Abstract
Inference is investigated for a multicomponent stress-strength reliability (MSR) under Type-II censoring when the latent failure times follow two-parameter Rayleigh distribution. With a context that the lifetimes of the strength and stress variables have common location parameters, maximum likelihood estimator of MSR along with the existence and uniqueness is established. The associated approximate confidence interval is provided via the asymptotic distribution theory and delta method. Meanwhile, alternative generalized pivotal quantities-based point and confidence interval estimators are also constructed for MSR. More generally, when the lifetimes of strength and stress variables follow Rayleigh distributions with unequal location parameters, likelihood and generalized pivotal-based estimators are provided for MSR as well. In addition, to compare the equivalence of different strength and stress parameters, a likelihood ratio test is provided. Finally, simulation studies and a real data example are presented for illustration.
Highlights
Let the lifetimes of the i.i.d. system components be distributed according to cumulative distribution function (CDF) FX (·) and probability density function (PDF) f X (·) and the associated stress variables have the distribution with PDF f Y (·)
Since it is difficult to pursue the exact distribution of the maximum likelihood estimator (MLE) for Rs,k, the exact confidence interval cannot be obtained either
approximate confidence interval (ACI) are provided by using a large sample theory and delta technique
Summary
Suppose that n s-out-of-k G systems are put on a life-test experiment, each system contains k i.i.d. strength components subject to a common stress. Based on the failure mechanism of the s-out-of-k G system, failure samples for strength and stress variables are observed as follows, Observed strength variables. Xis } are independent first s strength samples for the ith system and Yi is the associated common stress variable, i = 1, 2, . Let the lifetimes of the i.i.d. system components be distributed according to CDF FX (·) and PDF f X (·) and the associated stress variables have the distribution with PDF f Y (·). The joint density function of (3) can be expressed as:.
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