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1.
In many industrial applications, it is not always feasible to continuously monitor the life testing experiments to collect lifetime data. Moreover, intermediate removals of the test units from the life testing experiment are sometimes essential. Progressive Type‐I interval censoring schemes are useful in these scenarios. Optimal planning of such progressive Type‐I interval censoring schemes is an important issue to the experimenter, as the optimal plans can achieve the desired objectives using much lesser resources. This article provides Bayesian D‐optimal progressive Type‐I interval censoring schemes, assuming that the lifetime follows a log‐normal distribution. An algorithm is provided to find the optimal censoring schemes and the number of inspections. The algorithm is then used to obtain the optimal Bayesian progressive Type‐I interval censoring schemes in 2 different contexts. The resulting optimal Bayesian censoring schemes are compared with the corresponding locally optimal censoring schemes. A detailed sensitivity analysis is performed to investigate the effect of prior information. The sampling variation associated with the optimal censoring schemes is visualized through a simulation study.  相似文献   

2.
For a period of mission time, only zero‐failure data can be obtained for high‐quality long‐life products. In the case of zero‐failure data reliability assessment, the point estimates and confidence interval estimates of distribution parameters cannot be obtained simultaneously by the current reliability assessment models, and the credibility of the assessment results may be reduced if they are obtained at the same time. A new model is proposed for consistency problem in this paper. In the proposed model, the point estimates of reliability can be obtained by the lifetime probability distribution derived from matching distribution curve method, while the confidence interval estimates of reliability can be obtained by using new samples generated from the lifetime probability distribution according to parameter bootstrap method. By analyzing the zero‐failure data of the torque motors after real operation, the results show that the new model not only meets the requirements of reliability assessment but also improves the accuracy of reliability interval estimation.  相似文献   

3.
Thanks to continuously advancing technology and manufacturing processes, the products and devices are becoming highly reliable. However, performing the life tests of these products at normal operating conditions becomes extremely difficult, if not impossible, due to their long life spans. This can result in missed opportunities to introduce the products to the market in a timely manner and eventually loss of the market share. This problem is solved by accelerated life tests where the test units are subjected to higher stress levels than the normal usage level so that information on the lifetime parameters can be obtained more quickly. The lifetime at the design condition is then estimated through extrapolation using a regression model. In this work, the design optimization of a simple step‐stress accelerated life test under progressive type I censoring is studied with nonuniform step durations for assessing the reliability characteristics of a solar lighting device. Allowing the intermediate censoring to take place at the stress change time point, the nature of the optimal stress duration is demonstrated under various design criteria including D‐optimality, C‐optimality, A‐optimality, and E‐optimality. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable, and the effect of the intermediate censoring proportion is assessed on the design efficiency.  相似文献   

4.
In this paper, a progressive‐stress accelerated life test under progressive type‐II censoring is considered. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. The maximum likelihood and Bayes estimates of the model parameters are obtained. The approximate and credible confidence intervals of the estimators are derived. Furthermore, a real lifetime data set is analyzed to illustrate the proposed procedures. Finally, the simulation studies are used to compare between 2 different designs of the progressive‐stress test (simple and multiple ramp‐stress tests).  相似文献   

5.
In this paper, control charts for monitoring the exponential type‐II censoring samples are investigated. Such data are very common in many practical inspection scenarios in reliability context when items are replaced in groups after a period of time. The average time to signal, which involves both the number and the time of samples inspected until a signal occurs, is a good criterion to evaluate the performance of control charts. We propose an average time to signal‐unbiased control chart with known parameter and compare the proposed method with the traditional ones. The results indicate the proposed control chart is more sensitive to system deterioration. Then the effects of parameter estimation on the proposed control charts are evaluated. Because the control limits with estimated parameters result in more false alarms, an adjusted control chart with estimated parameters is proposed and the self‐starting control chart based on a sequential sampling scheme is adopted to solve the phase I problem. Finally, two examples are given to illustrate the implementation of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

6.
In this paper, we propose a new variable control chart under type II or failure‐censored reliability tests by assuming that the lifetime of a part follows the Weibull distribution with fixed and stable shape parameter. The purpose is to monitor the mean and the variance of a Weibull process. In fact, the mean and the variance are related to the scale parameter. The necessary measures are given to calculate the average run length (ARL) for in‐control and shifted processes. The tables of ARLs are presented for various shift constants and specified parameters. A simulation study is given to show the performance of the proposed control chart. The efficiency of the proposed control chart is compared with a control chart based on the conditional expected value under type II censoring. An example is also given for the illustration purpose.  相似文献   

