Floyd W. Spencer

System-based component-test plans and operating characteristics: binomial data

Component-test plans are often designed by allocating system reliability among the systems components, then choosing individual component plans suitable for demonstrating achievcment of each components reliability goal. This approach does not consider how much information relative to the system reliability goal is provided by the ensemble of component tests. We consider the notion of system reliability operating characteristic (OC) curves, based on the component tests, and illustrate their use in designing or evaluating an overall test program. By specifying OC values (akin to producers and consumers risks), optimum, system-ortented component-test plans can be derived. These ideas are illustrated for a series system, and for a simple series-parallel system, with binomial data.

Sonic Infrared (IR) Imaging and Fluorescent Penetrant Inspection Probability of Detection (POD) Comparison

Sandia National Laboratories Airworthiness Assurance Nondestructive Inspection Validation Center (AANC) implemented two crack probability of detection (POD) experiments to compare in a quantitative manner the ability of Sonic Infrared (IR) Imaging and fluorescent penetrant inspection (FPI) to reliably detect cracks. Blind Sonic IR and FPI inspections were performed on titanium and Inconel® specimens having statistically relevant flaw profiles. Inspector hit/miss data was collected and POD curves for each technique were generated and compared. In addition, the crack lengths for a number of titanium and Inconel® reference standards were measured before and after repeated Sonic IR inspections to determine if crack growth occurred.

A design-of-experiments approach to characterizing the effects of sonic IR variables

Sonic IR has shown potential as a viable nondestructive inspection technique for crack detection by demonstrating that clearly identifiable signals can be generated where known cracks exist in certain structures1,2. However, before a technique can be used in a field environment, the factors that affect the reproducibility of the technique must be evaluated and their effect on the results of the technique understood. This will enable the control of these factors in the execution of an inspection procedure at, for example, an Air Force Depot Maintenance facility. In this program, sponsored by the Air Force Research Laboratory, we are taking a Design of Experiments (DoE) approach to determine the effect of several key variables on the results obtained from Sonic IR testing. A set of small samples with known fatigue cracks was tested according to a statistically designed test matrix. The design of this test matrix, the experimental setup, the test results, and conclusions will be presented.

The Calculation and Use of Confidence Bounds in POD Models

At a qualitative level the calculation of a statistical confidence interval for a quantity X is an attempt to answer the question: “How variable could X have been and still be consistent with the data that have been observed?” Models used in POD estimation fit an entire curve to the data in hand. However, the quantity of interest, X(p), is often a single point on the curve, such as the flaw size for which the probability of detection is equal to p. In order to make a confidence statement about X(p) the uncertainty about the parameter estimates are translated to the uncertainty about X(p). Often the calculation is made for each p and the results displayed as a curve. Curves derived in such a manner are not themselves POD‐curves, although often interpreted as such. In this paper the most often recommended method in the statistical literature, based on likelihoods, are presented. It is shown that the methodology extends naturally to models incorporating additional parameters to model specific POD behaviors.

Characterizing the Effects of Sonic IR Variables on Turbine Disk Inspection Using a Design of Experiments Approach

Sonic IR has shown potential as a viable nondestructive inspection technique, but many questions remain as to how to optimize the technique for detectability and reliability. There are many adjustable variables that influence the performance of this technique and it is not known how, or if, these variables interact with each other. In this program, sponsored by the Air Force Research Laboratory, we are taking a Design of Experiments (DoE) approach to the issue. Small samples with known fatigue cracks were tested and reported on previously. In our current work, we placed fatigue cracks in the non‐symmetrical anti‐rotation features of scrapped F100‐PW‐220 1st‐stage high pressure turbine disks and conducted controlled experiments measuring peak crack response. This paper will discuss the design of this test matrix for the turbine disks, the experimental setup, test results, and conclusions.

The Design for Tractable Analysis (DTA) Framework: A Methodology for the Analysis and Simulation of Complex Systems

The Design for Tractable Analysis (DTA) framework was developed to address the analysis of complex systems and so-called “wicked problems.†DTA is distinctive because it treats analytic processes as key artifacts that can be created and improved through formal design processes. Systems (or enterprises) are analyzed as a whole, in conjunction with decomposing them into constituent elements for domain-specific analyses that are informed by the whole. After using the Systems Modeling Language (SysML) to frame the problem in the context of stakeholder needs, DTA harnesses the Design Structure Matrix (DSM) to structure the analysis of the system and address questions about the emergent properties of the system. The novel use of DSM to “design the analysis†makes DTA particularly suitable for addressing the interdependent nature of complex systems. The use of DTA is demonstrated by a case study of sensor grid placement decisions to secure assets at a fixed site.

On the design of component test plans based on system reliability objectives

Consideration is given to the case of a series system of different components and binomial component data. For the case of equal numbers of units tested of each component (which can be shown to minimize total cost, subject to the risk constraints), the operating characteristic envelope is readily derived. From this envelope component test plans that satisfy the specified risks can be derived from equations that involve the cumulative binomial distribution function. Existing tables pertaining to acceptance sampling plans based on the binomial distribution can be used to determine the required number of component tests.<<ETX>>

Corrosion structured experiment

Ten-percent material loss is a common corrosion level that makes a structural repair or replacement necessary in the large transport aircraft industry. For this reason a fundamental question of any NDT technique to be applied for the detection of faying surface corrosion is whether it is capable of reliably detecting corrosion that results in 10 percent parent material loss. The structured experiment approach discussed in this presentation is designed not only to answer the fundamental question concerning the reliability of detecting faying surface corrosion in lap splice structures, but also to provide quantification of the material loss that can reliably be achieved including levels of less than 10% corrosion.

Probability of Detection Estimation for HIT/MISS Data When Detection Cannot Be Attributed to Specific Flaws: An Exploratory Data Analysis

Several approaches are explored to the estimation of a probability of detection curve when detection results are per “site,” but the site contains multiple flaws. Binary regression is used with different candidate explanatory flaw characteristic variables including flaw sizes and number of flaws. A model treating each flaw as an independent opportunity is also introduced. The different approaches are compared and discussed in the context of estimating a POD curve using specific eddy current bolt‐hole inspection data.

Visual inspection reliability of transport aircraft

The Federal Aviation Administration Technical Center has sponsored a visual inspection reliability program at its airworthiness assurance nondestructive inspection validation center (AANC). We report on the results of the benchmark phase of that program in which 12 inspectors were observed in two days of inspections on a Boeing 737 aircraft. All of the inspectors were currently employed with major airlines and all had experience inspecting the Boeing 737 aircraft. Each inspector spent 2 days at the AANC facility where they inspected to the same ten job cards. Each inspector was videotaped and all nonroutine repair actions were recorded for each inspector. Background information on each of the inspectors, including vision test results, was also gathered. The inspection results were correlated with the background variables. Aviation experience and a test time reflecting visual acuity were significantly correlated with performance factors. An analysis of the video tapes was performed to separate decision errors from search errors. Probability of detection curves were fit to the results of inspecting for cracks from beneath rivet heads in a task using prepared samples with known cracks.