a failure might occur. Censoring is based on failure modes.

Details

Censoring a datapoint means that the datapoint is excluded as a failure but included in the operating time of the piece of equipment. If you select the Censored check box, the data in the selected row is excluded. When you create a Reliability Distribution Analysis using a query or dataset as the data source, the GE Digital APM system automatically censors time values from the beginning of the Analysis Period to the first event and the time value from the last event to the end of the analysis. After the calculations for the analysis have been performed, each time that the query or dataset is refreshed, the censoring settings will be reset using the default criteria. Therefore, if you select a check box and refresh the data, the check boxes will no longer be selected.

Regardless of the data source you use, you can censor any failure data. Consider the following:

For Maximum Likelihood Estimators (MLE), the maximum number of censored datapoints is one (1) less than the total number of datapoints.
For Least Squares estimation, the maximum number of censored datapoints is two (2) less than the total number of datapoints.

Pump Failure

Assume that you want to determine the reasons due to which a pump failed.

A pump might have failed due to multiple reasons, such as rusted part, motor overheating, insufficient power supply, or power outage. Each of these reasons will have its own specific failure rate and probability density function. To determine the failure rate of "motor overheating", you must censor all other failure modes from the analysis.

Further, motor overheating might be caused due to multiple reasons, such as improper operation, improper application, and improper maintenance. The censoring feature allows you to separate the failure modes, and determine which is the dominant failure mode. Based on this information, you can decide what is needed to improve the motor performance.

Auto-Censoring

When you first create a Reliability Distribution Analysis, an automatically censored datapoint for each defined asset will appear on the plot. Each automatically censored datapoint represents the analysis End Date (specified on the Set Analysis Period window) for each defined asset.

GE Digital APM can:

Censor failures automatically when it cannot calculate the time between events. For example, failure on a specific asset where the analysis does not contain a start date.
Alert you that a datapoint is suspect. For example, in a Time to Failure type of distribution, an alert will be generated when the start date of an event overlaps the end date of a different event for the same asset. For this asset, suspect data is displayed in the Analysis Summary workspace.

Note: Although automatically censored datapoints appear on the plots, they do not appear in the Failures grid and, therefore, cannot be uncensored.

For a Reliability Distribution Analysis, when you pause on an automatically censored datapoint, the following information appears:

Auto-Censored
Name: Specified on the Assets tab of the Reliability Distribution Data Editor window.
Installation Date: Specified in the Assets section of the Reliability Distribution Data Editor window.
TTF value: Represents the time between the last failure date and the analysis End Date.

Modify the Confidence Level for a Reliability Distribution Analysis

About this task

The Confidence Level specifies how the optimistic and realistic scenarios will be selected in a Monte Carlo Simulation for TTR Distributions in an analysis. The Confidence Level indicates whether the distribution is within the confidence limits or not. The default Confidence Level for an analysis is 90 percent.

You can modify the Confidence Level in the Analysis Summary workspace or after selecting any of the plot tabs in the left pane.

Procedure

Access a Reliability Distribution Analysis for which you want to modify the Confidence Level.
If you want to modify the Confidence Level in the Analysis Summary workspace:
1. In the bottom section, select Distribution Options, and then select .
  
  The Confidence Level box is enabled.
  
  Note: If the Confidence Level box is disabled, select the Use Confidence check box to activate the Confidence Level and enable the Confidence Level box.
2. In the Confidence Level box, enter a numeric value between zero (0) and 100 to represent the desired Confidence Level, and then select .
  The GE Digital APM system displays the confidence intervals for the analysis based on the percentage you entered in the Confidence Level box.
-or-

If you want to change the Confidence Level after selecting one of the plot tabs (e.g., Probability Plot tab):
1. In the left pane, select the Probability Plot tab.
  The Probability Plot appears in the workspace.
2. In the upper-right corner of the workspace, select the Distribution Options list, and then select Confidence Level.
  The Set Confidence Level window appears.
3. Select the Use Confidence check box to activate the Confidence Level and enable the Confidence Level box.
4. In the Confidence Level box, enter a numeric value between zero (0) and 100 to represent the desired Confidence Level, and then select OK.
  The GE Digital APM system displays the confidence intervals for the analysis based on the percentage you entered in the Confidence Level box.

