Statistical Design of New Two-Stage Plans for Reliability Demonstration Testing

PurposeTo design an optimal accelerated degradation test (ADT) plan for light emitting diodes (LEDs).Design/methodology/approachThis paper presents a method for the optimum planning of ADTs. The method is applied to the design of an optimal plan for LEDs. An analytical method is developed for obtaining the optimal allocations of test units to minimize the variance of the transformed life estimation at the use stress level; a simulation method is used to help select the optimal test plan and evaluate the test plans' properties. Optimal stress levels, and optimal allocations of test units to the stress levels are determined to minimize the mean squared error (MSE) of the estimated mean life of LEDs at the use stress level.FindingsDifferent test plans result in different accuracy. The optimal test plan provides the most efficient use of test resources.Research limitations/implicationsThis paper focuses on designing an optimal plan using two test stress levels. Future research may extend to multiple stress levels.Practical implicationsWith increasing emphasis on reliability in industry, products are made more robust, and few failures are observed in a reasonable test period. Therefore, assessing product reliability using ADTs becomes very useful. This paper fulfills the need to scientifically design plans for these tests to provide more accurate estimates of the designed‐in and manufactured reliability for the same amount of test resources.Originality/valueThe methodologies developed in this paper can be used for other ADTs. This enables reliability and test engineers to get the most efficient use of their test resources.

Accelerated reliability demonstration under competing failure modes

<?Pub Dtl=""?> In this paper, the degradation based reliability demonstration test (RDT) plan design problems for long life products under a small sample circumstance are studied. Fixed sample method, sequential probability ratio test (SPRT) method, and sequential Bayesian decision method are provided based on univariate degradation testing. The simulation examples show the superiority of degradation based RDT methods compared with the traditional failure based methods, and the sequential-type methods have more test power than their fixed sample counterparts. The test power can be further improved by combining the test data of a reliability indicator with the data of its marker, based on which the bivariate fixed sample method and the sequential Bayesian decision method are defined. The simulation study shows the benefit from the combination. The degradation based RDT plan optimization model, and the corresponding searching-based solution algorithm using some heuristic rules discovered in the paper, are also presented. The case study of Rubidium Atomic Frequency Standard with a RDT plan design demonstrates the effectiveness of our methods on overcoming the difficulties of small samples in reliability demonstration of long life products.

Balancing producer and consumer risks in optimal attribute testing: A unified Bayesian/Frequentist design

Reliability demonstration is an important task in the product development process. The commonly used reliability demonstration test methods include bogey test, life test, and degradation test, among which the degradation test is known to be most efficient. However, its application in industry is still limited primarily due to the lack of appropriate test plans. This paper presents heuristic reliability demonstration test plans for the products whose performance characteristics can be modeled with the Weibull distribution. In particular, the paper describes degradation models, test method, test termination rules, and the calculation of reliability and confidence interval from degradation data. The paper delineates test plan models, which are solved for optimal sample size and test time using the proposed heuristic algorithm. The algorithm results in the lowest test cost and the shortest test time for the products that are expected to pass or fail the test at a high degree of confidence. A case study is presented to illustrate the proposed method, and shows that the heuristic test plan reduced the test time, and cost by 27%, and 29%, respectively. The paper also numerically compares the three test methods, and concludes that the degradation test method is most efficient in terms of test time, cost, and sample size.

Reliability tests are mandatory to evaluate new products prior to their release. The proper determination of a reliability test plan is crucial because an erroneous test plan can be very costly and misleading. This paper describes a probability-based method of designing a reliability demonstration test plan using both field customer usage and historical bench life test data. Statistical distribution analysis, Monte Carlo simulation (MCS) technique, and zero-failure test method are integrated into the probability-based method to create test plans that can more accurately evaluate product reliabilities for the required product service life using a small number of test samples.

The impact of overdispersion on the design of optimal reliability demonstration test plans for beta-binomial models with Weibull, gamma, and lognormal lifetime distributions is analyzed. Assuming limited producer and consumer risks, fixed-duration test plans with minimal sample sizes and optimal-duration test plans with minimum costs based on failure count data are determined by solving the corresponding nonlinear programming problems when the fluctuation of the failure probability is described by a beta distribution. If the test time is fixed, the overdispersion effect on the optimal sample size and decision criterion is important in most situations. The influence is less relevant when the engineer also wants to find the minimum-cost test time. Optimal-duration plans usually outperform fixed-duration schemes in terms of costs and robustness against overdispersion. The use of lot inspection schemes with optimal reliability test times is strongly recommended when the presence of overdispersed failure count data is suspected. Applications of the developed methodology to the manufacturing of microelectronic chips and semiconductor lasers are provided for illustrative and comparative purposes.

