Downloaded from https://www.everyspec.com ADS-79D-HDBK Reliability is the desired probability that the system will correctly detect a fault (that is, probability of detection). Confidence is the desired probability that this reliability will be obtained. When using 90/90 confidence and reliability levels in sample size determination, Eq (1) and (2) each yield 22 samples for zero occurrences of incorrect classification of faulted and un-faulted items.
The ramifications of this equation are that if it is required to have a vibratory CI/HI to demonstrate 90% reliability at a 90% confidence level, the fault must be correctly identified on 22 components with corresponding Tear Down Analyses (TDAs). In addition, 22 components without faults must maintain a false positive rate of less than 10%. These detections should be validated either on a validated test stand or on the actual aircraft. The CI/HI must demonstrate a 90% fault detection rate and a 90% correct classification of no fault conditions based on a threshold.
If justification is provided for reduced reliability/confidence for specific component/fault conditions, the number of samples may be reduced. For example, if the confidence and reliability can be reduced to 80%, only 8 samples are required for faulted and un-faulted conditions using equations one and two. Other methods may be investigated to determine their benefit in determining an appropriate sample size for extending or replacing legacy maintenance with vibratory CBM while still demonstrating high confidence and high reliability.
If one is pursuing alternative approaches, it is important to step back and review how the CI/HI reliability and performance is determined prior to identifying it as a candidate for CBM. I.4.2 Sample Size Method 2 The following example demonstrates one approach to assessing the ability of a CI to detect a component fault. This should be the first step in identifying the ability of a CI/HI to respond to a fault and replace a time based maintenance interval. The approach will be demonstrated by applying the process to one CI used to detect one type of fault on one specific component.
It should be noted that the component used for this analyses is not a candidate for on condition maintenance and is discussed for demonstration purposes. The focus is on one component, one type of fault and one CI. The component used for this example is the input pinion in the nose gearbox of the AH64 helicopter. CI data before and after replacement of the nose gearbox (NGB) of eleven AH-64D helicopters with pitted pinion teeth will be analyzed. 53 During tear down analyses of the NGB, pitting damage was observed and documented on several of the pinion teeth.
The CI for the pinion, referred to as the Sideband Index (SI) for the input gear, was recorded in the on-board health monitoring system when damage occurred and after replacement and will be used for this analysis. The Sideband Index (SI) is a measure of local gear faults. This CI is defined as the average sideband order of the fundamental gear meshing frequency. An increase in the magnitude of the sidebands of the fundamental gear meshing frequency indicates pinion tooth damage. A minimum sample size is required to answer the question - How many faulted components correctly detected by the CBM system are required for validation?
The approach applies a statistical analysis to a problem hypothesis statement. The general guidance of Section I.3 can be used as a reference on some of the statistical methods used in this approach. First, a hypothesis and test statistic must be defined to determine sample size. A hypothesis test is used to answer a question about the dataset. The question to be answered is ― Does the CI, input gear sideband index, respond to the failure mode, pitting on several pinion teeth?” The hypothesis is a quantitative statement that states something about the population is true. Samples , sub-sets of the population , are typically used to evaluate the hypothesis .
For this application, differences between two populations will be investigated. The hypothesis will be defined to determine if the CI for the 53 Antolick, L., J. D. Branning, D. Wade, and P. Dempsey. ―Evaluation of Gear Condition Indicator Performance on Rotorcraft Fleet,‖ Proceedings of the American Helicopter Society 66th Annual Forum, Phoenix, Arizona, May 11-13, 2010. 156