Change the Failure Type in a Reliability Distribution Analysis

About this task

You can change the failure type in the any of the plots selectable via the plot tabs in the left pane (i.e., Probability Plot tab, Failure Rate Plot tab, PDF Plot tab, CDF Plot tab, and Failure Probability tab). These instructions describe how to change the failure type in the Probability Plot

Procedure

Access a Reliability Distribution Analysis for which you want to change the failure type.
In the left pane, select the Probability Plot tab.

The Probability Plot appears in the workspace.
In the upper-right corner of the workspace, select Analysis Tasks, and then select Failure Type.

The Select Failure Type window appears.
Select the necessary failure type, and then select OK.

Note: If you change the failure type to Failures without replacement (as good as old), and then select the PM optimization tab, a red dot and line appears on the plot and a warning is displayed in the bottom section, indicating that PM Optimization calculations are not supported for failures without replacement and that the results are not valid.

The analysis is recalculated based on the selected failure type.

Modify the Analysis Period

Procedure

Access a Reliability Distribution Analysis for which you want to modify the Analysis Period.
In the left pane, select the Probability Plot tab.

The Probability Plot appears in the workspace.

Note: You can also modify the Analysis Period for a plot via the Failure Rate Plot, PDF Plot, CDF Plot, and Failure Probability.
In the upper-right corner of the workspace, select Analysis Tasks, and then select Analysis Period.

The Set Analysis Period window appears.
Clear the I want to use the first failure dates as the start date for this analysis. check box, and then enter or select the desired date.

Note: To ensure that all failure dates appear on the plots, make sure that the start date is before the date associated with the first datapoint. Only failures that occur after the start date will appear on the plots.
Clear the I want to use today's date as the end date for this analysis check box, and then enter or select the desired date.
Select OK.

The GE Digital APM system saves the Analysis Period and recalculates the analysis using the selected dates.

Note: If you want to change the Analysis Period back to the default Analysis Period, select the Start Date and End Date check boxes.

Choose the Time Units for an Analysis

About this task

The time units are used for expressing time values for calculations performed within an analysis. For example, a calculation may indicate the amount of time that lapsed between a failure event and the end date of the analysis period. This value would be expressed in the Time Units for the analysis.

Your Time Units selection will depend on what type of data you are using and what type of analysis you are performing. For example, in an analysis that shows the distribution of failures for a number of pieces of equipment or locations over many years, years might be an appropriate unit of time. For an analysis designed to evaluate failures for a single piece of equipment or location within a very specific time period, a smaller unit of time would be appropriate. For this reason, you can choose the Time Units that are most appropriate for a given analysis.

Note: Downtime for TTF calculations should always be provided using days. When the failure data contains downtime, the system selects Days by default.

Procedure

Access a Reliability Distribution Analysis for which you want to modify the Time Units.
In the left pane, select the Probability Plot tab.

The Probability Plot appears in the workspace.

Note: You can also modify the analysis period for a plot via the Failure Rate Plot, PDF Plot, CDF Plot, and Failure Probability.
In the upper-right corner of the workspace, select Analysis Tasks, and then select Time Unit.

The Select Time Units window appears.
In the Operating Time Unit list, select one of the following options:
- Hours
- Days
- Weeks
- Months
- Quarters
- Years
In the Downtime Unit list, select one of the following options:
- Hours
- Days
- Weeks
- Months
- Quarters
- Years
Select OK.

The GE Digital APM system automatically recalculates the analysis based on the new time units and displays the new units on the plots.

Rename a Reliability Distribution Analysis

Procedure

Access the Reliability Distribution Analysis whose name you want to change.
In the left pane, select the Probability Plot tab.

The Probability Plot appears in the workspace.

