PSAM 16 - Session Th11 Overview

PSAM 16 Conference Session Th11 Overview

Session Chair: Marcio Chagas Moura (marcio.cmoura@ufpe.br)

Paper 1 TO10

Lead Author: Tobias Leopold

Planning and evaluation of reliability demonstration testing with uncertainties
During the development of products, the proof of product reliability is often a challenging activity. Basic planning actions have to be executed in an early design stage of the product. First of all, two possible ways for the proof of reliability are available: testing without failures and testing with failures. Within the framework of this work, the focus will be on testing without failures, also called reliability demonstration testing (rdt). At the planning phase, the following questions have to be analysed: • What is probability of a successful rdt? • Which number of specimen and testing duration is necessary? • How to handle the unlike event of product failures while performing a rdt? • Which uncertainties have to be regarded and how to consider in the evaluation phase. Especially uncertainties and their consequences are part of this study. One example is the estimation of the shape parameter of a Weibull distributed failure characteristic in the planning phase. Possible sources for the estimation and the consequences of uncertainties of the estimation are analysed. After performing a rdt, the impact of uncertainties on the results are under consideration. The effects of uncertainties of the planning phase, e.g. uncertainties of the estimation of the Weibull shape parameter, to the demonstrated reliability and the confidence level are shown. Finally, case studies give an impression of the importance of the uncertainties. Some hints for the practical implementation close the whole topic.

Planning and evaluation of reliability demonstration testing with uncertainties

During the development of products, the proof of product reliability is often a challenging activity. Basic planning actions have to be executed in an early design stage of the product. First of all, two possible ways for the proof of reliability are available: testing without failures and testing with failures. Within the framework of this work, the focus will be on testing without failures, also called reliability demonstration testing (rdt). At the planning phase, the following questions have to be analysed: • What is probability of a successful rdt? • Which number of specimen and testing duration is necessary? • How to handle the unlike event of product failures while performing a rdt? • Which uncertainties have to be regarded and how to consider in the evaluation phase. Especially uncertainties and their consequences are part of this study. One example is the estimation of the shape parameter of a Weibull distributed failure characteristic in the planning phase. Possible sources for the estimation and the consequences of uncertainties of the estimation are analysed. After performing a rdt, the impact of uncertainties on the results are under consideration. The effects of uncertainties of the planning phase, e.g. uncertainties of the estimation of the Weibull shape parameter, to the demonstrated reliability and the confidence level are shown. Finally, case studies give an impression of the importance of the uncertainties. Some hints for the practical implementation close the whole topic.

Paper TO10 | Download the paper file. | Download the presentation PowerPoint file.

Name: Tobias Leopold (tobias.leopold@hs-esslingen.de)

Bio: Tobias Leopold is Professor at Esslingen University of applied sciences since 2019. His Research interests are reliability engineering and statistics and its usage in product development and quality Engineering with a special focus on the automotive industry. Tobias Leopold gained industrial experience at Knorr-Bremse commercial vehicle systems, STIHL and BMW in the areas of reliability engineering, product development, testing and quality. He holds a doctoral degree in reliability engineering and is Design for Six Sigma Black Belt.

Country: DEU
Company: University Esslingen
Job Title: Professor

Paper 2 AL3

Lead Author: Alexander Grundler Co-author(s): Martin Dazer, martin.dazer@ima.uni-stuttgart.de Bernd Bertsche, bernd.bertsche@ima.uni-stuttgart.de

Efficient Reliability Demonstration using the Probability of Test Success and Bayes Theorem
In order to demonstrate the reliability of a component, the reliability engineer is often faced with multiple challenges. On the one hand the budget for testing is limited and on the other hand, the demonstration needs to be done as quick and with the most precise statistical information possible. To address these challenges, the concept of Probability of Test Success was developed. It enables the objective assessment of tests with regard to their chance of success and thus the ability to directly compare the tests as well as the planning of expenditure and cost estimation. Secondly, a great variety of approaches have been developed which, by means of Bayes' theorem, use available prior knowledge to correct the information obtained from the tests and thus reduce expenditures. However, the combination of the Probability of Test Success and Bayes' Theorem to plan efficient reliability demonstration tests has not been addressed up to now. Therefore, the aim of this paper is to do so. It is analysed how reliability demonstration tests can be planned using the Probability of Test Success (statistical power) as well as the Bayes theorem. The combined use of the two approaches reveals a considerable advantage. Not only is it possible to select the optimal test according to the boundary conditions by means of the prediction of demonstration success. In addition, the integration of prior knowledge by means of Bayes' theorem enables an additional significant reduction of expenditure. The presented approach is capable of planning and assessing failure-based tests as well as any censored and failure-free tests. The procedure is illustrated by way of a case study. The results show that the demonstration of reliability and its necessary test planning benefit greatly from the proposed combination of the two approaches. The most promising test is planned while also being the test with maximum efficiency with regards to cost, time and sample size.

