Number Of Test Units Research Articles

Optimal experimental designs for clustered read-out data of reliability tests via particle swarm optimization

Clustered data from a product’s reliability experiments may arise from many sources of heterogeneity in practice such as different test units suppliers, pieces of equipment, and operators. It is of interest for reliability practitioners to investigate how to plan such experiments with the aim of achieving the greatest test efficiency. In this paper, we develop optimal experimental designs of accelerated life tests under the interval censoring scheme when the obtained read-out observations are expected to be correlated and thereby clustered induced by two suppliers effects. The optimality condition is sought such that the design produces the minimum prediction variance at the product’s use condition. The correlated read-out data is modeled by a binomial generalized linear mixed model, and the Fisher information matrix is derived based on marginalized quantities in the covariance matrix. The particle swarm optimization is applied to search the design space and find the optimal solution with numerical stability under the complex nonlinear objective function. The optimal design shows the balanced test units allocations over two suppliers for each test condition. However, it is also found that degrees of such balance could be vary depending on the location of test condition, which allows flexible test units allocations for some test conditions when the number of test units from suppliers are imbalanced.

Optimal design of ramp-stress accelerated degradation tests based on the Wiener process

Ramp-stress accelerated degradation test (ADT) plans are developed under the assumption that the degradation characteristic follows a Wiener process. A ramp-stress (RS) test has an advantage over a constant-stress (CS) or step-stress (SS) test in that the difficulty of choosing appropriate stress levels in the latter can be alleviated. In addition, RS test plans could be more efficient than CS or SS test plans in terms of the test time or the number of test units. Optimal and compromise RSADT plans are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution under the normal use condition is minimized. The above planning methods are illustrated using a numerical example, and a sensitivity analysis procedure for assessing the robustness of the proposed test plan to the uncertainty in the pre-estimate of model parameters is provided.

Accelerated Degradation Tests Planning With Competing Failure Modes

Accelerated degradation tests (ADT) have been widely used to assess the reliability of products with long lifetime. For many products, environmental stress not only accelerates their degradation rate but also elevates the probability of traumatic shocks. When random traumatic shocks occur during an ADT, it is possible that the degradation measurements cannot be taken afterward, which brings challenges to reliability assessment. In this paper, we propose an ADT optimization approach for products suffering from both degradation failures and random shock failures. The degradation path is modeled by a Wiener process. Under various stress levels, the arrival process of random shocks is assumed to follow a nonhomogeneous Poisson process. Parameters of acceleration models for both failure modes need to be estimated from the ADT. Three common optimality criteria based on the Fisher information are considered and compared to optimize the ADT plan under a given number of test units and a predetermined test duration. Optimal two- and three-level optimal ADT plans are obtained by numerical methods. We use the general equivalence theorems to verify the global optimality of ADT plans. A numerical example is presented to illustrate the proposed methods. The result shows that the optimal ADT plans in the presence of random shocks differ significantly from the traditional ADT plans. Sensitivity analysis is carried out to study the robustness of optimal ADT plans with respect to the changes in planning input.

A Multiobjective Approach for Multistage Reliability Growth Planning by Considering the Timing of New Technologies Introduction

This paper proposes a new multiobjective multiple stage reliability growth planning (MO-MS-RGP) model. The model is based on multiobjective consideration of developing a new product, including the cost, time, and product reliability. The number of test units, test time, and the percentage of introduced new technologies are considered as decision variables in the model. Varying reliability growth rates are considered for each subsystem in each stage. Product new technologies or contents can be completely introduced in one stage or partially introduced to the product over multiple stages. New product development time limit and budget are considered as constraints in the MO-MS-RGP model. An integrated approach is developed to formulate and solve the proposed MO-MS-RGP problem. The approach starts with a multiobjective evolutionary algorithm, called multipleobjective particle swarm optimization to find a set of Pareto optimal solutions. Then, clustering methods are applied to cluster the solutions obtained by the evolutionary algorithm. Finally, the clustered solutions are ranked using a multiple criteria decision making method. A numerical example illustrates the application of the proposed MO-MS-RGP model for the reliability growth planning optimization of a next generation engine development.

Design of statistically and energy-efficient accelerated life testing experiments

The basic idea of Accelerated Life Testing (ALT) is to expose a limited number of test units of a product to harsher-than-normal operating conditions to expedite failures. Based on the failure time data collected in a short time period, an ALT model incorporating the underlying failure time distribution and life–stress relationship can be developed for predicting the reliability of the product under the normal operating condition. However, ALT experiments often consume significant amounts of energy due to the harsher-than-normal operating conditions created and controlled by test equipment. In this article, a new ALT design methodology is developed that has the objective of improving the statistical and energy efficiency of ALT experiments. The resulting statistically and energy-efficient ALT plan depends not only on the reliability of the product to be evaluated, but also on the physical characteristics of the test equipment and its controller. Particularly, the statistical efficiency of each candidate ALT plan needs to be evaluated and the corresponding controller capable of providing the required stress loadings must be designed and simulated to evaluate the total energy consumption of the ALT plan. In this article, mathematical formulations, computational algorithms, and simulation tools are provided to handle such complex experimental design problems. Numerical examples are provided to demonstrate the effectiveness of the proposed methodology in energy reduction in ALT.

