Reliability HotWire

Issue 104, October 2009

Hot Topics

New Features in RGA 7 for Reliability Growth Analysis and Fielded Repairable System Analysis

RGA 7 has just been released and the software is packed with new features to support more powerful applications for reliability growth models in developmental testing and fielded repairable systems. In this article, we present a brief overview of some of the most exciting new features in RGA 7.

Complete Reliability Growth Planning and Analysis Across Multiple Test Phases
Traditional reliability growth analysis models consider the data from a single phase of developmental testing. However, a reliability growth program often will be conducted across multiple phases. RGA 7 now offers an array of new analysis and management tools based on the Crow Extended and Crow Extended � Continuous Evaluation models, which provide the appropriate calculations for reliability growth program planning and multi-phase data analysis.

  • Crow Extended Model for Reliability Growth Planning
    In order to plan and execute an overall reliability growth program plan, the first step is to set an idealized reliability growth curve and a planned MTBF goal at each phase of the program. With this approach, test data can be tracked against goals so that early warning signals can be identified in time to make significant changes in order to meet the final MTBF goal for the product. RGA 7 utilizes the Crow Extended model for reliability growth planning. Unlike the traditional planning models, such as MIL-HBK-189, the Crow Extended model for reliability growth planning provides additional inputs that allow the model to account for a specific management strategy and delayed fixes with specified effectiveness factors. The model also provides a second curve that accounts for the average fix delay � the amount of test time from when the failure mode is discovered until the fix will be implemented in the units under test. A growth planning plot in RGA 7 is shown next.

Growth Planning Plot

  • Reliability Growth Analysis Across Multiple Test Phases Using the Crow Extended �Continuous Evaluation Model
    The Crow Extended - Continuous Evaluation model is designed for analyzing data across multiple test phases, while considering the data for all phases as one data set. It provides the flexibility to model the practical testing situation where the corrective actions may be applied immediately at the time of failure, at a later time during the same test phase, in between test phases, during a subsequent test phase or not implemented at all. The Crow Extended - Continuous Evaluation model is not constrained by the assumption that testing will be stopped when fixes are applied during a test phase or that all BD modes will be corrected at the end of the test. Based on this flexibility, the end time of testing is not predefined and the model can be continuously updated with new test data. This is the reason behind the name "continuous evaluation."
  • Multi-Phase Plotting
    The most powerful application of the Crow Extended � Continuous Evaluation model is in tracking reliability performance as the test progresses. RGA 7 allows analysis points at specified times to be plotted against the set goals that were specified using the reliability growth planning utility. An example of a MultiPhase plot in RGA 7 is shown next. It includes the nominal and actual idealized growth curves and the planned growth at each phase (calculated with the Crow Extended model in the Growth Planning Folio), together with the demonstrated, projected and growth potential MTBF values at each analysis point and phase (calculated using the Crow Extended - Continuous Evaluation model in a Multi-Phase data sheet) .

MultiPhase Plot

Operational Mission Profiles
During a development program, it is common practice for systems to be subjected to operational testing in order to evaluate the performance of the system under conditions that represent actual use. When the system must be tested for a variety of different mission profiles, it can be a challenge to make sure that the testing is applied in a balanced manner that will yield data suitable for reliability growth analysis. RGA 7's Mission Profile Folios are used to:

  • Create and manage an operational test plan that effectively balances all of the mission profiles that need to be tested.
  • Track the expected vs. actual usage during testing for all mission profiles and validate that the testing has been conducted in a manner that will yield data sets that are appropriate for reliability growth analysis.

In addition, in order for the growth model to be applied appropriately, RGA 7 can automatically group the data at specified "convergence points," which are pre-defined points at which the actual usage for each profile is managed so that it meets the expected usage.

The next figure shows the Mission Profile plot for the reliability growth testing of a Multi-Function Printer (MFP). The profiles for printing, copying and faxing are tracked against their expected usage values throughout the developmental testing. Two convergence points during the growth test and one at the end of the test are used to make sure that at those points the test data can be grouped and analyzed in a way that best simulates actual field usage.

Mission Profile Plot

Design of Reliability Tests for Repairable Systems
Design of Reliability Test (DRT) methods that are based on the parametric binomial, non-parametric binomial or exponential Chi-Squared methods are suitable for non-repairable items. However, when you want to design a reliability demonstration test for a repairable system that may fail and be restored multiple times during operation, another method is required. The failure process in a repairable system is considered to be a non-homogeneous Poisson process (NHPP) with a power law failure intensity. RGA 7 now provides a DRT utility that models the failure process in this way, enabling you to determine the amount of test time (or number of test units) that will be required to demonstrate a specified reliability goal (defined in terms of MTBF or failure intensity at a given time) for a repairable system.

The next figure shows an example of a calculation of the required test time per unit for a reliability demonstration test (assumption of beta = 1) to demonstrate an MTBF of 1000 hours (instantaneous and cumulative MTBF values are the same when beta = 1), with an 80% confidence level. The number of test units for the demonstration test is 6, and the total number of allowable failures for the test is 2. The result is that the required test time per unit is ~714 hours.

Repairable Systems DRT

In addition, if you wish to consider a range of possible options for the number of units and number of allowable failures, you can use the utility to generate a table like the one shown next.

Repairable Systems DRT Results Table

Monte Carlo Data Generation and SimuMatic�
When analyzing developmental systems for reliability growth or when conducting data analysis of fielded repairable systems, it is often useful to experiment with various "what if" scenarios or put together hypothetical analyses before having available data. This can help to find the best way to analyze data sets when they become available. With that in mind, RGA 7 offers two utilities based on Monte Carlo simulation: the Monte Carlo Data Generation utility and SimuMatic.

Monte Carlo data generation is a computational algorithm in which we randomly generate input variables that follow a specified probability distribution. We are interested in generating failure times for systems that we assume have specific characteristics. We expect the inter-arrival times of the failures to follow a non-homogeneous Poisson process with a Weibull failure intensity, as specified by the Crow-AMSAA (NHPP) model in the case of reliability growth analysis and by the power law model in the case of repairable system data analysis.

With SimuMatic, reliability growth analyses are performed a large number of times on data sets that have been created using Monte Carlo simulation. Essentially, RGA 7�s SimuMatic utility performs a user-defined number of Monte Carlo simulations based on user defined required test time or failure termination settings, and then recalculates the growth parameters for each of the generated data sets.

Monte Carlo simulation and SimuMatic can be used in order to:

  • Better understand reliability growth and repairable system concepts.
  • Experiment with the impact of sample size, test time and growth parameters on analysis results.
  • Construct simulation-based confidence intervals.
  • Better understand concepts behind confidence intervals.
  • Design reliability demonstration tests.

The next figure shows simulation-generated confidence bounds for the instantaneous MTBF vs. time, created using the SimuMatic utility.

SimuMatic Plot

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