برآورد بیزی پارامتر قابلیت اعتماد چندمولفه‌ای تحت داده‌های سانسور فزاینده پیوندی بهبود یافته

در این مقاله، تحت نمونه‌های سانسور فزاینده پیوندی بهبود یافته، برآورد بیزی پارامتر قابلیت اعتماد چندمولفه‌ای با مولفه‌های مقاومت غیر یکسان در توزیع گومپرتز تعمیم‌یافته یکه، بررسی می‌شود. این مسئله در سه حالت مختلف حل شده است. در حالت اول، فرض می‌شود که متغیرهای تنش و مقاومت دارای پارامترهای غیر مشترک نامعلوم هستند. در حالت دوم  فرض می‌شود که متغیرهای تنش و مقاومت دارای دو پارامتر مشترک و یک پارامتر غیر مشترک هستند به‌طوری‌که همه این پارامترها نامعلومند. در حالت سوم، فرض می‌شود که متغیرهای تنش و مقاومت دارای دو پارامتر مشترک معلوم و یک پارامتر غیر مشترک نامعلوم هستند. در هر کدام از این حالت‌ها، برآورد بیزی پارامتر قابلیت اعتماد چندمولفه‌ای با مولفه‌های مقاومت غیر یکسان، به‌دست می‌آیند. در نهایت با روش شبیه‌سازی مونت کارلو عملکرد برآوردهای مختلف با هم مقایسه شده و نتایج روی یک سری داده واقعی پیاده‌سازی می‌شوند.

bayesian estimation of multi-component reliability parameter under adaptive hybrid progressive censoring

in reliability theory, inference on a stress-strength parameter is very interesting for scientists. a multi-component system is referred to a system with more than one component. in this paper, we consider one system with two types of components because of computational complexity. this model isso general because the multi-component stress-strength parameter with onestrength variable and stress-strength parameter can be obtained from it.type-i and type-ii schemes are the two most essential censoring schemesamong different censoring schemes, and by mixing them, a hybrid scheme canbe derived. the active units cannot be omitted during the test by the aboveschemes, so a progressive scheme is introduced. in this paper, we studied theadaptive hybrid progressive censoring scheme, which is so general that somecensoring schemes can be obtained from it. also, in this scheme, the samplesize is deterministic and not random. moreover, reaching the n-th failuretimes is another advantage of this scheme. recently, the unit generalizedgompertz (ugg) distribution has been introduced as a new transformedmodel of the gompertz distribution. this distribution can be converted tosome famous distribution, which is a good candidate for fitting into the realdata set.material and methodsin this paper, the bayesian estimation of the multi-component reliability,with the non-identical-component strengths, under the adaptive hybrid progressivecensoring samples, in unit generalized gompertz distribution is considered. this problem was solved in three cases. in the first case, itis assumed that strengths and stress variables have unknown and uncommonparameters, i.e. x1 ∼ ugg(θ1, c1, λ1), x2 ∼ ugg(θ2, c2, λ2) andy ∼ ugg(θ, c, λ) . in this case, the bayes estimation of rs,k is approximatedby the mcmc method due to the lack of explicit forms. also, the hpd credibleinterval of rs,k is obtained in this case. in the second case, it is assumedthat strengths and stress variables have two common parameters and oneuncommon parameter , i.e. x1 ∼ ugg(θ1, c, λ), x2 ∼ ugg(θ2, c, λ) andy ∼ ugg(θ, c, λ), so that all of these parameters are unknown. in this case,using the mcmc method, the bayes estimation and the associated hpdcredible interval of rs,k are derived. in the third case, it is assumed that thecommon parameters in the second case are known. by this assumption, theexact bayesian estimation of rs,k is obtained. also, it is approximated vialindley’s approximation.results and discussionthe simulation results showed that the performance of the informative priorswas better than the non-informative ones. also, the exact estimation performedbetter than lindley’s approximation. moreover, the hpd interval,based on the informative priors, had a better performance based on noninformativepriors in terms of average lengths and coverage percentages.conclusionin this paper, in three cases, bayes estimation of the multi-component reliabilityis considered, when an adaptive hybrid progressive censoring samplescollect the data. in each case, bayes estimation of the multi-component reliabilityis obtained with different methods. different estimations are comparedin the monte carlo simulation, and the results are implemented on one realdata set.