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Article

Availability and Profit Analysis of a linear Consecutive 2-out-of-4 Repairable System with Units Exchange

1Department of Mathematics, Usmanu Danfodio University, Sokoto, Nigeria

2Department of Mathematical Sciences, Faculty of Science, Bayero University, Kano, Nigeria


American Journal of Applied Mathematics and Statistics. 2014, 2(2), 83-87
DOI: 10.12691/ajams-2-2-6
Copyright © 2014 Science and Education Publishing

Cite this paper:
U.A. Ali, Ibrahim Yusuf. Availability and Profit Analysis of a linear Consecutive 2-out-of-4 Repairable System with Units Exchange. American Journal of Applied Mathematics and Statistics. 2014; 2(2):83-87. doi: 10.12691/ajams-2-2-6.

Correspondence to: Ibrahim  Yusuf, Department of Mathematical Sciences, Faculty of Science, Bayero University, Kano, Nigeria. Email: Ibrahimyusuffagge@gmail.com

Abstract

In this paper, we study some reliability characteristics of a repairable linear consecutive 2-out-of-4 system. The system work when to two units in a row (consecutive) works. The system is attended by three repairmen. When an operating unit failed, a standby is switched on or an idle operating unit is exchange with the failed unit. The explicit expressions of the reliability characteristics such availability, busy period of the repairmen and profit function are derived. Some cases are analyzed graphically to investigate the impact of system parameters on availability and profit.

Keywords

References

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[[2]  I. Yusuf, Availability and profit analysis of 3-out-of-4 repairable system with preventive maintenance, International Journal of Applied Mathematical Research, 1 (4), 2012, pp 510-519.
 
[[3]  I. Yusuf, and B. Yusuf, Evaluation of reliability characteristics of two dissimilar network flow systems. Applied Mathematical Sciences, Vol. 7, No. 40, 2013, pp 1983-1999.
 
[[4]  I.Yusuf, and N. Hussaini, Evaluation of Reliability and Availability Characteristics of 2-out of -3 Standby System under a Perfect Repair Condition American Journal of Mathematics and Statistics, Vol. 2No. 5, 2012, pp 114-119.
 
[[5]  J. Shao, and L.R. Lamberson, Modeling shared-load k-out-of-n : G systems IEEE Trans. Reliab., 40: 1991.
 
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[6]  K.M. El-Said, Cost analysis of a system with preventive maintenance by using Kolmogorov’s forward equations method, American Journal of Applied Sciences, Vol. 5,No. 4, 2008, pp 405-410.
 
[7]  K.M.El-Said, and M.S. El-Sherbeny, Evaluation of reliability and availability characteristics of two different systems by using linear first order differential equations, Journal of Mathematics, and Statistics, Vol. 1 No. 2, 2005, pp 119-123.
 
[8]  M. Y. Haggag, “Cost analysis of a system involving common cause failure and preventive maintenance, ”Journal of Mathematics and Statistics, Vol. 5, No. 4, 2009, pp 305-310.
 
[9]  Y. Barron, E. Frostig and B.Levikson, Analysis of r out of n systems with several repairmen, exponential life times and phase type repair times: an algorithmic approach. Eur. J. Oper. Res. Algorithm Approach 169, 2006, pp 202-225.
 
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Article

Recurrence Relations for Single and Product Moments of Generalized Order Statistics from Extreme Value Distribution

1Hindu College, University of Delhi, Delhi, India


American Journal of Applied Mathematics and Statistics. 2014, 2(2), 77-82
DOI: 10.12691/ajams-2-2-5
Copyright © 2014 Science and Education Publishing

Cite this paper:
Kamal Nain Kapoor. Recurrence Relations for Single and Product Moments of Generalized Order Statistics from Extreme Value Distribution. American Journal of Applied Mathematics and Statistics. 2014; 2(2):77-82. doi: 10.12691/ajams-2-2-5.

Correspondence to: Kamal  Nain Kapoor, Hindu College, University of Delhi, Delhi, India. Email: kamal.180968@gmail.com

Abstract

In this paper, we establish some recurrence relations satisfied by single and product moments of Generalized Order Statistics from Extreme Value Distribution. These recurrence relations are independent of left truncated point and therefore are also applicable for Logistic as well as for half Logistic distributions studied in Balakrishnan (1985) and Saran and Pandey (2012). For a particular case these results verify the corresponding results of Saran and Pandey (2004) and Kumar (2010).

