# RGA Glossary

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**"A" Mode:**A failure mode for which a corrective action will not be implemented.

**Actual Growth Potential Factor:**The failure intensity of the M modes (total number of distinct unfixed BD modes) after corrective actions have been implemented for them, using the actual values for the effectiveness factors. This metric is used in the Crow Extended - Continuous Evaluation model.

**Actual Growth Potential Failure Intensity:**The minimum attainable failure intensity based on the current management strategy. This metric is used in the Crow Extended - Continuous Evaluation model.

**Actual Growth Potential MTBF:**The maximum attainable MTBF based on the current management strategy. This metric is used in the Crow Extended - Continuous Evaluation model.

**Actual Idealized Growth Curve:**The reliability growth planning curve for the Crow extended model that takes into account the fix delay.

**Actual Projected Failure Intensity:**The projected failure intensity based on the current management strategy. This metric is used in the Crow Extended - Continuous Evaluation model.

**Actual Projected MTBF:**The projected MTBF based on the current management strategy.

**Allowable Failures:**Maximum number of failures that can occur during the demonstration test and still pass the test. Used in the design of reliability tests for repairable systems.

**AMSAA:**Army Materiel Systems Analysis Activity.

**Average Actual EF:**An average of the effectiveness factors (EF) for the BD modes that takes into account the point at which the corrective action will be implemented. If the fix is going to be implemented at a later time or during another phase, then the EF value for the mode at the current analysis point is set to zero. If the delayed fix is going to be implemented at the current analysis point, then the EF value is set to the specified value for the mode. This metric is used in the Crow Extended - Continuous Evaluation model.

**Average Fix Delay:**The average test time required to incorporate corrective actions into the configuration. A fix delay can be specified for each phase of the reliability growth plan.

**Average Nominal EF:**An average of the effectiveness factors (EF) for the BD modes assuming all fixes for the seen BD modes will be implemented.

**"BC" Mode:**For the Crow Extended model, it is a failure mode for which a corrective action will be implemented during the test. For the Crow Extended - Continuous Evaluation model, it is a failure mode for which a corrective action will be implemented at the time of failure.

**"BD" Mode:**For the Crow Extended model, it is a failure mode for which a corrective action will be delayed until the end of the test. For the Crow Extended - Continuous Evaluation model, a failure mode for which a corrective action will be implemented at some point in time after the failure time.

**BD Mode Failure Intensity:**See Discovery Rate Failure Intensity.

**Beta:**The shape parameter for the Crow-AMSAA (NHPP) and Crow Extended models. Beta must be greater than zero.

**Chi-Squared GOF Test:**A goodness-of-fit test that evaluates the hypothesis that the data follows a non-homogeneous Poisson process (NHPP). This goodness-of-fit test is used in grouped data types.

**Common Beta Hypothesis Test:**Tests the hypothesis that all systems in the data set have similar values of beta.

**Cramér-von Mises:**A goodness-of-fit test that evaluates the hypothesis that the data follows a non-homogeneous Poisson process (NHPP). This goodness-of-fit test is used for non-grouped data types.

**Discovery Rate Beta:**Indicates whether the interarrival times between unique BD modes are getting larger or smaller. In most cases, we want this value to be less than 1 assuming that most failures will be identified early on and that their inter-arrival times will become larger as the test progresses.

**Discovery Rate Failure Intensity:**The failure intensity of the unseen BD modes. This is represented by [math]\displaystyle{ h(t)\,\! }[/math].

**Discovery Rate MTBF:**The rate at which the next new unique BD mode will be observed. This is represented by the inverse of [math]\displaystyle{ h(t)\,\! }[/math].

**Demonstrated/Achieved Failure Intensity:**The Instantaneous failure intensity at the termination time.

**Demonstrated/Achieved MTBF:**The Instantaneous MTBF at the termination time.

**Effectiveness Factor:**The portion of the BD mode's failure intensity that is expected to be removed based on the planned corrective action. This applies only to delayed fixes.

**Failure Intensity:**The probability of failure within the next [math]\displaystyle{ \Delta(t)\,\! }[/math] given that the system may or may not have failed.

**Failure Intensity Modes Seen:**The failure intensity for the failure modes that have been seen during the test. This is calculated by subtracting the failure intensity of the modes that have not been seen from the total system failure intensity.

**Failure Truncated:**Indicates that the test was stopped at a failure time. A test can either be failure truncated or time truncated.

**Goal MTBF:**The MTBF requirement when determining a reliability growth plan.

**Growth Potential Design Margin (GPDM):**A safety margin when setting target MTBF values for the reliability growth plan. It is common for systems to degrade in terms of reliability when a prototype product is going into full manufacturing. The degradation is due to variations in material, processes, etc. Furthermore, the in-house reliability growth testing usually overestimates the actual product reliability because the field usage conditions may not be perfectly simulated during growth testing. Typical values for the GPDM are around 1.2. Higher values yield less risk for the program, but require a more rigorous reliability growth test plan. Lower values imply higher program risk, with less "safety margin."

**Growth Potential Failure Intensity:**Minimum failure intensity that can be attained with the current management strategy. The minimum failure intensity will be attained when all unique BD modes have been observed and fixed. This metric is used in the Crow Extended model.

**Growth Potential MTBF:**Maximum MTBF that can be attained with the current management strategy. The maximum MTBF will be attained when all unique BD modes have been observed and fixed.

**Growth Rate:**Represents the rate at which the MTBF of the system is increasing. The growth rate for the Crow-AMSAA (NHPP) model is equal to [math]\displaystyle{ 1 - \beta\,\! }[/math] and is therefore a value greater than or equal to zero,but less than 1. For the Duane Model, the growth rate ([math]\displaystyle{ \alpha\,\! }[/math]) is the negative of the slope of the line on the cumulative failure intensity vs. time plot. A growth rate that is equal to 1 implies an infinite MTBF growth.

