QCP Calculations and Plots for Traditional RGA

For reliability growth data analysis only.

Weibull++ includes a Quick Calculation Pad (QCP) for computing useful metrics, as well as multiple plots that allow you to visualize the results of your analyses. This topic describes the calculations and plots you can obtain from traditional reliability growth analysis (i.e., the analysis of developmental testing data with the assumption that fixes are applied immediately after a failure and before testing resumes).

Note: When you analyze data from multiple systems, Weibull++ combines the data to create a single equivalent system. Any plots generated for the combined data set and analyses via the Quick Calculation Pad will be based on the equivalent system. See Times-to-Failure Data from Multiple Systems for more information about how the software combines the data for analysis.

QCP Calculations

You can open the Quick Calculation Pad (QCP) by choosing Growth Data > Analysis > Quick Calculation Pad or by clicking the icon on the control panel.

To perform a calculation, select the appropriate option and enter any required inputs in the Inputs area, then click Calculate. For more detailed information about all the options available in the QCP, see Quick Calculation Pad (QCP).

The types of calculations available depend on the selected data type.

Times-to-failure data types

Two values can be calculated for either the MTBF or Failure Intensity:

  • The Instantaneous value is the MTBF/FI over a small interval dt that begins at a specified time. For example, an instantaneous MTBF of 5 hours after 100 hours of operation means that, over the next small interval dt that begins at 100 hours, the average time between failures will be 5 hours.

  • The Cumulative value is the MTBF/FI from time = 0 up to a specified end time. For example, a cumulative MTBF of 5 hours from 0 to 100 hours means that the average time between failures was 5 hours over the 100-hour period.

The Time Given option allows you to calculate the mission duration given any of the following metrics:

  • Cumulative MTBF

  • Instantaneous MTBF

  • Cumulative failure intensity (FI)

  • Instantaneous failure intensity (FI)

Number of Failures is the cumulative number of failures that are expected to occur by a specified time, based on the fitted model.

Discrete data types

For the Discrete-Sequential data sheet with the Crow-AMSAA (NHPP) or Duane models, the following calculations are available:

  • Two values can be calculated for either the Reliability or Probability of Failure:
    • The Cumulative value is the reliability/prob. of failure from time = 0 up to a specified end time. For example, a reliability of 0.85 from 0 to 100 hours means that, on average, the reliability was 0.85 over the 100-hour period.
    • The Instantaneous value is the reliability/prob. of failure over a small interval dt that begins at a specified time. For example, an instantaneous reliability of 0.85 at 100 hours duration means that, over the next small interval dt that begins at 100 hours, the average reliability will be 0.85.
  • The Stage Given option allows you to calculate at which stage a specific metric will be achieved. You can specify the following metrics:
    • Cumulative reliability
    • Cumulative probability of failure
    • Instantaneous reliability
    • Instantaneous probability of failure

    • Number of Failures is the cumulative number of failures that are expected to occur by a specified time, based on the fitted model.

For the Discrete-Mixed data sheet with the Crow-AMSAA or Crow Extended models, the following calculations are available:

  • Two values can be calculated for either the Reliability or Probability of Failure:
    • The Average value is the reliability/prob. of failure from time = 0 up to a specified end time.
    • The Instantaneous value is the reliability/prob. of failure over a small interval dt that begins at a specified time.

  • Number of Failures is the cumulative number of failures that are expected to occur by a specified time, based on the fitted model.

For all other discrete data sheets and models, the following calculations are available:

  • Reliability is the probability of the system operating without failure for a period of time.
  • Probability of Failure is also known as unreliability, and it is the inverse of the reliability.
  • The Stage Given option allows you to calculate at which stage the reliability will be achieved.

Reliability data type

  • Reliability is the probability of the system operating without failure for a period of time.
  • Probability of Failure is also known as unreliability, and it is the inverse of the reliability.
  • Time Given Reliability is the mission duration for a specified reliability value.

Plots

You can create plots by choosing Growth Data > Analysis > Plot or by clicking the icon on the control panel.

This section describes the types of plots you can create for traditional reliability growth analysis. The scaling, setup, exporting and confidence bounds settings are similar to the options available for all other reliability growth plot sheets. For more information on these common options, see Plots.

The types of plots you can create depend on the selected data type.

Times-to-failure data types

  • Cumulative Number of Failures shows how the number of failures is increasing over time. It plots the failure times on the x-axis and the cumulative number of failures on the y-axis. The points represent the actual failure times in the data set and the solution line represents the expected number of failures. The vertical line represents the test termination time.

  • MTBF vs. Time shows how the time between consecutive failures increases, decreases or remains constant over time. It plots the cumulative MTBF curve and the corresponding instantaneous MTBF curve on the same plot. The points represent the actual failure times in the data set, while the vertical line represents the test termination time. The horizontal lines represent the instantaneous MTBF over the marked interval, which is obtained by dividing the length of the interval with the number of failures in that interval. You can specify the length of the intervals by right-clicking the plot and choosing Show/Hide Items on the shortcut menu. In the window, enter the desired interval length in the Time Interval field.
  • Failure Intensity vs. Time shows how the rate of occurrence of failures increases, decreases or remains constant over time. It plots both the cumulative and instantaneous failure intensity curves on the same plot. The points represent the actual failure times in the data set, while the vertical line represents the failure time. The horizontal lines represent the instantaneous failure intensity over the marked interval, which is obtained by dividing the number of failures in that interval with the length of the interval. You can specify the length of the intervals by right-clicking the plot and choosing Show/Hide Items on the shortcut menu. In the window, enter the desired interval length in the Time Interval field.
  • System Operation is available only for multiple systems analysis. It shows the failure times of each system in the data set, along with the timeline for their equivalent system that is used for calculating analysis results. See Times-to-Failure Data from Multiple Systems for more information on how the software combines the data to build the equivalent system.

Discrete data types

The following plots are available when you use the Crow-AMSAA or Duane model with the Discrete-Sequential data sheet, or the Crow-AMSAA or Crow Extended model with the Discrete-Mixed data sheet:

  • Cumulative Number of Failures shows how the number of failures is increasing over time. It plots the failure times on the x-axis and the cumulative number of failures on the y-axis. The points represent the actual failure times in the data set and the solution line represents the expected number of failures. The vertical line represents the test termination time.

  • Reliability vs. Time shows how the reliability increases, decreases or remains constant over time. It plots both the cumulative and instantaneous reliability curves on the same plot.
  • Unreliability vs. Time shows how the probability of failure increases, decreases or remains constant over time. It plots both the cumulative and instantaneous probability of failure curves on the same plot.

For all other models and/or discrete data sheets, the following plots are available:

  • Reliability vs. Time shows the reliability values over time, capturing trends in the system’s failure behavior.
  • Unreliability vs. Time shows the probability of failure of the system over time.

Reliability data type

  • Reliability vs. Time shows the reliability values over time, capturing trends in the system’s failure behavior.
  • Unreliability vs. Time shows the probability of failure of the system over time.

Tip: Weibull++ includes two additional plot utilities you can use across all types of data: the overlay plot, which allows you to compare different data sets or models; and the side-by-side plot, which allows you to display different plots of a single data set all in a single window for easy comparison.

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