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References

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[[1]  Athar, H., Kheaja S. K. and Nayabuddin (2012). Expectation identities of Pareto distribution based on generalized order statistics. American Journal of Applied Mathematics and Mathematical Sciences, 1, 23-29.
 
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[[5]  Joshi, P. C. (1978). Recurrence relations between moments of order statistics from exponential and truncated exponential distributions. Sankhya, Ser. B, 39, 362-371.
 
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[6]  Joshi, P. C. (1982). A note on mixed moments of order statistics from exponential and truncated exponential distributions. J. Statist. Plann. Inf., 6, 13-16.
 
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[8]  Kamps, U. (1995b). A concept of generalized order statistics. J. Statist. Plann. Inf., 48, 1-23.
 
[9]  Kumar, D. (2010). Recurrence relations for single and product moments of generalized order statistics from pth order exponential distribution and its characterization, J. Statist. Res. Iran 7, 201-212.
 
[10]  Mohie El-Din, M. M., Mahmoud, M. A. W., Abu-Youssef, S. E. and Sultan, K. S. (1997). Order statistics from the doubly truncated linear exponential distribution and its characterizations. Commun. Statist.- Simul. Comput. 26, 281-290.
 
[11]  Nain, K. (2010 a). Recurrence relations for single and product moments of kth record values from generalized Weibull distribution and a characterization. International Mathematical Forum, 5, No. 33, 1645-1652.
 
[12]  Nain, K. (2010 b). Recurrence relations for single and product moments of ordinary order statistics from pth order exponential distribution. International Mathematical Forum, 5, No. 34, 1653 – 1662.
 
[13]  Pawlas, P. and Szynal, D. (2001). Recurrence relations for single and product moments of generalized order statistics from Pareto, Generalized Pareto and Burr distributions. Commun. Statist. Theor. Meth., 30, 739-746.
 
[14]  Saran, J. and Nain, K. (2012a). Recurrence relations for single and product moments of generalized order statistics from doubly truncated pth order Exponential Distribution, JKSA 23.
 
[15]  Saran, J. and Nain, K. (2012b). Relationships for moments of kth record values from doubly truncated pth order exponential and generalized Weibull distributions. ProbStat Forum., 05, 142-149.
 
[16]  Saran, J. and Nain, K. (2012c). Relationships for moments of kth record values from doubly truncated pth order exponential and generalized Weibull distributions. ProbStat Forum., 05, 142-149.
 
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Article

Some New Generalizations of Fuzzy Average Code Word Length and their Bonds

1University of Kashmir, Hazratbal, Srinagar, India


American Journal of Applied Mathematics and Statistics. 2014, 2(2), 73-76
DOI: 10.12691/ajams-2-2-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
M.A.K. Baig, Mohd Afzal Bhat, Mohd Javid Dar. Some New Generalizations of Fuzzy Average Code Word Length and their Bonds. American Journal of Applied Mathematics and Statistics. 2014; 2(2):73-76. doi: 10.12691/ajams-2-2-4.

Correspondence to: M.A.K.  Baig, University of Kashmir, Hazratbal, Srinagar, India. Email: baigmak62@gmail.com

Abstract

In this communication, we propose a new generalizations of fuzzy average codeword length La and study its particular cases. The results obtained not only generalize the existing fuzzy average code word length but all the known results are the particular cases of the proposed length. Some new fuzzy coding theorems have also been proved.

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References

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[[1]  Bhandari, N. R. Pal, Some new information measures for fuzzy sets, Information Sciences 1993; Vol. 67, No. 3: pp. 209-228.
 
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[[5]  J.N.Kapur, Measures of Fuzzy Information, Mathematical Science Trust Society, New Delhi; 1997.
 
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[8]  Lowen, R., Fuzzy Set Theory–Basic Concepts, Techniques and Bibliography, Kluwer Academic Publication. Applied Intelligence 1996; Vol. 31, No. 3: pp.283-291.
 
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Article

Increment Primes

1Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia


American Journal of Applied Mathematics and Statistics. 2014, 2(2), 66-72
DOI: 10.12691/ajams-2-2-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
P.M. Mazurkin. Increment Primes. American Journal of Applied Mathematics and Statistics. 2014; 2(2):66-72. doi: 10.12691/ajams-2-2-3.

