Abstract
In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress factors on the lifetimes of experimental units. In this paper, a step-stress model is considered in which the life-testing experiment gets terminated either at a pre-fixed time (say, Tm+1) or at a random time ensuring at least a specified number of failures (Say, y out of n). Under this model in which the data obtained are Type-II hybrid censored, the Kumaraswamy Weibull distribution is used for the underlying lifetimes. The maximum Likelihood estimators (MLEs) of the parameters assuming a cumulative exposure model are derived. The confidence intervals of the parameters are also obtained. The hazard rate and reliability functions are estimated at usual conditions of stress. Monte Carlo simulation is carried out to investigate the precision of the maximum likelihood estimates. An application using real data is used to indicate the properties of the maximum likelihood estimators.
Highlights
In order to obtain highly reliable products long life spans, consuming and expensive tests are often required to collect enough failure data
If it is held at the current stress, survivors will continue failing according to the cumulative distribution function (CDF) of that stress but starting at the age corresponding to previous fraction failed
A step–stress model is considered in which the life testing experiment gets terminated either at a prefixed time or at random time ensuring at least a specified number of failures
Summary
In order to obtain highly reliable products long life spans, consuming and expensive tests are often required to collect enough failure data. Accelerated life tests (ALT) allow the experimenter to apply sever stresses to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. In step–stress ALT, the stress for survival units is generally changed to a higher stress level at a predetermined time This model assumes that the remaining life of a unit depends only on the current cumulative fraction failed and current stress [Lydersen and Rausand (1987)]. A step–stress model is considered in which the life testing experiment gets terminated either at a prefixed time (say, Tm +1 ) or at random time ensuring at least a specified number of failures (say, r out of n ) Under this model in which the data obtained are Type–II hybrid censored, the case of two stress levels is proposed with underlying lifetimes being KUMW distributed. The statistical inference for simple step–stress life testing based on type–II hybrid censored is obtained in section (3)
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