7.
This article considers the design of two‐stage reliability test plans. In the first stage, a bogey test was performed, which will allow the user to demonstrate reliability at a high confidence level. If the lots pass the bogey test, the reliability sampling test is applied to the lots in the second stage. The purpose of the proposed sampling plan was to test the mean time to failure of the product as well as the minimum reliability at bogey. Under the assumption that the lifetime distribution follows Weibull distribution and the shape parameter is known, the two‐stage reliability sampling plans with bogey tests are developed and the tables for users are constructed. An illustrative example is given, and the effects of errors in estimates of a Weibull shape parameter are investigated. A comparison of the proposed two‐stage test with corresponding bogey and one‐stage tests was also performed. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

8.
Based on failures of a parallel‐series system, a new distribution called geometric‐Poisson‐Rayleigh distribution is proposed. Some properties of the distribution are discussed. A real data set is used to compare the new distribution with other 6 distributions. The progressive‐stress accelerated life tests are considered when the lifetime of an item under use condition is assumed to follow the geometric‐Poisson‐Rayleigh distribution. It is assumed that the scale parameter of the geometric‐Poisson‐Rayleigh distribution satisfies the inverse power law such that the stress is a nonlinear increasing function of time and the cumulative exposure model for the effect of changing stress holds. Based on type‐I progressive hybrid censoring with binomial removals, the maximum likelihood and Bayes (using linear‐exponential and general entropy loss functions) estimation methods are considered to estimate the involved parameters. Some point predictors such as the maximum likelihood, conditional median, best unbiased, and Bayes point predictors for future order statistics are obtained. The Bayes estimates are obtained using Markov chain Monte Carlo algorithm. Finally, a simulation study is performed, and numerical computations are performed to compare the performance of the implemented methods of estimation and prediction.  相似文献   

9.
Today, in reliability analysis, the most used distribution to describe the behavior of electronic products under voltage profiles is the Weibull distribution. Nevertheless, the Weibull distribution does not provide a good fit to lifetime datasets that exhibit bathtub‐shaped or upside‐down bathtub–shaped (unimodal) failure rates, which are often encountered in the reliability analysis of electronic devices. In this paper, a reliability model based on the beta‐Weibull distribution and the inverse power law is proposed. This new model provides a better approach to model the performance and fit of the lifetimes of electronic devices. To estimate the parameters of the proposed model, a Bayesian analysis is used. A case study based on the lifetime of a surface mounted electrolytic capacitor is presented, the results showed that the estimation of the proposed model differs from the inverse power law–Weibull and that it affects directly the mean time to failure, the failure rate, the behavior, and the performance of the capacitor under analysis.  相似文献   

10.
When lifetimes follow Weibull distribution with known shape parameter, a simple power transformation could be used to transform the data to the case of exponential distribution, which is much easier to analyze. Usually, the shape parameter cannot be known exactly and it is important to investigate the effect of mis‐specification of this parameter. In a recent article, it was suggested that the Weibull‐to‐exponential transformation approach should not be used as the confidence interval for the scale parameter has very poor statistical property. However, it would be of interest to study the use of Weibull‐to‐exponential transformation when the mean time to failure or reliability is to be estimated, which is a more common question. In this paper, the effect of mis‐specification of Weibull shape parameters on these quantities is investigated. For reliability‐related quantities such as mean time to failure, percentile lifetime and mission reliability, the Weibull‐to‐exponential transformation approach is generally acceptable. For the cases when the data are highly censored or when small tail probability is concerned, further studies are needed, but these are known to be difficult statistical problems for which there are no standard solutions. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

11.
Reliability experiments determine which factors drive product reliability. Often, the reliability or lifetime data collected in these experiments tend to follow distinctly non‐normal distributions and typically include censored observations. The experimental design should accommodate the skewed nature of the response and allow for censored observations, which occur when products do not fail within the allotted test time. To account for these design and analysis considerations, Monte‐Carlo simulations are frequently used to evaluate experimental design properties. Simulation provides accurate power calculations as a function of sample size, allowing researchers to determine adequate sample sizes at each level of the treatment. However, simulation may be inefficient for comparing multiple experiments of various sizes. We present a closed‐form approach for calculating power, based on the noncentral chi‐squared approximation to the distribution of the likelihood ratio statistic for large samples. The solution can be used to rapidly compare multiple designs and accommodate trade‐space analyses between power, effect size, model formulation, sample size, censoring rates, and design type. To demonstrate the efficiency of our approach, we provide a comparison to estimates from simulation.  相似文献   