Note: You can also modify the analysis period for a plot via the Failure Rate Plot, PDF Plot, CDF Plot, and Failure Probability.
In the upper-right corner of the workspace, select Analysis Tasks, and then select Rename.

The Set Analysis Name window appears.
In the Analysis Name box, enter a new name for the analysis.
In the Analysis Description box, enter a new description for the analysis, and then select OK.

The analysis name is updated in any appropriate sections on the Reliability Distribution page to reflect the change. In addition, the Description field in any appropriate sections will reflect any changes.

Access the Source Data for a Reliability Distribution Analysis

About this task

You can access the source data only if the analysis is based on a query or a dataset.

Procedure

Access a Reliability Distribution Analysis for which you want to view the source data.
In the left pane, select the Probability Plot tab.

The Probability Plot appears in the workspace.

Note: You can also view data for a plot via the Failure Rate Plot, PDF Plot, CDF Plot, or Failure Probability.
In the upper-right corner of the workspace, select Analysis Data, and then select Go To Source.
The fields on the page that appears display the analysis data associated with the selected Reliability Distribution Analysis and correspond to values that were used to create the analysis.
- For an analysis based on a query, the information returned by the query appears.
- For an analysis based on a dataset, the information stored in the dataset appears.
- For an analysis based on manually-entered data, you will receive the following error message:
  
  There is no source data to view since the analysis is based on manually entered data.
  
  To view data for an analysis based on manually-entered data, you can access the Reliability Distribution window.

Modify the Data in a Reliability Distribution Analysis

Procedure

Access a Reliability Distribution Analysis for which you want to modify the data.
In the left pane, select the Probability Plot tab.

The Probability Plot appears in the workspace.

Note: You can also modify the data for a plot via the Failure Rate Plot, PDF Plot, CDF Plot, PM optimization, and Failure Probability.
In the upper-right corner of the workspace, select Analysis Data, and then select Edit Data.

The Reliability Distribution Data Editor window appears, displaying the data associated with the selected Reliability Distribution Analysis.
As needed, modify the data in Failures and Assets tab.
Select OK.

The analysis is updated.

Results

For an analysis that is based on manually entered data, the changes that you make via the Reliability Distribution Data window will be saved for the analysis.
For an analysis that is based on a query or a dataset:
- The query or dataset will not be modified with the updated data. Additionally, any record returned by the query will not be updated with your changes. The changes will be saved to the analysis only.
- After you modify the data and save the analysis, the modified data will appear each time you open the analysis. If you want to revert to the original data, you can reload the original data to the analysis. In addition, if a query or dataset has changed in the database, you can reload the original data to the analysis in order for your analysis to contain those changes.

Reload Analysis Data in a Reliability Distribution Analysis

About this task

When you create and save an analysis that is based on a query or dataset, the GE Digital APM system takes a snapshot of the data that exists at the time of creation and saves it along with the analysis. When you open an existing analysis, the GE Digital APM system loads the data that was last saved with the analysis. This means that any changes to the underlying query or dataset will not be reflected automatically when you open an existing analysis.

Note: If the query or dataset has been deleted or renamed, when you try to open an associated analysis, an error message will appear, and the data will not be refreshed.

If you want to refresh an analysis based on changes to the underlying query or dataset or to load new data that has been added since the analysis was last saved (e.g., the analysis is based on a query that retrieves failures for a piece of equipment or location, and a new failure record has been added to the database), you will need to reload the analysis manually after opening it. When you reload the data, any manual changes made to the analysis data set will be deleted.

Note: Reloading analysis data resets the analysis period only if it is based on the analysis data. Start Dates and End Dates that have been set explicitly will not be overwritten.

Procedure

Access a Reliability Distribution Analysis for which you want to reload the data.
In the left pane, select Probability Plot.

The Probability Plot appears in the workspace.

Note: You can also reload the data for a plot via the Failure Rate Plot, PDF Plot, CDF Plot, PM optimization, and Failure Probability.
In the upper-right corner of the workspace, select Analysis Data, and then select Reload Data.

