56 research outputs found
Inspection policies in aircraft service
No full textAs aircraft structures begin to age (that is, as flight hours accumulate), existing subcritical cracks or new cracks can grow in some high‐stress points of the structural components. The usual approach is to inspect the structures periodically. Thus, a catastrophic accident during flight can be avoided. The problem then arises of choosing a sequence of inspection times which avoids both too many inspections, which may be costly, and too few inspections, that may also be costly due to a crack in an aircraft structure component not being detected for a long period. In this paper, a simple approach is proposed, where after each inspection (if a crack is not detected), we choose the next inspection point so that a crack may occur within an interval between successive inspection times with a given probability. It allows one to find the inspection policies for detection of initial cracks in critical structural components of aircraft under the assumption that the parameter values of the underlying distributions are unknown; this constraint is often met in practice. Furthermore, obtaining inspection schedules under crack propagation is considered. To illustrate the proposed technique based on ancillary statistics, numerical examples are given.
First Published Online: 14 Oct 201
Novel Approaches to Prediction of a Future Number of Failures Based on Previous In-Service Inspections
No full textIn this chapter, we present novel approaches to predictions of the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the previous in-service inspections of the same sample. The failure-time of such units is modeled with a distribution from a two-parameter Weibull distribution. The different cases of parametric uncertainty are considered. The pivotal quantity averaging approach proposed here for constructing point prediction and simple prediction limits emphasizes pivotal quantities relevant for eliminating unknown parameters from the problems and represents a special case of the method of invariant embedding of sample statistics into a performance index applicable whenever the statistical problem is invariant under a group of transformations, which acts transitively on the parameter space. For illustration, a numerical example is given. </jats:p
A New Technique for Optimization of Product Acceptance Process in Terms of Misclassification Probability
No full textA product acceptance process is an inspecting one in statistical quality control or reliability tests, which are used to make decisions about accepting or rejecting lots of products to be submitted. This process is important for industrial and business purposes of quality management. To determine the optimal parameters of the product acceptance process under parametric uncertainty of underlying lifetime models (in terms of misclassification probability), a new optimization technique is proposed. The most popular lifetime distribution used in the field of product acceptance is a two-parameter Weibull distribution, with the assumption that the shape parameter is known. Such oversimplified assumptions can facilitate the follow-up analyses, but may overlook the fact that the lifetime distribution can significantly affect the estimation of the failure rate of a product. Therefore, the situations are also considered when both Weibull distribution parameters are unknown. An illustrative numerical example is given. </jats:p
Estimation of warranty period for structural components of aircraft
No full textOne of the most important problems in fatigue analysis and design of aircraft structures is the prediction of fatigue crack growth in service. Available in‐service inspection data for various types of aircraft indicate that the fatigue crack damage accumulation in service involves considerable statistical variability. In this paper, we consider the problem of estimating the minimum time to crack initiation (or warranty period) for a number of aircraft structural components, before which no cracks (that may be detected) in materials occur, based on the results of previous warranty period tests on the structural components in question. This problem is a special case of a general class of problems concerned with the analysis of fatigue crack damage accumulation in aircraft service. The technique proposed here for solving this problem emphasizes pivotal quantities relevant for obtaining ancillary statistics. Attention is restricted to invariant families of distributions. Numerical examples are given.
First Published Online: 14 Oct 201
A New Technique for Vibration-Based Diagnostics of Fatigued Structures Based on Damage Pattern Recognition via Minimization of Misclassification Probability
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A Novel Approach to Finding Sampling Distributions for Truncated Laws Via Unbiasedness Equivalence Principle
No full textOptimization of Statistical Decisions for Age Replacement Problems via a New Pivotal Quantity Averaging Approach
No full textA New Approach to Dose Estimation in Drug Development Based on Maximization of Likelihood of Grouped Data
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