12.
Real‐time computer systems deployed in life‐critical control applications must be designed to meet stringent reliability specifications. The minimum acceptable degree of reliability for systems of this type is ‘7 nines’, which is not generally achieved. This paper aims at contributing to the achievement of that degree of reliability. To this end, this paper proposes a classification scheme of the fault‐tolerant procedures for redundant computer systems (RCSs). The proposed classification scheme is developed on the basis of the number of counteracted fault types. Table I is created to relate the characteristics of the RCSs to the characteristics of the fault‐tolerant procedures. A selection algorithm is proposed, which allows designers to select the optimal type of fault‐tolerant procedures according to the system characteristics and capabilities. The fault‐tolerant procedure, which is selected by this algorithm, provides the required degree of reliability for a given RCS. According to the proposed graphical model only a part of the fault‐tolerant procedure is executed depending on the absence or presence (type and sort) of faults. The proposed methods allow designers to counteract Byzantine and non‐Byzantine fault types during degradation of RCSs from N to 3, and only the non‐Byzantine fault type during degradation from 3 to 1 with optimal checkpoint time period. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

13.
Burn‐in is a quality control process used to minimize the warranty cost of a product by screening out defective products through prior operation for a period of time before sale. Two decision criteria used to determine the optimal burn‐in time are the maximization of the reliability of the delivered product and the minimization of the total cost, which are composed of the cost of burn‐in process and the cost of warranty claims. Because of uncertainty regarding the underlying lifetime distribution of the product, both the product reliability and the total cost are random variables. In this paper, the uncertainty in reliability and cost is quantified by use of Bayesian analysis. The joint distribution of reliability and cost is inferred from the uncertainty distribution of the parameters of the product lifetime distribution. To incorporate the uncertainty in reliability and cost as well as the tradeoff between them into the selection of optimal burn‐in time, the joint utility function of reliability and cost is constructed using the joint distribution of reliability and cost. The optimal burn‐in time is selected as the time that maximizes the joint utility function. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

14.
A common type of reliability data is the right censored time‐to‐failure data. In this article, we developed a control chart to monitor the time‐to‐failure data in the presence of right censoring using weighted rank tests. On the basis of the asymptotic properties of the rank statistics, we derived the generic formulae for the operating characteristic functions of the control chart to show the relationship between type I error probability, type II error probability, sample size, and hazard rate change. We presented case studies to illustrate the design procedure and the effectiveness of the proposed control chart system. We also investigated and compared the performance of the proposed monitoring procedure with some available monitoring techniques for nonconformities. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

15.
Traditional Duncan‐type models for cost‐efficient process monitoring often inflate type I error probability. Nevertheless, controlling the probability of type I error or false alarms is one of the key issues in sequential monitoring of specific process characteristics. To this end, researchers often recommend economic‐statistical designs. Such designs assign an upper bound on type I error probability to avoid excessive false alarms while achieving cost optimality. In the context of process monitoring, there is a plethora of research on parametric approaches of controlling type I error probability along with the cost optimization. In the nonparametric setup, most of the existing works on process monitoring address one of the two issues but not both simultaneously. In this article, we present two distribution‐free cost‐efficient Shewhart‐type schemes for sequentially monitoring process location with restricted false alarm probability, based, respectively, on the sign and Wilcoxon rank‐sum statistics. We consider the one‐sided shift in location parameter in an unknown continuous univariate process. Nevertheless, one can easily extend our proposed schemes to monitor the two‐sided process shifts. We evaluate and compare the actual performance of the two monitoring schemes employing extensive computer simulation based on Monte Carlo. We investigate the effects of the size of the reference sample and the false alarm constraint. Finally, we provide two illustrative examples, each based on a realistic situation in the industry.  相似文献   

