Optimal Test Design Research Articles

Methods of Optimal Accelerated Life Test Plans: A Review

Accelerated life tests (ALT) have been used as a powerful tool to obtain time based information on the life span or performance characteristics over time of the items. Tests are performed under higher stressed levels instead of under normal use constraints. Obtained information as tests results are used to make predictions about life span over time at the real use. Accelerated testing under different stresses continuously helps in improving product reliability and in formulating warranty policies. This paper aims to provide insight into the methods of optimal acceleration life test designs. We first present a review of literature on optimum design of accelerated life tests in chronological order over the last six decades. Second, we present life time distributions with their mean lifetime or qth quantity and life stress relationship with their different factors level. We also present a flow chart outlining the process of accelerated life test planning. Further, we present the estimation methods commonly employed in the field of accelerated life testing, including least squares estimation, maximum likelihood estimation, graphical estimation, and Bayesian estimation. Finally, we provide an analytical discussion on accelerated life testing. This review aims to assist researchers, reliability engineers, and scientists in enhancing the design and planning of accelerated life tests.

Optimal Test Design for Estimation of Mean Ability Growth.

The design of an achievement test is crucial for many reasons. This article focuses on a population's ability growth between school grades. We define design as the allocating of test items concerning the difficulties. The objective is to present an optimal test design method for estimating the mean and percentile ability growth with good precision. We use the asymptotic expression of the variance in terms of the test information. With that criterion for optimization, we propose to use particle swarm optimization to find the optimal design. The results show that the allocation of the item difficulties depends on item discrimination and the magnitude of the ability growth. The optimization function depends on the examinees' abilities, hence, the value of the unknown mean ability growth. Therefore, we will also use an optimum in-average design and conclude that it is robust to uncertainty in the mean ability growth. A test is, in practice, assembled from items stored in an item pool with calibrated item parameters. Hence, we also perform a discrete optimization using simulated annealing and compare the results to the particle swarm optimization.

Optimal test plans for accelerated life tests based on progressive type-I censoring with engineering applications

In reliability engineering studies, the accelerated life tests with optimal test design that balances cost constraints is particularly important since the lifetimes of electro-mechanical, electronic, and mechanical goods are typically modelled with this characteristic. Comparative optimal test plans for accelerated life tests are developed in a variety of applications, including engineering, biological, medical, and other related fields. In this study, we compare, under cost restriction with a specified budget, optimum multiple constant stress and step stress accelerated life tests based on progressive-type-I censoring. The goal is to assess the advantage provided by step-stress testing over constant-stress testing. In order to conduct an accelerated life test effectively, stress durations need to be carefully specified during the design stage due to limited resources in engineering practice. The estimated accuracy of the parameters of interest and the expense of the experiment are directly impacted by the stress durations. Under a prespecified budget and cost constraints, this article examines the optimal stress durations based on D-, E-, T-, C-, R-, and P-optimal criteria. These criteria are also contrasted together. We illustrate the application of the optimal durations using numerical and simulation examples. A study is conducted to determine how sensitive the optimal duration is to model parameter misspecification.

Optimal test design for reliability demonstration under multi-stage acceptance uncertainties

A reliability demonstration test (RDT) plays a critical role in safeguarding product reliability and making sure it meets the target requirement. When planning an RDT, the test planning parameters are determined before executing the RDT. There is uncertainty associated with the test result and whether the product will be acceptable and released into the market with additional costs resulting from the warranty service or whether a reliability growth process is needed to further improve the product’s reliability. Potentially, such a process could be repeated multiple times depending on how quickly the reliability growth process can improve product reliability. Existing RDT designs primarily consider the cost of RDT itself or over a single demonstration stage before the next possible RDT, and hence fail to fully address the uncertainty of all possible future RDTs and various pathways a product may go through in a multi-stage demonstration process. By focusing on binomial RDT (BRDT) plans based on failure count data, this paper proposes an optimal Bayesian BRDT design framework by explicitly quantifying the multi-stage acceptance uncertainties resulting from current and subsequent BRDTs. It allows the BRDT planning decision to be determined more holistically by anticipating the costs of warranty service and reliability growth along different pathways over multiple stages. A recursive information propagation algorithm is proposed to incorporate the prior belief of product reliability and allow it to evolve and update over multiple stages of BRDT. A case study is presented to illustrate the proposed multi-stage Bayesian BRDT design framework and demonstrate its cost-efficiency compared to existing strategies. A comprehensive sensitivity analysis is also provided to demonstrate the impact of the relative size of different cost components, reliability growth rate, and prior setting on the performance of the proposed method.