Efficient Reliability Demonstration using the Probability of Test Success and Bayes Theorem

In order to demonstrate the reliability of a component, the reliability engineer is often faced with multiple challenges. On the one hand the budget for testing is limited and on the other hand, the demonstration needs to be done as quick and with the most precise statistical information possible. To address these challenges, the concept of Probability of Test Success was developed. It enables the objective assessment of tests with regard to their chance of success and thus the ability to directly compare the tests as well as the planning of expenditure and cost estimation. Secondly, a great variety of approaches have been developed which, by means of Bayes' theorem, use available prior knowledge to correct the information obtained from the tests and thus reduce expenditures. However, the combination of the Probability of Test Success and Bayes' Theorem to plan efficient reliability demonstration tests has not been addressed up to now. Therefore, the aim of this paper is to do so. It is analysed how reliability demonstration tests can be planned using the Probability of Test Success (statistical power) as well as the Bayes theorem. The combined use of the two approaches reveals a considerable advantage. Not only is it possible to select the optimal test according to the boundary conditions by means of the prediction of demonstration success. In addition, the integration of prior knowledge by means of Bayes' theorem enables an additional significant reduction of expenditure. The presented approach is capable of planning and assessing failure-based tests as well as any censored and failure-free tests. The procedure is illustrated by way of a case study. The results show that the demonstration of reliability and its necessary test planning benefit greatly from the proposed combination of the two approaches. The most promising test is planned while also being the test with maximum efficiency with regards to cost, time and sample size.

Paper AL3 | Download the paper file. | Download the presentation PowerPoint file.

Name: Alexander Grundler (alexander.grundler@ima.uni-stuttgart.de)

Bio: Alexander Grundler received the B.Sc. degree in mechanical engineering from the University of Stuttgart, Stuttgart, Germany in 2014 and the M.Sc. degree in mechanical engineering from University of Stuttgart in 2017. He is currently the team lead of the reliability engineering department and Ph.D. candidate in the field of reliability engineering at the Institute of Machine Components, University of Stuttgart. His research is concerned with life testing and efficient reliability demonstration of systems using prior knowledge.

Country: DEU
Company: Institute of Machine Components, University of Stuttgart
Job Title: Team Lead Reliability Engineering

Paper 3 DA21

Lead Author: Martin Dazer Co-author(s): Alexander Grunder; alexander.grundler@ima.uni-stuttgart.de Achim Benz; achim.benz@ima.uni-stuttgart.de Philipp Mell; philipp.mell@ima.uni-stuttgart.de Marco Arndt; marco.arndt@ima.uni-stuttgart.de

Risk based reliability demonstration test planning for decision making under uncertainty
Reliability assurance by empirical data collected from lifetime tests is always subject to uncertainty and thus to a risk of making wrong decisions. The type-I statistical error is quantified and minimized over the generally known confidence interval to ensure that the reliability of the population in field operation is valid. The type-II statistical error quantifies the risk of a failed reliability test and thus the producer risk. A failed test generally means further iteration loops in the assurance process and should be avoided accordingly. However, in the context of reliability assurance, the type-II error is often neglected and consequently it is not known how high the probability of successful reliability demonstration is with the chosen test strategy. In this paper, a new method is presented that allows a calculation of the type-II error based on prior knowledge, which is called probability of test success (Pts). Pts enables the objective comparison of available test strategies for scenarios with a wide variety of boundary conditions such as accelerated testing, system and component testing or different reliability targets. In the end, the test strategy and the required number of specimens can be determined, which has the lowest residual risk under the available budget.

Risk based reliability demonstration test planning for decision making under uncertainty

Reliability assurance by empirical data collected from lifetime tests is always subject to uncertainty and thus to a risk of making wrong decisions. The type-I statistical error is quantified and minimized over the generally known confidence interval to ensure that the reliability of the population in field operation is valid. The type-II statistical error quantifies the risk of a failed reliability test and thus the producer risk. A failed test generally means further iteration loops in the assurance process and should be avoided accordingly. However, in the context of reliability assurance, the type-II error is often neglected and consequently it is not known how high the probability of successful reliability demonstration is with the chosen test strategy. In this paper, a new method is presented that allows a calculation of the type-II error based on prior knowledge, which is called probability of test success (Pts). Pts enables the objective comparison of available test strategies for scenarios with a wide variety of boundary conditions such as accelerated testing, system and component testing or different reliability targets. In the end, the test strategy and the required number of specimens can be determined, which has the lowest residual risk under the available budget.