A confirmation message appears, asking you to confirm that you want to overwrite the current data with the data stored in the database.

Note:
For an analysis based on manually-entered data, you will receive the following error message:

There is no source data to reload since the analysis is based on manually entered data.
Select Yes.

The analysis is updated to reflect the data currently stored in the query or dataset.

Note: If you are reloading analysis data that is based on a query and an index out of range error message appears, there is an error in the query. You should modify the query or recreate the analysis to reload the correct data.

Censor Data in a Reliability Distribution Analysis

Procedure

Access the Reliability Distribution Analysis that contains the plot within which you want to censor a datapoint.
In the left pane, select the plot within which you want to censor a datapoint.
In the plot, select the desired datapoint.

The Point Tooltip window appears.
Select Censor.

The selected datapoint is censored or ignored in the Reliability Distribution Analysis.

Perform a Preventive Maintenance Optimization

About this task

A PM Optimization involves several steps. Based on the MTBF and the calculation of the ratios, the system estimates the optimum time interval to maintain equipment.

Note:

PM Optimization is available only if Failures With Replacements was selected as the failure type via the Reliability Distribution Builder

or Failure Type window.

PM Optimization is not available when Beta is less than or equal to one (Beta <= 1).

Procedure

Access the Reliability Distribution Analysis on which you want to perform a Preventive Maintenance optimization.
In the left pane, select the PM optimization tab.

The PM optimization plot appears in the workspace.
In the upper-right corner of the workspace, select Maintenance Cost.

The Maintenance Cost window appears.

Note: If a PM Optimization has been performed previously, the Preventive Maintenance Optimization dialog box displays the results of the previous calculation.
Enter values in the Planned Cost box and the Unplanned Cost box. You can manually enter the cost or you can select a query and use it to populate a cost box.
Note: The value in the Unplanned Cost box must be greater than the value in the Planned Cost box.

To select an existing query stored in the catalog that contains the data that you want to use to populate a cost field:
1. Select Query next to the Planned Cost box or the Unplanned Cost box.
  The Select a query from the catalog window appears.
2. Select the needed query, and then select Open.
  Note: If you attempt to select a query that does not have any numeric fields, you will receive an error message.
  The cost box is populated with the name of the query you selected.
  Repeat steps 1 and 2 to select a query for the second cost field.
In the Currency box, enter the currency symbol for the cost.
Select OK.
The system validates the data, and the PM optimization workspace displays the PM optimization plot and following information:
- Planned Cost: The planned maintenance cost you entered on the Preventative Maintenance Optimization window.
- Unplanned Cost: The unplanned maintenance cost you entered on the Preventative Maintenance Optimization window.
- Optimal Preventative Maintenance Interval: The optimum interval during which you should perform maintenance on the piece of equipment you are analyzing.
- Estimated Maintenance Cost: The estimated maintenance cost per day for each piece of equipment during the optimal PM interval.
- Optimal Value inflection point: A value identified on the total cost curve.

About Preventive Maintenance Optimization

Preventative Maintenance (PM) Optimization uses the results of a Reliability Distribution Analysis to measure the optimum time to perform a Planned (Restorative) Maintenance (PM) procedure on a piece of equipment. PM optimization does not calculate minor maintenance schedules but determines the optimal time to perform major repairs or replace a piece of equipment until there is a minimal amount of cost and risk. PM optimization is only valid for wear-out failure modes and will not give accurate results for a Weibull analysis where Beta is less than 1.

Note: Interaction with graphs is not available on touch-screen devices.

Details

A PM optimization is composed of the following steps:

The calculation model is configured to acquire the necessary parameters, including Mean Time Between Failures (MTBF). MTBF is used to determine the probability that a piece of equipment will fail.
The cost ratio is determined. This ratio is the cost of planned Preventative Maintenance (PM) events versus the cost of unplanned maintenance events. You can manually enter the cost or select an existing query as the source of the cost data.
Based on the MTBF and the calculation of the ratios, the GE Digital APM system estimates the optimum time (interval) to maintain equipment. The cost per piece of equipment based on the Optimized Preventative Maintenance Interval is also displayed.
The GE Digital APM system creates optimization graphs, which gives the analyst the optimum time to conduct a repair or overhaul based upon the ratio of planned to unplanned repair costs. This ensures that repairs are conducted in a cost-effective manner, minimizing risk while maximizing time in service.