Multi-Parameter and Multi-Objective Optimization of Occupant Restraint System in Frontal Collision

To solve the constraints of multi-objective optimization of the driver system and high nonlinear problems, according to the relevant dimensions of a car, we build a simulation model with Hybrid III 50th dummy driver constraint system. The comparison of the driver mechanics index of the experimental data with the simulation data in the frontal crash shows that the accuracy of simulation model meets the requirements. The optimal Latin test design is adopted, and the global sensitivity analysis of the design parameters is carried out based on the Kriging model. The four most sensitive parameters are selected, and the parameters are solved by a multi-island genetic algorithm. And then the nonlinear programming quadratic line (NLPQL) algorithm is used to search for accurate optimization. The optimal parameters of the occupant restraint system are determined: the limiting force value of force limiter 2 985.603 N, belt extension 12.684%, airbag point explosion time 27.585 ms, and airbag vent diameter 27.338 mm, with the weighted injury criterion (WIC) decreased by 12.97%, the head injury decreased by 22.60%, and the chest compression decreased by 7.29%. The results show that the system integration of passive safety devices such as seat belts and airbags can effectively protect the driver.

Neural ordinary differential equation for sequential optimal design of fatigue test under accelerated life test analysis

The literature on fatigue analysis can be classified into parametric or analytic approaches that try to model the fatigue data with a specific distribution, such as the optimal sequential Accelerated Life Test (ALT), considering the fatigue life cycle and stress amplitude. To the best of our knowledge, no work incorporates the accelerated lifecycle distribution of fatigue data into the parametric approach, nor does it incorporate the complex relationships in the elastic–plastic behavior of the material in the ALT models using the sequential optimal test design. In this work, we define an optimization model that takes both parametric and analytic solutions into account and minimizes the negative log-likelihood of the ALT model when the fatigue lifecycle follows a lognormal distribution for several constraints extracted from physical attributes of elastic–plastic models and assumptions of the ALT approach, where model-based optimization is sequentially updated. We utilized a model-based deep neural network solution based on the differential equation of the analytical model to solve the optimization problem. Our simulation results based on empirical data prove the practical implementation of our approach and validate the result for obtaining the optimal test plan and estimated parameters of the ALT and elastic–plastic model.

신뢰성 성장관리 시험의 시험 시료 수 결정 방안

[영문 초록 작성] The number of test samples was calculated by setting the reliability growth management test period considering the weapon system development period. The optimal reliability growth management test design condition was 80% reliability, 60% confidence level, and 6 months of test period. At this time, it was analyzed that 4 test samples were required if 0 failure occurred, and 9 test samples were required if 1 failure occurred. Using the method of determining the number of samples presented in this paper, it can be used as a basis for acquiring a budget for the number of samples for reliability growth management when switching from the exploratory development stage to the system development stage.

