Ch. 1. Basic probabilistic models in reliability

Limnios, Nikolaos; Papadopoulos, Christos E.

doi:10.1016/s0169-7161(01)20003-0

Cited by 10 publications

(7 citation statements)

References 18 publications

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“…) dimana merupakan indeks waktu untuk periode tertentu; Balakrishnan [1] Untuk = 0, mesin dalam kondisi sangat baik dan belum pernah mengalami kerusakan sama sekali, artinya tingkat keandalan atau reliabilitas dari suatu mesin tersebut sangat baik sehingga (0) = 1. Dengan memandang partisi keadaan dan maka matriks peluang transisi dan distribusi awal (0) menjadi…”

Section: Reliabilitas Menggunakan Rantai Markovunclassified

“…Selanjutnya dicari nilai reliabilitas dengan menggunakan persamaan (7) ( ) = (0) 1 . Dengan menggunakan partisi tersebut, ruang keadaan = {0,1} disubtitusikan ke persamaan (7) sehingga diperoleh ( ) = [ 0 (0) 1 = 0,482051 + 0,323077 = 0,805128 maka nilai reliabilitas untuk = 1 adalah 0,805128, artinya pada hari ke-1 peluang mesin proofer tersebut menjalankan fungsinya dengan baik adalah 80,51%. Selanjutnya berdasarkan rantai Markov yang telah diperoleh peluang jangka panjangnya maka dengan cara yang sama, dicari nilai reliabilitas untuk = 2,3,4, … ,22.…”

Section: Hasil Dan Pembahasanunclassified

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Reliabilitas Suatu Mesin Menggunakan Rantai Markov (Studi Kasus: Mesin Proofer Di Pabrik Roti Super Jam Banten)

Andriani¹,

Firdaniza²,

Irianingsih³

2017

JMI

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ABSTRAKMesin merupakan alat vital perusahaan dalam membantu proses produksi. Setiap perusahaan mengharapkan proses produksi berjalan dengan lancar, tetapi terkadang terkendala dengan terjadinya kerusakan pada mesin, sehingga proses produksi terganggu dan menyebabkan kerugian bagi perusahaan. Kerusakan pada mesin dapat diminimalisir dengan melakukan evaluasi terhadap kondisi mesin tersebut secara teratur. Penelitian ini menggunakan rantai Markov untuk mengetahui peluang jangka panjang kondisi suatu mesin dan menganalisis reliabilitas dari mesin tersebut untuk memperkirakan waktu perawatan. Studi kasus dilakukan pada mesin Proofer di Pabrik Roti Super Jam Banten mulai tanggal 3 Maret 2014 sampai tanggal 31 Mei 2015. Dari penelitian ini diperoleh hasil bahwa peluang jangka panjang mesin Proofer dalam kondisi baik adalah 42,86% dan disarankan untuk melakukan perawatan rutin pada mesin tersebut minimal setiap 22 hari sekali.Kata kunci: mesin, rantai markov, reliabilitas. ABSTRACT A Machine is a vital tool in helping the PendahuluanMesin merupakan salah satu aspek terpenting dalam bidang industri manufaktur maupun industri jasa. Dalam kegiatan produksi, sangat diharapkan proses berlangsung secara lancar. Jika terdapat gangguan pada mesin maka kegiatan produksipun harus terhenti, sehingga produk yang dihasilkan tidak optimal dan menimbulkan kerugian bagi perusahaan. Kerusakan pada mesin dapat terjadi karena adanya human error, kurangnya perawatan dan sebagainya. Untuk mengevaluasi kondisi mesin diperlukan analisis rantai Markov untuk menentukan peluang jangka panjang dari kondisi mesin tersebut. Tingkat keandalan mesin yang rendah mengakibatkan kerugian bagi perusahaan dan kemungkinan membahayakan pekerja, sehingga diperlukan suatu pengukuran dan analisis tingkat keandalan atau reliabilitas suatu mesin untuk membantu perusahaan agar melakukan tindakan perawatan yang teratur.Berdasarkan waktu, dalam menentukan nilai reliabilitas suatu mesin dapat dilakukan dengan metode reliabilitas menggunakan rantai Markov kontinu; Sadek et.al,[4] dan metode reliabilitas menggunakan rantai Markov diskrit;Sadek et al, [5]. Dalam menentukan reliabilitas mesin, Sadek, et.al [5] tidak

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Section: Reliabilitas Menggunakan Rantai Markovunclassified

Section: Hasil Dan Pembahasanunclassified

Reliabilitas Suatu Mesin Menggunakan Rantai Markov (Studi Kasus: Mesin Proofer Di Pabrik Roti Super Jam Banten)

Andriani¹,

Firdaniza²,

Irianingsih³

2017

JMI

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“…Applying the total probability formula to the number of failures, the distribution of D can be expressed as an infinite sum of convolutions. In the Laplace transform domain, convolutions become multiplications, and the first and second raw moment of the distribution can be derived from the derivative of the transform [58]. Finally, since the probability of simultaneous multiple failures is extremely low, the infinite series can be approximated by the first few terms, where in practice the first two to three terms are sufficient.…”

Section: Unprotected Casementioning

confidence: 99%

Effective Risk Assessment in Resilient Communication Networks

2016

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The paper discusses business impact analysis in the context of resilient communication networks. It is based on the total (aggregated) penalty that may be paid by an operator when the services (identified with transport demands) provided are interrupted due to network failures. The level of penalty is expressed as a commonly accepted business risk measure, Value-at-Risk (VaR). First, the main concern over VaR, namely the theoretical lack of subadditivity, is discussed. The study shows that, in practice, disadvantages do not appear in resilient network design, and VaR can be used without the need to apply more complex and less informative measures. Second, a method for calculating the upper bound of the total penalty is presented. The assessment is performed for unprotected and protected services with a broad variety of compensation policies used to translate technical loss to monetarily expressed penalty. The proposed bounds are experimentally shown to be effective in comparison with alternative calculation methods, and also in the case when some of the assumptions taken during the modelling stage are not met.

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“…Frequently, the evolution of the system is conveniently described by multi-state models where the state of the system evolves in time according to a specified probabilistic structure (see, e.g., [4]). One of the most popular choices is for Markov chain models in continuous or discrete-time cases (see, e.g., [5]). Markov models rely on the Markovian property that informally states that the future state of a system is independent of its past evolution given the state occupied at present.…”

Section: Introductionmentioning

confidence: 99%

On the Computation of Some Interval Reliability Indicators for Semi-Markov Systems

et al. 2021

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In this paper, we computed general interval indicators of availability and reliability for systems modelled by time non-homogeneous semi-Markov chains. First, we considered duration-dependent extensions of the Interval Reliability and then, we determined an explicit formula for the availability with a given window and containing a given point. To make the computation of the window availability, an explicit formula was derived involving duration-dependent transition probabilities and the interval reliability function. Both interval reliability and availability functions were evaluated considering the local behavior of the system through the recurrence time processes. The results are illustrated through a numerical example. They show that the considered indicators can describe the duration effects and the age of the multi-state system and be useful in real-life problems.

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Ch. 1. Basic probabilistic models in reliability

Cited by 10 publications

References 18 publications

Reliabilitas Suatu Mesin Menggunakan Rantai Markov (Studi Kasus: Mesin Proofer Di Pabrik Roti Super Jam Banten)

Reliabilitas Suatu Mesin Menggunakan Rantai Markov (Studi Kasus: Mesin Proofer Di Pabrik Roti Super Jam Banten)

Effective Risk Assessment in Resilient Communication Networks

On the Computation of Some Interval Reliability Indicators for Semi-Markov Systems

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