: The principal reliability demonstration test methods are identified and their characteristics reviewed. The use of a graphic procedure for the design and analysis of fixed time tests is discussed and examples illustrating application to the design of Classical, Bayes and Hybrid plans are given. The graphic procedure is also applied to evaluate the effect on the Bayes posterior risks as a function of different prior distributional characteristics and to make comparisons between the different test methods. A technique for constructing the operating characteristic (O.C.) curve for any fixed time test is presented and the O.C. data for various test plans are tabulated.

A reliability demonstration test plan derivation method based on subsystem test data

: This report documents the recent design and/or analysis of sequential reliability test plans for three systems. Also included in this report is a new, simulation-based method for designing a hypergeometric test plan for acceptance of maintenance troubleshooting procedures based on sequential sampling. The design and analysis of sequential test plans is computationally challenging thus implementation in software is essential. For this reason, each chapter and appendix of this report was written in Mathematica, a leading commercial mathematics software. The test designs and analyses contained within this report constitute a basic set of templates for sequential test planning in the future.

Accelerated life testing (ALT) is a method for estimating the reliability of products at normal operating conditions from the failure data obtained at the severe conditions. We propose an ALT model based on the proportional odds (PO) assumption to analyze failure time data and investigate the optimum ALT plans for multiple-stress-type cases based on the PO assumption. We present the PO-based ALT model and propose the parameter estimation procedures by approximating the general baseline odds function with a polynomial function. Numerical examples with experimental data and Monte Carlo simulation data verify that the PO-based ALT model provides more accurate reliability estimate for the failure time data exhibiting PO properties. The accuracy of the reliability estimates is directly affected by the reliability inference model and how the ALT is conducted. The latter is addressed in the literature as the design of ALT test plans. Design of ALT test plans under one type of stress may mask the effect of other critical types of stresses that could lead to the component's failure. The extended life of today's products makes it difficult to obtain enough failures in a reasonable amount of testing time using single stress type. Therefore, it is more realistic to consider multiple stress types. This is the first research that investigates the design of optimum ALT test plans with multiple stress types. We formulate nonlinear optimization problems to determine the optimum ALT plans. The optimization problem was solved with a numerical optimization method. Reliability practitioners could choose different ALT plans in terms of the stress loading types. In this dissertation we conduct the first investigation of the equivalency of ALT plans, which enables reliability practitioners to choose the appropriate ALT plan according to resource restrictions. The results of this research show that one can indeed develop efficient test plans that can provide accurate reliability estimate at design conditions in much shorter test duration than the traditional test plans. Finally, we conduct experimental testing using miniature light bulbs. The test units are subjected to different stress types. The results validate the applicability of the PO-based ALT models.

Optimal lot sentencing based on defective counts and prior acceptability

Reliability demonstration test (RDT) is a critical and necessary step before the acceptance of an industrial system. Generally, a RDT focuses on designing a test plan through which one can judge whether the system reliability indices meet specific requirements. There are many established RDT plans, but few have incorporated the reliability growth aspects of the corresponding products. In this paper, we examine a comprehensive test plan that involves information concerning the reliability growth stage. An approach for RDT under the assumption of the power‐law model is proposed. It combines data related to the growth stage with those pertaining to the test stage of the product to reduce the cost of the test. Through simulation studies and numerical examples, we illustrate the characteristics of the test plan and significant reduction in test costs through our approach. Copyright © 2017 John Wiley &amp; Sons, Ltd.

A propellantless propulsion experiment design and testing plan are described. The concept was initially presented during the Space Technology and Applications International Forum of 2001 and the experiment was initially presented during the Joint Propulsion Conference of 2001. New information is provided on how the experiment relates to the Human Exploration of Development of Space, the results of peer reviews, a cost estimate performed by a major U.S. aerospace company, and an alternative magnet design to reduce the cost of the experiment and potentially improve the reliability of the system. Recent improvements in high power solid state switches and superconducting magnets may have made propellantless propulsion possible. Propulsion may occur during the non‐steady state ramp‐up of a very rapidly pulsed, high power magnet. Propulsion would not occur after the first 100 nanoseconds of each pulse, since the magnetic field will have reached steady state. The United States Department of Energy Office of High Energy Physics provided some of the funding for the developed a no maintenance superconducting magnet that can carry 2,000 amperes per square millimeter and a switch which can provide 100 nanosecond ramp‐ups at a rate of 0.4 megahertz, and at 9,000 volts and 30 amperes.

Accelerated life testing (ALT) using multiple stresses is commonly used in practice to resemble the operating stresses at normal operating conditions and obtain failure observations in a much shorter time. However, to date, there is little research into the theory of planning ALT for reliability estimation with multiple stresses. ALT with multiple stresses can result in a large number of stress-level combinations which presents a challenge for implementation. In this article, we propose an approach for the design of ALT plans with multiple stresses and formulate multistress test plans based on different objectives and practical constraints. We develop a simulated annealing algorithm to efficiently determine the testing plan parameters. We demonstrate the proposed method with examples based on an actual test conducted using three stress types. The obtained optimal test plans are compared with those based on fractional factorial design. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 468–478, 2013