Optimal Test Design for Knowledge-based Screening

Optimal Test Design for Knowledge-based Screening

Understanding performance in test taking: The role of question difficulty order

Standardized assessments are widely used to determine access to educational resources with important consequences for later economic outcomes in life and to evaluate and compare educational systems. However, many design features of the tests themselves may lead to psychological reactions influencing performance. In particular, the level of difficulty of the earlier questions in a test may affect performance in later questions. How should we order test questions according to their level of difficulty such that test performance offers an accurate assessment of the test taker's aptitudes and knowledge? We conduct a field experiment with about 19,000 participants in collaboration with an online teaching platform where we randomly assign participants to different orders of difficulty and we find that ordering the questions from easiest to most difficult yields the lowest probability to abandon the test, as well as the highest number of correct answers. We obtain similar results when exploiting the random variation of difficulty across test booklets in the Programme for International Student Assessment (PISA) for the years 2009, 2012, and 2015, which provides additional external validity to the experiment. We conclude that question difficulty order in tests has important policy implications for optimal test design and performance. It additionally may have important implications for ranking candidates, as well as for the evaluation and comparison of educational institutions and systems.

Application of Intersection Method for Multi-Objective Optimization in Optimal Test with Desirable Response Variable

This paper aims to conduct applications of intersection method for multi-objective optimization in optimal test design with desirable response variable. The partial favourable probability of the desirable response variable of the test is evaluated according to the type of “one side desirability problem” or “one range desirability problem” and the requirements of desirable response first; then the evaluation of total favourable probability Pt of the multi-objective optimization test design is conducted according to the common procedure of the "intersection" method for multi-object optimization of performance indicators of the test. Finally, regression analysis is performed for the total favourable probability and response variables to get maximum total favourable probability and optimal configuration of the optimal test with desirable response variable. As application examples of the intersection method for the test designs of maximizing yield with constraints of viscosity and molecular weight and the maximizing conversion rate with constraints of desirable thermal activity are given in detail, satisfied results are obtained.

Design Methods for the Lethality of Fragmentation Warhead based on a Multi-Objective Optimization Algorithm

Abstract Fragmentation warhead is the main weapon used to damage personnel and light armored objectives, with the lethal parameters primarily consisting of the number and velocity of fragments. Increasing the lethality of fragmentation warhead is currently the most important development direction for fragmentation warhead. The formation process of natural fragment is complicated and there are several factors that affect the properties of fragment, so there are still many techniques of developing the lethality of fragmentation warhead. In this paper, our object is to focus on the optimization design for the lethality of fragmentation warhead, based on the optimal Latin hypercube test design method and the radial basis function neural network surrogate modelling, taking the number of effective fragments per unit mass and the average kinetic energy of the effective fragments as the optimization objectives, and the explosive charge, the fragment material, the overall structure and initiation method are considered, respectively. The Pareto optimal solution sets under different design variables are obtained, and the optimal matching of multiple design parameters is realized, establishing the integration design method for “explosive - material-structure” of the fragmentation warhead. The research results can provide technical support for the structural optimization design of the fragmentation warhead.

On the Information Obtainable from Comparative Judgments

Personality tests employing comparative judgments have been proposed as an alternative to Likert-type rating scales. One of the main advantages of a comparative format is that it can reduce faking of responses in high-stakes situations. However, previous research has shown that it is highly difficult to obtain trait score estimates that are both faking resistant and sufficiently accurate for individual-level diagnostic decisions. With the goal of contributing to a solution, I study the information obtainable from comparative judgments analyzed by means of Thurstonian IRT models. First, I extend the mathematical theory of ordinal comparative judgments and corresponding models. Second, I provide optimal test designs for Thurstonian IRT models that maximize the accuracy of people’s trait score estimates from both frequentist and Bayesian statistical perspectives. Third, I derive analytic upper bounds for the accuracy of these trait estimates achievable through ordinal Thurstonian IRT models. Fourth, I perform numerical experiments that complement results obtained in earlier simulation studies. The combined analytical and numerical results suggest that it is indeed possible to design personality tests using comparative judgments that yield trait scores estimates sufficiently accurate for individual-level diagnostic decisions, while reducing faking in high-stakes situations. Recommendations for the practical application of comparative judgments for the measurement of personality, specifically in high-stakes situations, are given.

