Dear friends, we are happy to release this video on relatively unknown subject of Extended Reliability Growth Model! Please watch our previous videos on the subject of Reliability Growth before watching this video.
Links are provided below:
Reliability Growth Introduction and Duane Model
Crow AMSAA Reliability Growth Model
This video from the Institute of Quality and Reliability introduces the Extended Crow-AMSAA Reliability Growth Model, building upon the basic Crow-AMSAA (AMSAA) model. It addresses scenarios where corrective actions to improve reliability are delayed rather than implemented immediately during testing.
Need for the Extended Model
Traditional reliability growth models like Duane and the standard Crow-AMSAA assume a “test, analyze, and fix” strategy, where corrective actions are taken during the test, leading to observed reliability growth. However, in reality, corrective actions can be:
- Delayed until after the test (“Test, Find, Test” strategy): The failure intensity remains constant during the test, then sharply drops after all fixes are implemented.
- Partially implemented during and after the test (“Test, Fix, Find, Test” strategy): Some corrective actions are completed during the test, while others are delayed.
When corrective actions are delayed, we need a way to project the future failure intensity and Mean Time Between Failures (MTBF), which is where the Extended Crow-AMSAA model comes in.
Extended Crow-AMSAA Model Concepts
In this extended model, failures are categorized to account for delayed fixes:
- Type A Failures: No corrective action is taken, either because it’s not feasible or not economically justified. These failure modes contribute a constant failure intensity (λA).
- Type B Failures: Corrective actions are planned but are taken after the test (delayed). These are further broken down into specific failure modes (B1, B2, etc.). Each B-type failure mode is assumed to follow an exponential distribution.
The goal is to project the new, lower failure intensity and higher MTBF once all planned corrective actions for Type B failures are implemented. This projection requires assessing the effectiveness factor (D) for each Type B failure mode, which quantifies how much a corrective action will reduce the failure rate (ranging from 0 to 1).
Illustrative Example: All Corrective Actions Delayed (Test, Find, Test)
The video walks through an example where a machine was tested for 400 hours, experiencing 42 failures.
- Categorize Failures:
- Type A: 10 failures, leading to a constant failure intensity of λA=10 failures/400 hours=0.025.
- Type B: 32 failures across 16 distinct modes (B1 to B16). The initial failure intensity for Type B failures is λB=32 failures/400 hours=0.08.
- The total observed failure intensity during the test was 0.025+0.08=0.105, with an MTBF of 1/0.105≈9.52 hours.
- Assess Effectiveness of Corrective Actions: For each B-type failure mode, an effectiveness factor (D) is assigned, representing the anticipated reduction in its failure rate after the corrective action. The remaining failure intensity for each B-type mode is calculated as (1−Dj)×(number of occurrences of Bj/total test time). The average effectiveness factor $- \left(\bar{D}\right) -$ for all B-type failures is also calculated.
- Projected Failure Intensity (λP): The projected failure intensity after all corrective actions are implemented is the sum of three components:
- λA (failure intensity from Type A failures, as no action is taken).
- The sum of the remaining failure intensities of Type B failures (due to partial effectiveness of corrective actions).
- The projected failure intensity of Type B failure modes that would have occurred had the fixes been in place, calculated using the Crow-AMSAA model’s m(t) function (abTb−1) and multiplied by the average effectiveness factor $- \left(\bar{D}\right) -$. Note that for the Crow-AMSAA calculation for Type B failures, only the first occurrence of each B-type failure mode is used to estimate the constants ‘a’ and ‘b’.
- Calculate Projected MTBF: The projected MTBF is the reciprocal of the total projected failure intensity (1/λP).
In the example, the calculated projected failure intensity (λP) was approximately 0.0661, leading to a projected MTBF of approximately 15.13 hours. This indicates a significant improvement from the initial 9.52 hours.
Other Scenarios
The video also briefly mentions the “Test, Fix, Find, Test” scenario, where some corrective actions are completed during the test and others are delayed. This involves further classification of Type B failures into BC (corrected during test) and BD (delayed after test). The calculations become more detailed and are referred to the original research paper.
The Extended Crow-AMSAA model provides a crucial methodology for realistically estimating future reliability when corrective actions are not immediately implemented during testing, offering a more complete picture of a system’s reliability growth.
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