Exact and Approximated Reliability of a 2-dimensional consecutive k-out-of-n:F system

An approximation method to obtain the reliability of a 2-dimensional consecutive k-out-of-n: F system
is discussed. Although analysis to obtain exact reliability requires many calculation resources for a
system with a large number of components, the proposed approximation method obtains the reliability
easily by giving an assumption on the maximum number of failed components in an operable system.
This approximated reliability is exact when the total number of failed components is less than the
assumed maximum number. The accuracy of the new method is confirmed by numerical examples.

Modeling Inefficiencies in a Reliability System Using Stochastic Frontier Regression

For some reliability systems, it is possible to have the system reliability smaller than the reliability obtained using the configuration of the components. This may be due to the inefficiency of the system. By inefficiency, we mean any tendency or attribute that will bring down the performance of the system from the level the configuration is capable of or expected to provide or designed for. This sets a maximum limit (or frontier) for the performance of the system. Therefore, deviation of the observed level from this limit would then be an indicator of the inefficiency. In this paper, we have made an attempt to model inefficiencies in the working of a reliability system, and to define an inefficiency index. The paper discusses the practical estimation of the coefficient of inefficiency in the system performance. The stochastic frontier regression methods are used to estimate the inefficiency. The validity of the methodology has been assessed for an exponential model, using a limited simulation study. The inefficiency indices proposed in this paper are simple, as they must be to be useful to engineers. We found that the suggested indices & their estimation procedures work well.


Download

An O(k^2·log(n)) algorithm for computing the reliability of consecutive-k-out-of-n: F systems

This study presents an O(k2·log(n)) algorithm for computing the reliability of a linear as well as a circular consecutive-k-out-of-n: F system. The proposed algorithm is more efficient and much simpler than the O(k3·log(n/k)) algorithm of Hwang & Wright.


Download

Competing causes of failure and reliability tests for Weibull lifetimes under type I progressive censoring

For many high reliability products where very few items are expected to fail during the test period, testing undernormal conditions is not feasible. Further, the requirement for high reliability increases the need for test procedures which yield valuable degradation and other useful information for improving product reliability. Thus in some manufacturing and other experiments, various types of failure censored and accelerated life tests are commonly employed for life testing. In this paper we discuss Type I progressively censored variable-sampling plans for Weibull lifetime distributions under competing causes of failure. The proposed procedure is attractive as it yields useful degradation-related information for improving product quality. In addition, the procedure is useful when a test is conducted under severe time constraint and/or when the experimenter wishes to save costly specimens or scarce test facilities for other use.


Download

Discounted warranty cost of minimally repaired series systems

Many factors should be considered in modeling DWC (discounted warranty cost) of repairable systems or products including system structure, components failure processes, methods of discounting as well as the warranty policy itself. In this paper, we present DWC models for repairable series systems. In particular, a free repair warranty policy and a pro-rata warranty policy are studied. The impact of repair actions on components failure times is assumed to be minimal, hence NHPPs are used to describe the failure processes. Two types of discounting methods are considered in this paper: a continuous discount function and a discrete discount function. Expressions for both the expected value and variance of DWC are derived. The applications of our findings can be seen in warranty design, warranty reserve determination and risk analysis. Our approach incorporates the information of system structure, the value of time and the impact of repair actions, which are of great importance to warranty cost prediction and evaluation, but have not been sufficiently studied in the literature of warranty analysis.


Download

Generalized multi-state k-out-of-n:G systems

In a binary k-out-of-n:G system, k is the minimum number of components that must work for the system to work. Let 1 represent the working state and 0 the failure state, k then indicates the minimum number of components that must be in state 1 for the system to be in state 1. This paper defines the multi-statek-out-of-n:G system: each component and the system can be in 1 of M+1 possible states: 0, 1, ..., M. In Case I, the system is in state ⩾j iff at least kj components are in state ⩾j. The value of kj I 1 can be different for different required minimum system-state level j. Examples illustrate applications of this definition. Algorithms for reliability evaluation of such systems are presented


Download

What designers of microelectronic systems should know about arrays spared by rows and columns

Perhaps the most common fault tolerant architecture configures a nominal t×a·t array using b·t dedicated sparerows and c·t dedicated spare columns. Despite an extensive literature, two problems about row-column sparing appear unresolved: how to minimize the area of the layout and how to minimize the maximum wirelength. This paper answers these questions, consolidates results, and describes the implications for the designer. An outstanding conjecture is counterexampled by using a graph-theoretic procedure to lay out arrays spared bydedicated rows and columns, in area proportional to the number of array elements. However, dedicated sparing is somewhat more costly than homogeneous extraction of at×a·t array from a (1+b)·t×(a+c). T array. Complementing our results for layout, we quantify the worst-case and probabilistic fault tolerance for both dedicated and homogeneous sparing, as a function of the nominal aspect ratio a⩾1, the redundancy parameters b, c, and the scale parameter t. In the process, we contribute to the solution to an open question in extremal graph theory, the problem of Zarnnkiewicz: what is the least integer Z(t; a, b, c) such that every (1+b)·t×(a+c)·t binary array with Z ones contains a t×a·t subarray having no zeros? Whereas the mathematical literature traditionally focuses on subarrays possessing a constant number of rows or columns, we are interested in scalable constructions for microelectronics. Reflecting this priority, we derive exact formulae for Z(t; a, b, c) when the extracted subarray, grows in proportion to embedding array


Download
Subscribe to: Posts (Atom)