Data-Driven Optimal Test Selection Design for Fault Detection and Isolation Based on CCVKL Method and PSO

Accurate fault detection and isolation (FDI) relies on the information collection. This can be done by the optimal test selection which can also reduce the life cost of engineering systems. In recent years, some researchers have made lots of achievement on solving the test selection design (TSD) problem. However, few of them concerned a method to deal with the ambiguity problem caused by the multiple fault modes. In this article, a data-driven-based method for test selection is proposed to build an accurate TSD model. Then, we propose a copula function on cross validation-based Kullback–Leibler divergence (CCVKL) method to construct an accurate constraint model. An improved discrete binary particle swarm optimization (IBPSO) algorithm is used to obtain the optimal test design solution. The proposed method also in comparison to three other existing methods are performed in an electrical circuit.

TestDesign: an optimal test design approach to constructing fixed and adaptive tests in R

TestDesign: an optimal test design approach to constructing fixed and adaptive tests in R

Merging One's Way to the Top: AB Inbev versus Heineken

AbstractLeuven's Den Hoorn brewery, now AB Inbev SA, has become the world's largest brewing group by far, but critics say the company overpaid for its acquisitions. In this article, we study typical stock market reactions to the many takeover announcements by AB Inbev and the industry's runner-up, Heineken. Unlike Heineken's, the market leader's takeover announcements were met by, on average, a –2% price reaction in the stock market in the announcement month, but most of that is already undone in the next month. For Heineken, the same pattern shows up, only faster: the V-shaped reaction takes a few weeks rather than a few months. Such V-reactions may actually reflect a temporary rise in uncertainty rather than overpaying. The finding that reactions are reversed and heterogeneous across firms, raises issues of interpretation and optimal test design of event studies. (JEL Classifications: G12, G14, G17)

Two parallel short forms to measure disease- and treatment-associated knowledge in rheumatoid arthritis: application of item response theory.

ObjectiveThe aim was to develop two disease- and treatment-related knowledge about RA (DataK-RA) short forms using item response theory-based linear optimal test design.MethodsWe used the open source Excel add-in solver to program a linear optimization algorithm to develop two short forms from the DataK-RA item bank. The algorithm was instructed to optimize precision (i.e. reliability) of the scores for both short forms, subject to a number of constraints that served to ensure that each short form would include unique items and that the short forms would have similar psychometric properties. Agreement among item response theory scores obtained from the different short forms was assessed using the Bland–Altman method and Student’s paired t-test. Construct validity and relative efficiency of the short forms was evaluated by relating the score to age, sex and educational attainment.ResultsTwo short forms were derived from the DataK-RA item bank that satisfied all content constraints. Both short forms included 15 unique items and yielded reliable scores (r > 0.70), with low ceiling and floor effects. The short forms yielded statistically indistinguishable mean scores according to Student’s paired t-test and Bland–Altman analysis. Scores on short forms 1 and 2 were associated with age, sex and educational attainment to a similar extent.ConclusionIn this study, we developed two DataK-RA short forms with unique items, yet similar psychometric properties, that can be used to assess patients pre‐ and post‐test interventions aimed at improving disease-related knowledge in RA patients.

Research on Application of Electric Vehicle Collision Based on Reliability Optimization Design Method

When mentioning multidisciplinary design optimization methods, the deterministic optimum design is frequently applied to set the constraint boundary. Furthermore, only a small amount of space tolerances (or uncertainty) is available in the process of design, manufacture and operation. Therefore, deterministic optimum design lacking uncertainty cannot meet the needs of reliability-based design optimization. In this paper, reliability optimization design method, finite element (FE) analysis, optimal Latin hypercube test design and response surface approximation model are combined to optimize the side structure of electric vehicles and improve its crashworthiness. Firstly, a side impact FE model of the electric vehicle is established and verified in this paper. Then, the dimensions and the material yield strength of the force-bearing structure in the vehicle are selected as design variables, and the impact speed in the actual collision is selected as a random variable to optimize the car crashworthiness in the side impact using the 95% reliability optimization method. The results show that the 95% reliability optimization design increases the total energy absorption of the side components by 9.45%, the intrusion of the B-pillar and the vehicle door inner panel decreased by 10.42% and 14.75%, respectively. The intrusion speed of the B-pillar and the inner panel of the vehicle door decreases by 10.35% and 17.78%, respectively. By comparing the results of traditional deterministic optimization and reliability optimization methods, the latter can better satisfy the crash safety objectives, and improve the reliability of vehicle body design.

