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In this paper, the author proposed an optimization design for a step-stress accelerated life test (SSALT) with two stress variables for the generalized exponential (GE) distribution under progressive type-I censoring.

In this paper, two stress variables were considered. Progressive censoring and accelerated life testing were used to reduce the time and cost of testing. It was assumed that the lifetimes of the test units followed a GE distribution. The effects of changing stress were considered as a cumulative exposure model. A log-linear relationship between the scale parameter of the GE distribution and the stress was proposed. The maximum likelihood estimators and approximate and bootstrap confidence intervals (CIs) for the model parameters were obtained. An optimum test plan was developed using minimization of the asymptotic variance (AV) of the percentile life under the usual operating condition.

According to the simulation results, the bootstrap CIs of the model parameters gave more accurate results than approximate CIs through the length of CIs. The sensitivity analysis was performed to illustrate the effect of initial estimates on optimal values that has been studied. Simulation results also indicated that the optimal times were not too sensitive to the initial values of parameters; thus, the proposed design was robust.

In most studies, only one accelerating stress variable is used. Sometimes accelerating one stress variable does not yield enough failure data. Thus, two stress variables may be needed for additional acceleration. In this paper, two stress variables are considered. The inclusion of two stress variables in a test design will lead to a better understanding of the effect of two simultaneously operating stress variables. Also, the author assumes that the failure time of the test units follows a GE distribution. It is observed that the GE distribution can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. Also, most studies in this field have focused on the derivation of optimum test plans. In this paper, the author examined the estimation of model parameters and the optimization of the test design. In this paper, the asymptotic and bootstrap CIs for the model parameters are calculated. In addition, a sensitivity analysis is performed to examine the effect of the changes in the pre-estimated parameters on the optimal hold times. For determining the optimal test plan, due to nonlinearity and complexity of the objective function, the particle swarm optimization (PSO) algorithm is developed to calculate the optimal hold times. In this method, the research speed is very fast and optimization ability is more.

The purpose of this paper is to consider the general k level step-stress accelerated life test with the Rayleigh lifetime distribution for units subjected to stress under progressive Type-I censoring.

The parameter of this distribution is assumed to be a log-linear function of the stress, and a tampered failure rate model holds. The progressive Type-I censoring reduces the cost of testing. Due to constrained resources in practice, the test design must be optimized carefully. A numerical study is conducted to illustrate the optimum test design based on several four optimality criteria under the constraint that the total experimental cost does not exceed a pre-specified budget.

This paper compares unconstrained and constrained optimal k level step-stress test. Based on the results of the simulation study, the cost constraint reduces cost and time of the test and it also, in the most cases, increases the efficiency of the test. Also, the T-optimal design is lowest cost and time for testing and it is found more optimal in both conditions.

In this paper, various optimization criteria for selecting the stress durations have been used, and these criteria are compared together. Also, because of affecting the stress durations on the experimental cost, the author optimize under the constraint that the total experimental cost does not exceed a pre-specified budget. The efficiency of the unconstrained test in comparison with constrained test is discussed.

Accelerated life tests (ALTs) are used to make timely assessments of the lifetime distribution of highly reliable materials and components. Life test under accelerated environmental conditions may be fully accelerated or partially accelerated. In fully accelerated life testing, all the test units are run at accelerated condition, while in partially accelerated life testing, they are both run at normal and accelerated conditions. The products can fail due to one of the several possible causes of failure which need not be independent. The purpose of this paper is to design constant-stress PALT with dependent competing causes of failure using the tampered failure rate model.

Gumbel–Hougaard copula is used to model and measure the dependence between the life times of competing causes of failure. The use of the copula simplifies the model specification and gives a general class of distributions with the same dependent structure and arbitrary marginal distributions.

The optimal plan consists in finding optimum allocation of test units in different chambers by minimizing the reciprocal of the determinant of Fisher Information Matrix. The confidence interval for the estimated values of the design parameters has been obtained and sensitivity analysis carried out. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.

The model formulated can help reliability engineers obtain reliability estimates quickly of high reliability products that are likely to last for several years.

Accelerated life test is undertaken to induce early failure in high-reliability products likely to last for several years. Most of these products are exposed to several fatal risk factors and fail due to one of them. Examples include solar lighting device with two failure modes: capacitor failure, and controller failure. It is necessary to assess each risk factor in the presence of other risk factors as each one cannot be studied in isolation. The purpose of this paper is to explore formulation of optimum time-censored accelerated life test model under modified ramp-stress loading when different failure causes have independent exponential life distributions.

The modified ramp-stress uses one test chamber in place of the various chambers used in the normal ramp-stress accelerate life test thus saving experimental cost. The stress-life relationship is modeled by inverse power law, and for each failure cause, a cumulative exposure model is assumed. The method of maximum likelihood is used for estimating design parameters. The optimal plan consists in finding out relevant experimental variables, namely, stress rate and stress rate change point(s).

The optimal plan is devised using D-optimality criterion which consists in finding out optimal stress rate and optimal stress rate change point by maximizing logarithm of determinant of Fisher information matrix to the base 10. This criterion is motivated by the fact that the volume of joint confidence region of model parameters is inversely proportional to square root of determinant of Fisher information matrix. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.

The model formulated can help reliability engineers obtain reliability estimates quickly of high-reliability products that are likely to last for several years.

Most of the literature on the design of accelerated life test (ALT) plan focus on a single system (subsystem) totally disregarding its internal configuration. Many a times it is not possible to identify the components that cause the system failure or that the cause can only be identified by a subset of its components resulting in a masked observation. The purpose of this paper is to deal with the planning of ramp-stress accelerated life testing for a high-reliability parallel system comprising two dependent components using masked failure data. Such a testing may prove to be useful in a twin-engine aircraft. A ramp-stress results when stress applied on the system increases linearly with time.

