Ioannis S. Triantafyllou

On the signature of coherent systems and applications

In the present article we provide a formula that facilitates the evaluation of the signature of a reliability structure by a generating function approach. A simple sufficient condition is also derived for proving the nonpreservation of the IFR property for the systems lifetime (when the components are IFR) by exploiting the signature of the system. As an application of the general results, we deduce recurrence relations for the signature of a linear consecutive k-out-of-n: F system. We establish a simple relation between the signature of a linear and a circular system and investigate the IFR preservation property under the formulation of such systems.

A Distribution-Free Control Chart Based on Order Statistics

In this article, we introduce a new distribution-free Shewhart-type control chart that takes into account the location of a single order statistic of the test sample (such as the median) as well as the number of observations in that test sample that lie between the control limits. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of the chart is that, due to its nonparametric nature, the false alarm rate and in-control run length distribution are the same for all continuous process distributions, and so will be naturally robust. Tables are provided for the implementation of the chart for some typical ARL values and false alarm rates. The empirical study carried out reveals that the new chart is preferable from a robustness point of view in comparison to a classical Shewhart-type chart and also the nonparametric chart of Chakraborti et al. (2004).

Consecutive-Type Reliability Systems: An Overview and Some Applications

The family of consecutive-type reliability systems is under investigation. More specifically, an up-to-date presentation of almost all generalizations of the well-known consecutive -out-of- : system that have been proposed in the literature is displayed, while several recent and fundamental results for each member of the aforementioned family are stated.

Failure Rate and Aging Properties of Generalized Beta- and Gamma-generated Distributions

In the present article we study several characteristics of the families of generalized beta- and gamma- generated distributions introduced by Alexander et al. (2011) and Zografos and Balakrishnan (2009), respectively. Simple formulas are established for calculating the failure rate of the members of the aforementioned families by exploiting the failure rate of the parent distribution. In addition, the aging properties of the generalized beta- and gamma-generated distributions are explored in terms of the corresponding aging behavior of the parent family.

Reliability Study of Military Operations: Methods and Applications

This chapter offers a reliability study of several speculative military scenarios and some general results concerning well-known reliability systems. More specifically, four different consecutive type systems are investigated and treated as operational tactics of defensive or offensive military schemes. Structural properties of these scenarios, such as the signature vector or the reliability function, are studied in details and several conclusions concerning the effectiveness of the aforementioned military operations are deduced. In addition, some recursive relations for the calculation of the signature coordinates of well-known reliability structures are also proved. Finally, for illustrative purposes some figures are also displayed in order to depict the operation rules of the reliability structures that are under investigation.

Nonparametric control charts based on order statistics: Some advances

ABSTRACT In this article, we introduce new nonparametric Shewhart-type control charts that take into account the location of two order statistics of the test sample as well as the number of observations in that sample that lie between the control limits. Exact formulae for the alarm rate, the run length distribution and the average run length (ARL) are all derived. A key advantage of the new charts is that, due to its nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the proposed charts for some typical FAR and ARL values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations, while they seem preferable from a robustness point of view in comparison with the distribution-free control chart of Balakrishnan et al. (2009).

Reliability Analysis of Coherent Systems with Exchangeable Components

In this paper we study reliability properties of coherent systems consisting of n exchangeable components. We focus on the aging behavior of a reliability structure and several results are reached clarifying whether a system displays the IFR/DFR property or not. More specifically, a necessary and sufficient condition is deduced for a system’s lifetime to be IFR, while additional signature-based conditions aiming at the same direction are also delivered. For illustration purposes, special cases of well-known reliability systems and specific lifetimes’ distributions are considered and studied in detail.

Mixed Three-State

In this paper, we study a three-state k-out-of- n system with n independent components ( k = (k1,k2)). Each component can be in a perfect functioning state (state “2”), partially working (state “1”), or failed (state “0”). We assume that, at time t = 0, n1 components are in a partially working state while the rest n2 components are fully functioning ( n = n1 + n2). The system is considered to be at state “1” or above if at least k1 components are working (fully or partially). If at least k1 components are working and at least k2 components are in a perfect functioning state, we shall say that the system is at state “2”. In this paper, we develop formulae for the survival functions corresponding to the two different systems states described above. For illustration purposes, a numerical example which assumes that the degradation occurs according to a Markov process is presented.