**Homogeneous Poisson Process (HPP):**A homogeneous process is equivalent to the widely used Poisson distribution. In this scenario, the system's failure intensity is not affected by age. Therefore, the expected number of failures associated with the system is accumulated at a constant rate. It is a special case of the Crow-AMSAA (NHPP) model when [math]\displaystyle{ \beta = 1\,\! }[/math].

**Initial Failure Intensity:**The failure intensity inherent to the system prior to any testing.

**Initial MTBF:**The MTBF inherent to the system prior to any testing.

**Integrated Reliability Growth Testing (IRGT):**A process where reliability growth testing is conducted as part of existing testing procedures. This is less expensive than conducting a formal reliability growth test. IRGT is usually implemented at the same time as the basic reliability tasks. The test conditions under IRGT are usually less than the actual customer use conditions.

**Lambda:**The scale parameter for the Crow-AMSAA (NHPP) and Crow Extended models. Lambda must be greater than zero.

**Laplace Trend Test:**Tests the hypothesis that a trend does not exist within the data. The Laplace trend test can determine if the system is deteriorating, improving or if a trend does not exist.

**Likelihood Value**: The log-likelihood value returned by the likelihood function given the estimated parameters. This value is returned when maximum likelihood estimation (MLE) is used to estimate the parameters.

**Management Strategy Ratio:**Defines the portion of the system's failure intensity that will be addressed by corrective actions. A management strategy ratio equal to 1 indicates a perfect management strategy. In this case, a corrective action will be implemented for every mode that is seen. A typical value is 0.95, which indicates that 5% of the system's failure intensity will not be addressed (i.e., 5% will be "A" Modes).

**Maturity Factor:**The ratio of the initial MTBF to the final MTBF.

**MIL-HDBK-189:**Military handbook for reliability growth management. MIL-HDBK-189C can be downloaded by clicking here.

**Minimal Repair:**This is a situation where the repair of a failed system is just enough to get the system operational again (i.e., no renewal).

**MTBF Modes Seen:**The inverse of the failure intensity for the modes that have been seen during the test. See Failure Intensity Modes Seen.

**Nominal Growth Potential Factor:**The failure intensity of the M modes (total number of distinct unfixed BD modes) after corrective actions have been implemented for them, using the nominal values for the effectiveness factors. This metric is used in the Crow Extended - Continuous Evaluation model.

**Nominal Growth Potential Failure Intensity:**The minimum attainable failure intensity if all delayed corrective actions are implemented for the modes that have been seen, and delayed corrective actions are also implemented for the unseen BD modes, assuming testing would continue until all unseen BD modes are revealed. This metric is used in the Crow Extended - Continuous Evaluation model.

**Nominal Growth Potential MTBF:**The maximum attainable MTBF if all delayed corrective actions are implemented for the modes that have been seen, and delayed corrective actions are also implemented for the unseen BD modes, assuming testing would continue until all unseen BD modes are revealed. This metric is used in the Crow Extended - Continuous Evaluation model.

**Nominal Idealized Growth Curve:**The reliability growth planning curve for the Crow Extended model that does not take into account the fix delay. The nominal curve assumes that all fixes are implemented instantaneously. Reliability growth is realized instantaneously on this curve since there is not a delay associated with the implemented fixes.

**Nominal Projected Failure Intensity:**The projected failure intensity assuming all delayed fixes for the modes that have been seen are implemented.

**Nominal Projected MTBF:**The projected MTBF assuming all delayed fixes for the modes that have been seen are implemented. This metric is used in the Crow Extended - Continuous Evaluation model.

**Non-Homogeneous Poisson Process (NHPP):**The NHPP is generally used to model the reliability of a repairable system. An NHPP is an extension of the HPP process. The NHPP allows for the system failure intensity to change with system age. Therefore, the expected number of failures associated with the system is not accumulated at a constant rate.

**p ratio:**The probability of not incorporating a corrective action by time [math]\displaystyle{ T\,\! }[/math].

**Planned Growth:**MTBF or failure intensity specified during a phase for the Crow Extended model for reliability growth planning.

**Projected Failure Intensity:**The estimated failure intensity that will be reached if the proposed delayed corrective actions are implemented, with the specified effectiveness factors. This metric is used in the Crow Extended model.

**Projected MTBF:**The estimated MTBF that will be reached if the proposed delayed corrective actions are implemented with the specified effectiveness factors. This metric is used in the Crow Extended model.

**Reliability Growth:**The positive improvement in a parameter or metric over a period of time due to changes in the system's design or manufacturing process.

**Statistical Test for Effectiveness of Corrective Actions:**A statistical test that can determine if the average failure intensity for phase 2 is statistically less than the average failure intensity for phase 1. This test can also determine if the average failure intensity for phase 2 is statistically less than the demonstrated failure intensity at the end of phase 1. This test is used with multi-phase data sets.

**Stochastic Process:**A sequence of interdependent random events.

**Termination Time:**In developmental testing, this is equal to the total accumulated test time of all systems. For repairable systems, this is equal to the age of the oldest system.

**Test-Fix-Test:**A testing procedure where all corrective actions are implemented during the test.

**Test-Find-Test:**A testing procedure where all corrective actions are delayed until the end of the test.

**Test-Fix-Find-Test:**A testing procedure where some corrective actions are implemented during the test, while others are delayed until the end of the test.

**Time Truncated:**Indicates that the test was stopped after a specific amount of test time. A test can either be failure truncated or time truncated.