Sains Malaysiana 42(7)(2013): 981–987

Modeling Repairable System Failure with Repair History and Covariates

(Model Sistem Kegagalan Dibaiki dengan Sejarah Pembaikan dan Kovariat)

Samira Ehsani*

Department of Mathematics, Faculty of Science, University Putra Malaysia

43400, Serdang, Selangor D.E. Malaysia

Jayanthi Arasan & Noor Akma Ibrahim

Laboratory of Computational Statistics and Operations Research, Institute for Mathematical Research

University Putra Malaysia, 43400, Serdang, Selangor D.E. Malaysia

Received: 4 March 2010/Accepted: 2 February 2013

ABSTRACT

In this paper, we extended a repairable system model under general repair that is based on repair history, to incorporate covariates. We calculated the bias, standard error and RMSE of the parameter estimates of this model at different sample sizes using simulated data. We applied the model to a real demonstration data and tested for existence of time trend, repair and covariate effects. Following that we also conducted a coverage probability study on the Wald confidence interval estimates. Finally we conducted hypothesis testing for the parameters of the model. The results indicated that the estimation procedure is working well for the proposed model but the Wald interval should be applied with much caution.

Keywords: Covariate; general repair; repairable system

ABSTRAK

Dalam kertas ini, kami melanjutkan model sistem dibaiki di bawah pembaikan am yang berdasarkan sejarah pembaikan, dengan menggabungkan kovariat. Kami mengira ralat, sisihan piawai dan PMRKD bagi penganggar parameter-parameter model ini pada sampel yang berbeza saiz dengan menggunakan data simulasi. Kami menguna pakai model ini kepada data demonstration sebenar dan telah menguji kewujudan kecenderungan masa, kesan pembaikan dan kovariat. Berikutan itu kami juga menjalankan kajian liputan kebarangkalian bagi anggaran selang keyakinan ‘Wald’. Akhirnya kami menjalankan pengujian hipotesis bagi parameter-parameter model. Keputusan yang diperoleh menunjukkan bahawa prosedur penganggaran berjalan lancar bagi model yang dicadangkan tetapi selang ‘Wald’ harus digunakan dengan berhati-hati.

Kata kunci: Kovariat; perbaikan umum; sistem diperbaiki

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*Corresponding author; email: ehsani_samira@yahoo.com