16.
We present an efficient numerical method for solving indirect boundary integral equations that describe the dynamics of a flat two‐dimensional (2‐D) crack in all modes of fracture. The method is based on a piecewise‐constant interpolation, both in space and time, of the slip‐rate function, by which the original equation is reduced to a discrete convolution, in space and time, of the slip‐rate and a set of analytically obtained coefficients. If the time‐step interval is set sufficiently small with respect to the spatial grid size, the discrete equations decouple and can be solved explicitly. This semi‐analytic scheme can be extended to the calculation of the wave field off the crack plane. A necessary condition for the numerical stability of this scheme is investigated by way of an exhaustive set of trial runs for a kinematic problem. For the case investigated, our scheme is very stable for a fairly wide range of control parameters in modes III and I, whereas, in mode II, it is unstable except for some limited ranges of the parameters. The use of Peirce and Siebrits' ε‐scheme in time collocation is found helpful in stabilizing the numerical calculation. Our scheme also allows for variable time steps. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

17.
This paper describes a new scheme to improve the efficiency of time‐domain BEM algorithms. The discussion is focused on the two‐dimensional elastodynamic formulation, however, the ideas presented apply equally to any step‐by‐step convolution based algorithm whose kernels decay with time increase. The algorithm presented interpolates the time‐domain matrices generated along the time‐stepping process, for time‐steps sufficiently far from the current time. Two interpolation procedures are considered here (a large number of alternative approaches is possible): Chebyshev–Lagrange polynomials and linear. A criterion to indicate the discrete time at which interpolation should start is proposed. Two numerical examples and conclusions are presented at the end of the paper. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

18.
In lifetime prediction, the effect of a certain use environment on the lifetime is taken into account by using an acceleration factor that is specific to that use environment. The fact that the product may be used in different countries with differing environmental conditions results in a set of acceleration factor values. Prior to this paper, the effect of multiple field environments has been taken into account by using an average value of the acceleration factors obtained for several use environments. As the magnitudes of the acceleration factors (each specific to a certain use environment) vary a lot, the use of the average value has resulted in unrealistic lifetime estimates. The unrealism related to the use of the average value can be avoided when using the mixture‐of‐distributions concept, since the true acceleration factor values, instead of an average value, can then be used. In this paper, the mixture‐of‐distributions concept is applied for the first time to evaluate the effect of multiple use environments (thermal cycling) on the lifetime of a component population. By using this concept, it is possible to evaluate all of the key figures of reliability for the whole population based on the fractions of the component population that are used in multiple, different use environments. This approach can be applied when allocating maintenance and spare parts for a product that is used worldwide. The mixture‐of‐distributions concept in lifetime prediction is demonstrated by analyzing the test results of some ceramic leadless chip carrier components. Acceleration factors in four alternative field environments are estimated by running thermo‐mechanical finite element analysis simulations. The lifetime performance of the whole component population used in certain alternative field environments is then evaluated by applying the mixture‐of‐distributions concept. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

19.
Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained. This paper deals with estimation of the stress strength reliability model R = P(Y < X) when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter. The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples. Two progressive Type-II hybrid censoring schemes were used, Case I: A sample size of stress is the equal sample size of strength, and same time of hybrid censoring, the product of spacing function under progressive Type-II hybrid censoring schemes. Case II: The sample size of stress is a different sample size of strength, in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T ∈ (0,∞). The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed. A comparison study with classical methods as the maximum likelihood estimation method is discussed. Furthermore, to compare the performance of various cases, Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures. Finally, two real datasets are analyzed for illustrative purposes, first data for the breaking strengths of jute fiber, and the second data for the waiting times before the service of the customers of two banks.  相似文献   

20.
Right‐censored failure time data is a common data type in manufacturing industry and healthcare applications. Some control charting procedures were previously proposed to monitor the right‐censored failure time data under some specific distributional assumptions for the observed failure times and censoring times. But these assumptions may not be always satisfied in the real‐world data. Therefore, a more generalized control chart technique, which can handle different types of distributions of the data, is highly needed. Considering the limitations of existing methodologies for detecting changes of hazard rate, this paper develops a generalized statistical procedure to monitor the failure time data in the presence of random right censoring when abundant historical failure times are available. The developed method makes use of the one‐sample nonparametric rank tests without any specific assumptions of the data distribution. The operating characteristic functions of the control chart are derived on the basis of the asymptotic properties of the rank statistics. Case studies are presented to show the effectiveness of the proposed control chart technique, and its performance is investigated and compared with some Shewhart‐type control charts based on the conditional expected value weight. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

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