Downloaded from https://www.everyspec.com ADS-79D-HDBK Table I-II lists the sample size requirement given reliability goal and number of allowable failures at various confidence levels using Eq (1) 45 . It can be observed that the required sample size increases with higher reliability goal or confidence level. The sample requirement for the case of zero failures varies from 5 (75% of reliability with 75% confidence) to 459 (99% of reliability with 99% confidence). In addition, the sample size increases significantly with the increased number of allowed failures during the test.
For example, twenty-two single sample CI/HI readings from separate components are needed to demonstrate a reliability goal of 90% with 90% of confidence if no failure to correctly categorize faulted and un-faulted components is allowed. For the same target (90% of reliability with 90% confidence) the number of total number of single sample CI/HI readings from separate components increases to 38 if one failure is allowed during the test. The sample size increases further to 91 if 5 failures are allowed. Due to the high cost associated with reliability demonstration of complex systems, it is highly desirable to reduce the required number of samples.
One way of achieving the goal is for the system to include redundancy (such as on-board monitoring with multiple sensors). The risk of sensor failure can be mitigated through data fusion among the sensors and continuous/frequent monitoring, accordingly, may reduce the reliability goal. If there is a significant amount of time between early detection of CI/HI and final failure, the requirement of reliability of detection can be reduced. In addition, the existing knowledge of physics of failure, legacy fielded data, or sensor performance data obtained from developmental stage can be used to reduce the sample size through Bayesian Inference.
The reliability literature has several conflicting "rules of thumb" for sample size. One is that it is usually sufficient to test between 5 and 20 independent times; another is that you generally have to test at least 30 independent times. Military Handbook 781A 46 says that for reliability acceptance, one should test at least three independent times per lot and preferably 10%, up to a limit of 20, tests per lot. Because of such conflicting information, it is understandable that selection of a sample size requirement may be confusing.
But the reason for lack of consistency in the rules of thumb is they are based on different assumptions about what constitutes acceptable confidence and reliability levels. Once these are established (a choice made with a view to defending oneself should a decision come under close public scrutiny), there is no longer any question what the sample size should be. Additional sample size information may also be found in ASTM E 122-09 47 which provides numerous equations and examples for sampling processes and material lots.
I.4 DETAILED GUIDANCE The following subsections provide detailed guidance for determining sample sizes to verify and validate CIs/HIs for use in condition based monitoring systems intended to replace or modify legacy maintenance inspections or TBOs. I.4.1 Sample Size Method 1 To achieve a sufficient sample size for validation of CBM algorithms, one approach is to apply reliability criteria to the CI/HI. Sample size can be determined using binomial pass/fail criteria for reliability testing. 45 Abernethy, B., Robert, ―The New Weibull Handbook – Reliability & Statistical Analysis for Predicting Life, Safety, Survivability, Risk, Cost, and Warranty Claims,‖ Fourth Edition, 2000.
46 MIL-HDBK-781, Department of Defense Handbook, ―Reliability Test Methods, Plans, and Environments for Engineering, Development, Qualification, and Production,‖ April 1996. 47 ASTM E 122-09, American Society for Testing and Materials, ―Standard Practice for Calculating Sample Size to Estimate, with Specified Precision, the Average for a Characteristic of a Lot or Process,‖, 1999. 153