The limitation to using a PM optimization is it will always give a result for the statistical distribution on which it is based. This does not mean that it will always make sense to do a PM at the interval specified. In particular, design flaws that manifest themselves as poor reliability can more effectively be addressed through redesign rather than PM.

Access Reliability Distribution Analysis Report

Procedure

Access the Reliability Distribution Analysis whose report you want to access.
In the upper-right corner of any workspace within the selected Probability Distribution Analysis, select Report.
The Reliability Distribution Analysis report appears in a new browser tab. By default, the report contains the following sections:
- Plots
- Analysis Summary
- Statistical Distribution Information
- Assets
- Failure Data

About Reliability Distribution Analysis Report

The baseline GE Digital APM database includes the Reliability Distribution Analysis report, which you can use to view a summary of the results of a Reliability Distribution Analysis.

The Reliability Distribution Analysis report is built from the following Catalog items:

The main report, DistributionAnalysisReport, which is stored in the Catalog folder \\Public\Meridium\Modules\Reliability Manager\SSRS.
The subreport, SubreportDistributionAnalysis, which is stored in the Catalog folder \\Public\Meridium\Modules\Reliability Manager\Reports.
The subreport, assetSubreportDistribution, which is stored in the Catalog folder \\Public\Meridium\Modules\Reliability Manager\Reports.
The supporting queries that supply data in the main report and subreports, which are stored in the Catalog folder \\Public\Meridium\Modules\Reliability Manager\Reports. The following supporting queries are available:
- ReliabilityDistributionQuery
- ReliabilityDistributionTTR
- ReliabilityExponentialTTF
- ReliabilityExponentialTTR
- ReliabilityLognormalTTF
- ReliabilityLognormalTTR
- ReliabilityNormalTTF
- ReliabilityNormalTTR
- ReliabilityWeibullTTF
- ReliabilityWeibullTTR

Throughout this documentation, we refer to the main report, the subreports, and the supporting queries collectively as the Reliability Distribution Analysis report.

Analysis Summary Section

The Analysis Summary section of the Reliability Distribution report displays information that is stored in the Reliability Distribution record and Distribution records that are linked to the Reliability Distribution record.

The following table lists each item in the Analysis Summary section and the corresponding Reliability Distribution or Distribution record field whose data is displayed in the report.


Report Item	Record	Record Field
Analysis Name	Reliability Distribution	Analysis ID
Analysis Description	Reliability Distribution	Short Description
Analysis Start	Reliability Distribution	Analysis Start Date
Analysis End	Reliability Distribution	Analysis End Date
Number of Assets	Reliability Distribution	Assets
Number of Failures	Reliability Distribution	Number of Failures
Censored Failures	Reliability Distribution	Censored Failures
MTBF	Reliability Distribution	MTBF
MTTR	Reliability Distribution	MTTR
Use Confidence	Reliability Distribution	Use Confidence
Confidence Level	Distribution	Confidence Level
Last Modified	Reliability Distribution	LAST UPDT DT
Modified By	Reliability Distribution	LAST UPBY SEUS KEY Note: The name of the Security User associated with this value is displayed in the report.

Statistical Distribution Information Section

The Statistical Distribution Information section of the Reliability Distribution report displays information that is stored in each Distribution record that is linked to the Reliability Distribution record. Each Distribution record is a member of one of four Distribution subfamilies in which records can exist: Exponential, Lognormal, Normal, or Weibull.

The following subsections are displayed for each Distribution record that is linked to the Reliability Distribution:

In the <Variable> Distribution subsection, <Variable> is the value that is stored in the Variable field in the Distribution record that is linked to the Reliability Distribution record. Throughout the documentation, we will refer to this subsection as the Distribution subsection.

