Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

Optimum Constant-stress Plan for Accelerated Life Test with Censoring Ⅱ

In this paper, we obtain the optimum plan by discussing a constant-stress accelerated life test (ALT) satisfying the condition (3.3) at k stresses under an exponential distribution.

Optimal Design of Multiple Stress Constant Accelerated Life Test Plan on Non-rectangle Test Region

For optimal design of constant stress accelerated life test（CSALT） with two-stress, if the stresses could not reach the highest levels simultaneously, the test region becomes non-rectangular. For optimal CSALT design on non-rectangle test region, the present method is only focused on non-rectangle test region with simple boundary, and the optimization algorithm is based on experience which can not ensure to obtain the optimal plan. In this paper, considering the linear-extreme value model and the optimization goal to minimize the variance of lifetime estimate under normal stress, the optimal design method of two-stress type-I censored CSALT plan on general non-rectangular test region is proposed. First, two properties of optimal test plans are proved and the relationship of all the optimal test plans is determined analytically. Then, on the basis of the two properties, the optimal problem is simplified and the optimal design method of two-stress CSALT plan on general non-rectangular test region is proposed. Finally, a numerical example is used to illustrate the feasibility and effectiveness of the method, The result shows that the proposed method could obtain the optimal test plan on non-rectangular test regions with arbitrary boundaries. This research provides the theory and method for two-stress optimal CSALT planning on non-rectangular test regions.

Analysis of Incomplete Data of Accelerated Life Testing with Competing Failure Modes

Data obtained from accelerated life testing （ALT） when there are two or more failure modes, which is commonly referred to as competing failure modes, are often incomplete. The incompleteness is mainly due to censoring, as well as masking which might be the case that the failure time is observed, but its corresponding failure mode is not identified. Because the identification of the failure mode may be expensive, or very difficult to investigate due to lack of appropriate diagnostics. A method is proposed for analyzing incomplete data of constant stress ALT with competing failure modes. It is assumed that failure modes have s-independent latent lifetimes and the log lifetime of each failure mode can be written as a linear function of stress. The parameters of the model are estimated by using the expectation maximum （EM） algorithm with incomplete data. Simulation studies are performed to check＇model validity and investigate the properties of estimates. For further validation, the method is also illustrated by an example, which shows the process of analyze incomplete data from ALT of some insulation system. Because of considering the incompleteness of data in modeling and making use of the EM algorithm in estimating, the method becomes more flexible in ALT analysis.

Bayesian sequential testing for exponential life system with reliability growth

A Bayesian sequential testing method is proposed to evaluate system reliability index with reliability growth during development.The method develops a reliability growth model of repairable systems for failure censored test,and figures out the approach to determine the prior distribution of the system failure rate by applying the reliability growth model to incorporate the multistage test data collected from system development.Furthermore,the procedure for the Bayesian sequential testing is derived for the failure rate of the exponential life system,which enables the decision to terminate or continue development test.Finally,a numerical example is given to illustrate the efficiency of the proposed model and procedure.

Estimation for constant-stress accelerated life test from generalized half-normal distribution

In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.

Constant-step stress accelerated life test of VFD under Weibull distribution case

Constant-step stress accelerated life test of Vacuum Fluorescent Display (VFD) was conducted with increased cathode temperature. Statistical analysis was done by applying Weibull distribution for describing the life, and Least Square Method (LSM)for estimating Weibull parameters. Self-designed special software was used to predict the VFD life. Numerical results showed that the average life of VFD is over 30000 h, that the VFD life follows Weibull distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. Accurate calculation of the key parameter enabled rapid estimation of VFD life.

Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.

Design of Accelerated Life Test Plans——Overview and Prospect

Accelerated life test(ALT) is currently the main method of assessing product reliability rapidly, and the design of efficient test plans is a critical step to ensure that ALTs can assess the product reliability accurately, quickly, and economically. With the promotion of the national strategy of civil-military integration, ALT will be widely used in the research and development(R&D) of various types of products, and the ALT plan design theory will face further challenges. To aid engineers in selecting appropriate theories and to stimulate researchers to develop the theories required in engineering, with focus on the demands for theory research that arise from the implementation of ALT, this paper reviews and summarizes the development of ALT plan design theory. The development of the theory and method for planning optimal ALT for location-scale distribution, which is the most applied and mature theory of designing the optimal ALT plan, are described in detail. Taking this as the center of radiation, some problems that ALT now faces, such as the verification of the statistical model, limitation of sample size, solutions of resource limits, optimization of the test arrangement, and management of product complexity, are discussed, and the general ideas and methods of solving these problems are analyzed. Suggestions for selecting appropriate ALT plan design theories are proposed, and the urgent solved theory problems and opinions of their solutions are proposed. Based on the principle of convenience for engineers to select appropriate methods according to the problems found in practice, this paper reviews the development of optimal ALT plan design theory by taking the engineering problems arising from the ALT implementation as the main thread, provides guidelines on selecting appropriate theories for engineers, and proposes opinions about the urgent solved theory problems for researchers.

Statistical Analysis for Constant-stress Partially Accelerated Life Test with Interval Censored Data

In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.

Life prediction and test period optimization research based on small sample reliability test of hydraulic pumps

Hydraulic pumps belong to reliable long-life hydraulic components. The reliability evaluation includes characters such as long test period,high cost,and high power loss and so on. Based on the principle of energy-saving and power recovery,a small sample hydraulic pump reliability test rig is built,and the service life of hydraulic pump is predicted,and then the sampling period of reliability test is optimized. On the basis of considering the performance degradation mechanism of hydraulic pump,the feature information of degradation distribution of hydraulic pump volumetric efficiency during the test is collected,so an optimal degradation path model of feature information is selected from the aspect of fitting accuracy,and pseudo life data are obtained. Then a small sample reliability test of period constrained optimization search strategy for hydraulic pump is constructed to solve the optimization problem of the test sampling period and tightening end threshold,and it is verified that the accuracy of the minimum sampling period by the non-parametric hypothes is tested. Simulation result shows it could possess instructional significance and referenced value for hydraulic pump reliability life evaluation and the test's research and design.