Paper DA21 | Download the paper file. | Download the presentation pdf file. Download the presentation PowerPoint file.

Name: Martin Dazer (dazer@ima.uni-stuttgart.de)

Bio: Martin Dazer is a researcher with a special focus on Reliability Engineering. He is working as the Head of the Reliability & Driveline Department at the Institute of Machine Components from the University of Stuttgart. He is supervising about 15 Phd students and 10 national and international research projects. The research focus of the Department is on Life Test planning & Reliability Demonstration, Life data analysis, Availability of repairable systems, Prognostics & Health Management and Reliability in Driveline Applications. Martin Dazer holds a Doctoral degree in Reliability Engineering and is also a Reliability Black Belt.

Country: DEU
Company: University of Stuttgart
Job Title: Head of Department

Paper 4 AC15

Lead Author: Achim Benz Co-author(s): Alexander Grundler, alexander.grundler@ima.uni-stuttgart.de Martin Dazer, martin.dazer@ima.uni-stuttgart.de Bernd Bertsche, bernd.bertsche@ima.uni-stuttgart.de

Reliability Demonstration Test Planning for different Distributions of Field Load Spectra
In recent decades, product development cycles have become significantly shorter, with increasing reliability requirements and simultaneously decreasing budgets for tests. Even though a lot of knowledge about the failure behavior of the product can be generated by simulations, in the end a test is needed to demonstrate the reliability of the product. In order to select a test that optimally uses the resources of time, cost and number of samples for the desired reliability level with a sufficient confidence level, a simulation is performed. Previous work by Herzig et al. and Grundler et al. applied the concept of Probability of Success (PoS) for Success Run and End of Life tests introduced by Dazer et al. to consider accelerated Success Run and End of Life tests besides different failure mechanisms. This involved Monte Carlo simulations to derive the correlations of a successful test with the costs incurred, time, number of samples and the achievable demonstrated reliability. Previous work by Benz et al. introduces the concept of PoS for field load spectra deriving the demonstrated damage. This work led to questions dealing with the MLE bias correction that is needed when the individual load levels of the load profile are evaluated. Also the extrapolation error for accelerated tests to field level need to be investigated for different distributions of load spectra. For this purpose, a parameter study for individual parameters and test load levels of a test scenario will be evaluated in order to quantify multiple bias correction methods and the impact of distributions shapes of load spectra.

Reliability Demonstration Test Planning for different Distributions of Field Load Spectra

In recent decades, product development cycles have become significantly shorter, with increasing reliability requirements and simultaneously decreasing budgets for tests. Even though a lot of knowledge about the failure behavior of the product can be generated by simulations, in the end a test is needed to demonstrate the reliability of the product. In order to select a test that optimally uses the resources of time, cost and number of samples for the desired reliability level with a sufficient confidence level, a simulation is performed. Previous work by Herzig et al. and Grundler et al. applied the concept of Probability of Success (PoS) for Success Run and End of Life tests introduced by Dazer et al. to consider accelerated Success Run and End of Life tests besides different failure mechanisms. This involved Monte Carlo simulations to derive the correlations of a successful test with the costs incurred, time, number of samples and the achievable demonstrated reliability. Previous work by Benz et al. introduces the concept of PoS for field load spectra deriving the demonstrated damage. This work led to questions dealing with the MLE bias correction that is needed when the individual load levels of the load profile are evaluated. Also the extrapolation error for accelerated tests to field level need to be investigated for different distributions of load spectra. For this purpose, a parameter study for individual parameters and test load levels of a test scenario will be evaluated in order to quantify multiple bias correction methods and the impact of distributions shapes of load spectra.

Paper AC15 | Download the paper file. | Download the presentation pdf file.

Name: Achim Benz (achim.benz@ima.uni-stuttgart.de)

Bio: Achim Benz studied Mechanical Engineering at the University of Stuttgart in Germany and received his academic degree Master of Science in 2018. He is working as a research assistant in the field of reliability engineering at the Institute of Machine Components. He is pursuing his Ph.D. studies with a focus on life testing for power electronics such as inverters etc.

Country: DEU
Company: Institut of Machine Components
Job Title: Research Assistant