Optimal progressive group censoring scheme under cost considerations for pareto distribution

In this article, optimal design under the restriction of pre-determined budget of experiment is developed for the Pareto distribution when the life test is progressively group censored. We use the maximum-likelihood method to obtain the point estimator of the Pareto parameter. We propose two approaches to decide the number of test units, the number of inspections, and the length of inspection interval under limited budget such that the asymptotic variance of estimator of Pareto parameter is minimum. A numerical example is given to illustrate the proposed method. Some sensitivity analysis is also studied.

Design of optimum multiple-stress accelerated life testing plans based on proportional odds model

Accelerated Life Testing (ALT) is used to obtain failure time data quickly under high stress levels in order to predict product life and performance under the design stress. Most of the previous work on designing ALT plans is focused on the application of a single stress. However, as components or products become more reliable due to technological advances, it becomes more difficult to obtain significant amount of failure data within a reasonable amount of time using single stress only. Multiple-stress ALTs have been employed as a means of overcoming such difficulties. In this paper, we design optimum multiple-stress ALT plans based on the Proportional Odds (PO) model. The optimum combinations of stress levels and the number of test units allocated to each combination are determined such that the variance of the reliability prediction of the product over a pre-specified period of time is minimised. The proposed ALT plan is illustrated by a numerical example.

Planning of progressive group-censoring life tests with cost considerations

This paper considers a life test under progressive type I group censoring with a Weibull failure time distribution. The maximum likelihood method is used to derive the estimators of the parameters of the failure time distribution. In practice, several variables, such as the number of test units, the number of inspections, and the length of inspection interval are related to the precision of estimation and the cost of experiment. An inappropriate setting of these decision variables not only wastes the resources of the experiment but also reduces the precision of estimation. One problem arising from designing a life test is the restricted budget of experiment. Therefore, under the constraint that the total cost of experiment does not exceed a pre-determined budget, this paper provides an algorithm to solve the optimal decision variables by considering three different criteria. An example is discussed to illustrate the proposed method. The sensitivity analysis is also studied.

A Bayes approach to simultaneous evaluation of similar assemblies

Simultaneous qualification testing of similar electronic-assembly designs that have the same reliability objectives lends itself to a Bayes approach. The author presents a method for obtaining the number of units to be put on test (test units) and the number of survivors required for this problem. The Bayes approach can reduce the total number of test units. The similarity of any two assemblies can be qualified using projected failure rates of components common to each design and components that differ between them. Under binomial sampling, survival probabilities follow the conjugate beta distribution. Two systems of linear equations are developed. Their solutions are vectors that describe, for each design: (1) the number of test units, and (2) the minimum number of survivors to demonstrate the reliability objective. >

The Optimum Number of Test Units for Military Standard 781-B

The sequential tests of MIL-STD 781-B are based upon the accumulated test hours of a number of test units. The number of test units, however, is not specified and may be varied to suit the testing ...

The precision of virus end-point determinations.

Using Newcastle disease virus (NDV), the precision of a virus assay system in which 10-fold dilution steps were employed was compared with that of a system using narrower dilution steps and an increased number of test units for each dilution level. A comparison of the accuracy obtained by using a complex single titration was made with that obtained by combining the results of three smaller titrations. It is suggested that the latter is a more valuable method as it will reduce any technical errors which would pass unnoticed in a single titration.

ESTIMATION OF THE NUMBER OF INFECTIOUS BACTERIAL OR VIRAL PARTICLES BY THE DILUTION METHOD.

Seligman, Stephen J. (University of California, Los Angeles), and M. Ray Mickey. Estimation of the number of infectious bacterial or viral particles by the dilution method. J. Bacteriol. 88:31-36. 1964.-For viral or bacterial systems in which discrete foci of infection are not obtainable, it is possible to obtain an estimate of the number of infectious particles by use of the quantal response if the assay system is such that one infectious particle can elicit the response. Unfortunately, the maximum likelihood estimate is difficult to calculate, but, by the use of a modification of Haldane's approximation, it is possible to construct a table which facilitates calculation of both the average number of infectious particles and its relative error. Additional advantages of the method are that the number of test units per dilution can be varied, the dilutions need not bear any fixed relation to each other, and the one-particle hypothesis can be readily tested.