Consecutive sliding window systems

This paper proposes a new model that generalizes the linear multi-state sliding window system to the case of m consecutive overlapping windows. In this model the system consists of n linearly ordered multi-state elements. Each element can have different states: from complete failure up to perfect functioning. A performance rate is associated with each state. The system fails if in each of at least m consecutive overlapping groups of r consecutive elements (windows) the sum of the performance rates of elements belonging to the group is lower than a minimum allowable level. An algorithm for system reliability evaluation is suggested which is based on an extended universal moment generating function. Examples of evaluating system reliability and elements' reliability importance indices are presented.

[1]  S. Papastavridis,et al.  Optimal-arrangement and importance of the components in a consecutive-k-out-of-r-from-n:F system , 1991 .

[2]  N. Balakrishnan,et al.  Optimal step-stress test under progressive type-I censoring , 2004, IEEE Transactions on Reliability.

[3]  B. Saperstein.  On the Occurrence of n Successes Within N Bernoulli Trials , 1973 .

[4]  H. T. Hahn,et al.  Reliability and Quality Control , 2013 .

[5]  Bernard Saperstein,et al.  The Generalized Birthday Problem , 1972 .

[6]  Z. M. Psillakis,et al.  A simulation algorithm for computing failure probability of a consecutive-k-out-of-r-from-n:F system , 1995 .

[7]  Tamás Szántai,et al.  New bounds on the reliability of the consecutive k-out-of-r-from-n: F system , 2000, Reliab. Eng. Syst. Saf..

[8]  David A. Wagner,et al.  A Generalized Birthday Problem , 2002, CRYPTO.

[9]  J.B. Nelson.  Minimal-Order Models for False-Alarm Calculations on Sliding Windows , 1978, IEEE Transactions on Aerospace and Electronic Systems.

[10]  Jun Cai,et al.  Reliability of a large consecutive-k-out-of-r-from-n:F system with unequal component-reliability , 1994 .

[11]  Y. L. Tong,et al.  A rearrangement inequality for the longest run, with an application to network reliability , 1985, Journal of Applied Probability.

[12]  Joseph Naus.  Probabilities for a Generalized Birthday Problem , 1974 .

[13]  Igor Ushakov.  Universal Generating Functions , 2013 .

[14]  Gregory Levitin.  Consecutive k-out-of-r-from-n system with multiple failure criteria , 2004, IEEE Transactions on Reliability.

[15]  Anatoly Lisnianski.  Estimation of boundary points for continuum-state system reliability measures , 2001, Reliab. Eng. Syst. Saf..

[16]  Michael Sfakianakis,et al.  Reliability of a consecutive k-out-of-r-from-n:F system , 1992 .

[17]  Gregory Levitin,et al.  The Universal Generating Function in Reliability Analysis and Optimization , 2005 .

[18]  Shun-Chen Niu,et al.  Reliability of Consecutive-k-out-of-n:F System , 1981, IEEE Transactions on Reliability.

[19]  Yves Dutuit,et al.  New insights into the assessment of k-out-of-n and related systems , 2001, Reliab. Eng. Syst. Saf..

[20]  Gregory Levitin,et al.  Linear multi-state sliding-window systems , 2003, IEEE Trans. Reliab..