The following table lists each item in the Distribution subsection and the corresponding Distribution record field whose data is displayed in the report.


Report Item	Distribution Field
Distribution Type	Distribution Type
Operating Time Units	Units
Fit Method	Fit Method
R2	R-Squared
Mean	Mean
Standard Deviation	Standard Deviation
Median	Median

The Parameters subsection contains information stored in a Distribution record (i.e., Weibull, Lognormal, Exponential, or Normal record). The Weibull, Lognormal, Exponential, or Normal record is linked to the Reliability Distribution record. The items that appear in the Parameters subsection will be different, depending on the type of Distribution record.

The following table lists each item in the Parameters subsection for a Weibull record whose data is displayed in the report. For a Weibull record, one row is displayed for each of the following field captions: Beta, Eta, and Gamma.


Report Item	Weibull Field
Beta
Value	Beta
Low	Beta Low
High	Beta High
Calculated	Beta Fixed
Eta
Value	Eta
Low	Eta Low
High	Eta High
Calculated	Eta Fixed
Gamma
Value	Gamma
Low	Gamma Low
High	Gamma High
Calculated	Gamma Fixed

The following table lists each item in the Parameters subsection for a Lognormal record whose data is displayed in the report. For a Lognormal record, one row is displayed for each of the following field captions: Mu, Sigma, and Gamma.


Report Item	Lognormal Field
Mu
Value	Mu
Low	Mu Low
High	Mu High
Calculated	Mu Fixed
Sigma
Value	Sigma
Low	Sigma Low
High	Sigma High
Calculated	Sigma Fixed
Gamma
Value	Gamma
Low	Gamma Low
High	Gamma High
Calculated	Gamma Fixed

The following table lists each item in the Parameters subsection for an Exponential record whose data is displayed in the report. For an Exponential record, one row is displayed for the field caption MTBF.


Report Item	Exponential Field
MTBF
Value	MTBF
Low	MTBF Low
High	MTBF High
Calculated	MTBF Fixed

The following table lists each item in the Parameters subsection for a Normal record whose data is displayed in the report. For a Normal record, one row is displayed for each of the following field captions: Mean, Standard Deviation.


Report Item	Normal Field
Mean
Value	Mean
Low	Mean Low
High	Mean High
Calculated	Mean Fixed
Standard Deviation
Value	Standard Deviation
Low	Standard Deviation Low
High	Standard Deviation High
Calculated	Standard Deviation Fixed

The Goodness of Fit Test subsection displays information from the corresponding Distribution record.

The Kolmogorov-Smirnov test is the only test used to measure goodness of fit, so the Name column in the report is populated automatically with the value Kolmogorov-Smirnov test. The following table lists each remaining item in the Goodness of Fit Test subsection and the corresponding Distribution record field whose data is displayed in the report.


Report Item	Distribution Field
Statistic	GOF Statistic
P-Value	GOF P-Value
Passed	Passed

Assets Section

The Assets section of the Reliability Distribution report displays information that is stored in the Failure Data field in the Reliability Distribution record.

The following values are displayed in the Assets section:

Asset ID
Installation Date
Last Replacement
Present Age
Future Age
Present Failure Probability
Future Failure Probability

Functional Failures Section

The Functional Failures section of the Reliability Distribution report displays information that is stored in the Failure Data field in the Reliability Distribution record.

The following values are displayed in the Failure Data section:

Asset ID
Failure Date
TTF
Downtime
Ignore
Censored
Remarks

Analysis Plots Section

The Analysis Plots section of the Reliability Distribution report displays the graphs that are displayed in the Time to Failure Distribution section or accessed via the left pane in the Analysis Summary workspace for the selected analysis.

The Plots section displays the following graphs:

Probability Plot
Failure Rate Plot
Probability Density Function Plot
Cumulative Distribution Function Plot
Preventative Maintenance Optimization Plot