Sequential fault diagnosis strategy with imperfect tests considering life cycle cost

The problem of sequential fault diagnosis is to construct a diagnosis tree that can isolate the failure sources with minimal test cost. Pervious sequential fault diagnosis strategy generating algorithms only consider the execution cost at application stage, which may result in a solution with poor quality from the view of life cycle cost. Furthermore, due to the fact that uncertain information exists extensively in the real-world systems, the tests are always imperfect. In order to reduce the cost of fault diagnosis in the realistic systems, the sequential fault diagnosis problem with imperfect tests considering life cycle cost is presented and formulated in this work, which is an intractable NP-hard AND/OR decision tree construction problem. An algorithm based on AND/OR graph search is proposed to solve this problem. Heuristic search based on information theory is applied to generate the sub-tree in the algorithm. Some practical issues such as the method to improve the computational efficiency and the diagnosis strategy with multi-outcome tests are discussed. The algorithm is tested and compared with previous algorithms on the simulated systems with different scales and uncertainty. Application on a wheel momentum system of a spacecraft is studied in detail. Both the simulation and application results suggest that the cost of the diagnosis strategy can be reduced significantly by using the proposed algorithm, especially when the placement cost of the tests constitutes a large part of the total cost.

Inference and optimal design on step-stress partially accelerated life test for hybrid system with masked data

Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations(MLEs)of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover,two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality criteria.Finally, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.

Novel Accelerating Life Test Method and Its Application by Combining Constan Stress and Progressive Stress

Constant stress accelerated life tests(ALTs) can be applied to obtain a high estimation accuracy of reliability measure?ments, but these are time?consuming tests. Progressive stress ALTs can yield failures more quickly but cannot guaran tee the estimation accuracy of reliability measurements. In this paper, a progressive?constant combination stress ALT is proposed to combine the merits of both tests. The optimal plan, in which the design variables are the initial pro?gressive stress level, the progressive stress ramp rate, the sample allocation proportion of the progressive stress and the constant stress level, is determined using the principle of minimizing the asymptotic variance of the maximum likelihood estimator of the natural log reliable life for the connectors. A comparison between the optimal PCCSALT plan and the CSALT plan with the same sample size and estimation accuracy shows that the test time is reduced by 13.59% by applying the PCCSALT.

Life test research of a high specific impulse Hall thruster HEP-140MF

In this study,a high specific impulse Hall thruster,HEP-140 MF,having a high discharge voltage,was used to accelerate ions.We aimed to obtain a high specific impulse and an acceleration zone moving downstream toward the channel exit to reduce wall sputtering erosion of the walls of the discharge channel,hence ensuring an enhanced lifetime.To study the lifetime characteristics of the high specific impulse Hall thruster,a life test was performed on the HEP-140 MF thruster for the first time,and performance parameters,such as thrust,specific impulse,and efficiency,were measured.Changes in the performance parameters and evolutions in the surface profiles of the discharge channel wall were summarized.The reasons contributing to these changes during the life test were analyzed.Moreover,the accelerated life test method was validated on the HEP-140 MF.

ACCELERATED LIFE TEST STUDIES OF NEW COATED DISPENSER CATHODES

The life of impregnated Ba-W cathodes with a new construction have been evaluated using an accelerated life test at three different temperatures (1170℃,1130℃,1090℃) and constant current density (2A/cm^2).According to the relationship of life with operating temperatures,an accelerated equation has been set up.The cathode life at normal operating temperature is deducted based on the accelerated equation.The results show that life of the novel cathode exceeds 190,000 hour at a current density of 2A/cm^2.

Design and realization of lamp life test instrument

This paper introduces an instrument and method for lamp life test. The design of the instrument is divided into three steps： the oyerall design scheme, hardware circuit design and host machine programming. The instrument contains luminance and temperature sensors which can measure luminance of the lamp lighting and environment temperature in the instrument body. Then, the measure data can be transmitted to PC via the wireless transceiver modules for real-time monitoring. The luminance degradation curve based on the measure data is used to reckon the life of the lamp. In the end, the method for processing measurement data is given.

Bayesian Analysis in Partially Accelerated Life Tests for Weighted Lomax Distribution

Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress,such as pressure,temperature,vibration,voltage,or load to induce early failures.In this paper,a step stress partially accelerated life test(SSPALT)is regarded under the progressive type-II censored data with random removals.The removals from the test are considered to have the binomial distribution.The life times of the testing items are assumed to follow lengthbiased weighted Lomax distribution.The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax.The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix.The Bayesian estimators cannot be obtained in the explicit form,so the Markov chain Monte Carlo method is employed to address this problem,which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters.The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations.In addition,to compare the performance of the considered confidence intervals for different parameter values and sample sizes.The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter,for different sample sizes,observed failures,and censoring schemes,in most cases.Also,the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes,observed failures,and censoring schemes,in most cases.Further performance comparison is conducted by the experiments with real data.

A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull distribution.We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot acceptance.The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve values.In addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan.The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.

Acceptance Sampling Plans with Truncated Life Tests for the Length-Biased Weighted Lomax Distribution

In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned time.For the new suggested ASPs,the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained.In addition,the values of the corresponding operating characteristic function and the associated producer’s risks are calculated.Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans;one data set contains the first failure of 20 small electric carts,and the other data set contains the failure times of the air conditioning system of an airplane.Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes.It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study.The suggested acceptance sampling plans are recommended for practitioners in the field.