A parallel system with two dependent components is taken with dependency modeled by Gumbel-Hougaard copula. The stress-life relationship is modeled using inverse power law, and cumulative exposure model is assumed to model the effect of changing stress. The method of maximum likelihood is used for estimating design parameters. The optimal plan consists in finding optimal stress rate using D-optimality criterion.

The optimal plan consists in finding optimal stress rate using D-optimality criterion by minimizing the reciprocal of the determinant of Fisher information matrix. The proposed plan has been explained using a numerical example and carrying out a sensitivity analysis.

The model formulated can help reliability engineers obtain reliability estimates quickly of high-reliability products that are likely to last for several years.

In this paper, the authors design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this paper we design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this study, the authors design accelerated life test under Type-I censoring when the lifetime of test items follows PID and also provides its application in the field of warranty policy. The following conclusion is made on the basis of this study. (1) An inverse relationship is shown between the shape parameter with the expected total cost and expected cycle time, while the shape parameter directly relates to the expected cost rate (see Table 5). (2) A direct relationship is shown between the scale parameter with the expected total cost and expected time cycle, while the inverse relationship is shown with the expected cost rate (see Table 5). (3) An inverse relationship is shown between the replacement age and the expected cost rate, while there are direct relationships between expected total cost and expected time cycle (see Table 5).

This paper is neither published or neither accepted anywhere.

In order to reduce avoidably lengthy duration required to test highly reliable products under usage stress, accelerated life test sampling plans (ALTSPs) are employed. This paper aims to build a decision model for obtaining optimal sampling plan under accelerated life test setting using Type-I hybrid censoring scheme for products covered under warranty.

The primary decision model proposed in this paper determines ALTSP by minimizing the relevant costs involved. To arrive at the decision model, the Fisher information matrix for Type-I hybrid censoring scheme under accelerated life test setting is derived. The optimal solution is attained by utilizing appropriate techniques following a nonlinear constrained optimization approach. As a special case, ALTSP for Type-I censoring is obtained using the same approach. ALTSP under Type-I hybrid censoring using the variance minimization approach is also derived.

On comparing the optimal results obtained using the above mentioned approaches, it is found that the cost minimization approach does better in reducing the total cost incurred. Results also show that the proposed ALTSP model under cost function setting has considerably lower expected testing time. Interesting findings from the sensitivity analysis conducted using a newly introduced failure dataset pertaining to locomotive controls are highlighted.

The research introduces a model to design optimum ALTSP for Type-I hybrid censoring scheme. The practical viability of the model makes it valuable for real-life situations. The practical application of the proposed model is exemplified using a real-life case.

Degradation measurement of some products requires destructive inspection; that is, the degradation of each unit can be observed only once. For example, observation on the mechanical strength of interconnection bonds or on the dielectric strength of insulators requires destruction of the unit. Testing high-reliability items under normal operating conditions yields a small amount of degradation in a reasonable length of time. To overcome this problem, the items are tested at higher than normal stress level – an approach called an accelerated destructive degradation test (ADDT). The present paper deals with formulation of constant-stress ADDT (CSADDT) plan with the test specimens subject to stress induced by temperature and voltage.

The stress–life relationship between temperature and voltage is described using Zhurkov–Arrhenius model. The fractional factorial experiment has been used to determine optimal number of stress combinations. The product's degradation path follows Wiener process. The model parameters are estimated using method of maximum likelihood. The optimum plan consists in finding out optimum allocations at each inspection time corresponding to each stress combination by using variance optimality criterion.

The method developed has been explained using a numerical example wherein point estimates and confidence intervals for the model parameters have been obtained and likelihood ratio test has been used to test for the presence of interaction effect. It has been found that both the temperature and the interaction between temperature and voltage influence the quantile lifetime of the product. Sensitivity analysis is also carried out.

Most of the work in the literature on the design of ADDT plans focusses on only a single stress factor. An interaction exists among two or more stress factors if the effect of one factor on a response depends on the levels of other factors. In this paper, an optimal CSADDT plan is studied with one main effect and one interaction effect. The method developed can help engineers study the effect of elevated temperature and its interaction with another stress factor, say, voltage on quantile lifetime of a high-reliability unit likely to last for several years.

This research provides some evidence by the vine copula approach, suggesting the significant and symmetric causal relation between subsections of Baltic Exchange and hence concluding that investing in different indexes, which is currently a risk diversification system, is not a correct risk reduction strategy.

The daily observations of Baltic Capesize Index (BCI), Baltic Handysize Index (BHSI), Baltic Dirty Tanker Index (BDTI) and Baltic LNG Tanker Index (BLNG) over an eight-year period have been used. After collecting data, calculating the return and estimating the marginal distribution of return rates for each of the indexes applying asymmetric power generalized autoregressive conditional heteroskedasticity and autoregressive moving average (APGARCH-ARMA), and with the assumption of skew student's t-distribution, the dependence of Baltic indexes was modeled based on Vine-R structures.

A positive and symmetrical correlation was observed between the study groups. High and low tail dependence is observed between all four indexes. In other words, the sector business groups associated with each of these indexes react similarly to the extreme events of other groups. The BHSI has a pivotal role in examining the dependency structure of Baltic Exchange indexes. That is, in addition to the direct dependence of Baltic groups, the dependence of each group on the BHSI can transmit accidents and shocks to other groups.

Since the Baltic Exchange indexes are tradable, these findings have implications for portfolio design and hedging strategies for investors in shipping markets.

Vine copula structures proves the causal relationship between different Baltic Exchange indexes, which are derived from different types of markets.