Correspondence to: P.M.  Mazurkin, Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia. Email: kaf_po@mail.ru

Abstract

The increment of prime numbers was a clear indication. Increase - the number increases, the addition of something. If the number of prime numbers, figuratively called the "ladder of Gauss-Riemann", the increase may well be likened to the steps, separated from the ladder itself. We prove that the law is obeyed z2(i2=2)=1/2-1/2cos(πP(n)/2) in the critical line i2=2 of the second digit binary number system. This functional model was stable and in other quantities of prime numbers (3000 and 100 000). The critical line is the Riemann column i2=2 binary matrix of a prime rate. Not all non-trivial zeros lie on it. There is also a line of frames, the initial rate (yields patterns of symmetry) and left the envelope binary number 1. Cryptographers cannot worry: even on the critical line growth of prime numbers z2i=1/2-1/2cos(πPj/2) contain the irrational number π=3.14159….

Keywords

References

[[1]  Don Zagier. The first 50 million prime numbers. URL: http://www.ega-math.narod.ru/Liv/Zagier.htm.
 
[[2]  Mazurkin P.M. Biotechnical principle and stable distribution laws // Successes of modern natural sciences. 2009. № 9, 93-97.
 

Article

Series Primes in Binary

1Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia


American Journal of Applied Mathematics and Statistics. 2014, 2(2), 60-65
DOI: 10.12691/ajams-2-2-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
P.M. Mazurkin. Series Primes in Binary. American Journal of Applied Mathematics and Statistics. 2014; 2(2):60-65. doi: 10.12691/ajams-2-2-2.

Correspondence to: P.M.  Mazurkin, Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia. Email: kaf_po@mail.ru

Abstract

To prove the famous Riemann hypothesis, that the real part of the root is always exactly equal to 1/2, a series of 500 and the other prime numbers has been converted from decimal to binary number system. At the same time was a clear non-trivial zeros. Any prime number can be represented as quantized into binary digital signal. Quantization step to not dilute a number of prime numbers is 1. Number of levels (binary digits) depends on the power of the quantized number of primes. As a result, we get two types of zeros - the trivial and nontrivial. Capacity of a finite number of primes must be taken based on the completeness of block incidence matrix. Average statistical indicator is a binary number, and influencing variable - itself a prime number. The binary representation allows to visualize and geometric patterns in the full range of prime numbers.

Keywords

References

[[1]  Gashkov S.B. Number systems and their applications. M. MCCME, 2004. 52.
 
[[2]  Signal. URL: http://ru.wikipedia.org/wiki/%D0%A1%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB.
 

Article

Proof the Riemann Hypothesis

1Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia


American Journal of Applied Mathematics and Statistics. 2014, 2(2), 53-59
DOI: 10.12691/ajams-2-2-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
P.M. Mazurkin. Proof the Riemann Hypothesis. American Journal of Applied Mathematics and Statistics. 2014; 2(2):53-59. doi: 10.12691/ajams-2-2-1.

Correspondence to: P.M.  Mazurkin, Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia. Email: kaf_po@mail.ru

Abstract

In the proof of the correctness of the Riemann hypothesis held strong Godel's incompleteness theorem. In keeping with the ideas of Poja and Hadamard's mathematical inventions, we decided to go beyond the modern achievements of the Gauss law of prime numbers and Riemann transformations in the complex numbers, knowing that at equipotent prime natural numbers will be sufficient mathematical transformations in real numbers. In simple numbers on the top left corner of the incidence matrix blocks are of the frame. When they move, a jump of the prime rate. Capacity of a number of prime numbers can be controlled by a frame, and they will be more reliable digits. In the column i=1 there is only one non-trivial zero on j=(0,∞). By the implicit Gaussian "normal" distribution , where Pj - a number of prime numbers with the order-rank j. On the critical line of the formula for prime numbers . By "the famous Riemann hypothesis is that the real part of the root is always exactly equal to 1/2" is obtained - the vibration frequency of a series of prime numbers is equal π/2, and the shift of the wave - π/4.

Keywords

References

[[1]  Don Zagier. The first 50 million prime numbers. URL: http://www.ega-math.narod.ru/Liv/Zagier.htm.
 
[[2]  Number. URL: http://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE.
 
[[3]  Mazurkin P.M. Biotechnical principle and sustainable laws of distribution // Successes of modern natural sciences. 2009. № 9, 93-97.
 
[[4]  Mazurkin PM The statistical model of the periodic system of chemical elements D.I. Mendeleev. Yoshkar-Ola: MarSTU, 2006. 152.
 
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