Active fault diagnosis for uncertain systems using optimal test designs and detection through classification

Fault detection and isolation (FDI) is becoming increasingly difficult due to the complexity and uncertainty of modern systems. For industrial systems with explicit models available, model-based active FDI tests can improve the capability for fault diagnosis. These tests should be determined and evaluated prior to implementation to minimize on-site computational costs. In this paper, a methodology is presented for the design optimization and assessment of tests for active fault diagnosis. The objective is to maximize the information from system outputs with respect to faults while minimizing the correlation between faults and uncertainty. After a test is designed, it is deployed with a k-nearest neighbor algorithm combined with principal component analysis.Two case studies are used to verify the proposed methodology, a three-tank system and a diesel engine.

Optimal designs for the generalized partial credit model.

Analysing ordinal data is becoming increasingly important in psychology, especially in the context of item response theory. The generalized partial credit model (GPCM) is probably the most widely used ordinal model and has found application in many large-scale educational assessment studies such as PISA. In the present paper, optimal test designs are investigated for estimating persons' abilities with the GPCM for calibrated tests when item parameters are known from previous studies. We find that local optimality may be achieved by assigning non-zero probability only to the first and last categories independently of a person's ability. That is, when using such a design, the GPCM reduces to the dichotomous two-parameter logistic (2PL) model. Since locally optimal designs require the true ability to be known, we consider alternative Bayesian design criteria using weight distributions over the ability parameter space. For symmetric weight distributions, we derive necessary conditions for the optimal one-point design of two response categories to be Bayes optimal. Furthermore, we discuss examples of common symmetric weight distributions and investigate under what circumstances the necessary conditions are also sufficient. Since the 2PL model is a special case of the GPCM, all of these results hold for the 2PL model as well.

Multi-line Adaptive Perimetry (MAP): A New Procedure for Quantifying Visual Field Integrity for Rapid Assessment of Macular Diseases.

PurposeIn order to monitor visual defects associated with macular degeneration (MD), we present a new psychophysical assessment called multiline adaptive perimetry (MAP) that measures visual field integrity by simultaneously estimating regions associated with perceptual distortions (metamorphopsia) and visual sensitivity loss (scotoma).MethodsWe first ran simulations of MAP with a computerized model of a human observer to determine optimal test design characteristics. In experiment 1, predictions of the model were assessed by simulating metamorphopsia with an eye-tracking device with 20 healthy vision participants. In experiment 2, eight patients (16 eyes) with macular disease completed two MAP assessments separated by about 12 weeks, while a subset (10 eyes) also completed repeated Macular Integrity Assessment (MAIA) microperimetry and Amsler grid exams.ResultsResults revealed strong repeatability of MAP and high accuracy, sensitivity, and specificity (0.89, 0.81, and 0.90, respectively) in classifying patient eyes with severe visual impairment. We also found a significant relationship in terms of the spatial patterns of performance across visual field loci derived from MAP and MAIA microperimetry. However, there was a lack of correspondence between MAP and subjective Amsler grid reports in isolating perceptually distorted regions.ConclusionsThese results highlight the validity and efficacy of MAP in producing quantitative maps of visual field disturbances, including simultaneous mapping of metamorphopsia and sensitivity impairment.Translational RelevanceFuture work will be needed to assess applicability of this examination for potential early detection of MD symptoms and/or portable assessment on a home device or computer.