Some Properties of the Poisson Distribution with an Application to Reliability Testing

Rajgopal, Jayant; Mazumdar, M.; Savits, Thomas H.

doi:10.1017/s0269964800003454

Cited by 10 publications

(3 citation statements)

References 4 publications

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“…This in turn requires φ m (β)/(-ln R 0 ) ≤ φ m (1-α)/(-ln R 1 ), or equivalently, (-ln R 1 )/(-ln R 0 ) ≤ φ m (1-α)/φ m (β). Since R 1 >R 0 the LHS of this last inequality is strictly less than 1, and it has been shown [13] that if α+β<1 as assumed, the ratio in the RHS is strictly increasing in m and approaches 1 as m approaches ∞. Therefore we can find t 1 ,t 2 ,...,t n that satisfy (12) and (13) for all m≥m * where m * is defined as…”

Section: A Component Test Plan For the Weibull Distributionmentioning

confidence: 89%

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System-Based Component Test Plans for Reliability Inferences

Rajgopal¹,

Mazumdar²

1998

Series on Quality, Reliability and Engineering Statistics

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This paper addresses the design of system-based component test plans for demonstrating reliability of a series system. There are two primary contributions of this work. First, unlike most of the prior work in this area which has relied on the component failure times being exponentially distributed, this paper examines another common failure time distribution, namely the Weibull distribution and develops a test plan that exploits the relationship between the Weibull and the exponential distributions. Second, it introduces the notion of imperfect interfaces between components within the system which is another issue that all prior work has ignored, and results in plans that also call for system level tests.

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Section: A Component Test Plan For the Weibull Distributionmentioning

confidence: 89%

“…It is clear that for both (12) and (13) to be satisfied m should satisfy B(m)≤A(m). This in turn requires φ m (β)/(-ln R 0 ) ≤ φ m (1-α)/(-ln R 1 ), or equivalently, (-ln R 1 )/(-ln R 0 ) ≤ φ m (1-α)/φ m (β).…”

Section: A Component Test Plan For the Weibull Distributionmentioning

confidence: 99%

System-Based Component Test Plans for Reliability Inferences

Rajgopal¹,

Mazumdar²

1998

Series on Quality, Reliability and Engineering Statistics

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“…The LHS of this last inequality is strictly less than 1, and it has been shown by Rajgopal et al [17] that as long as a b`1, the ratio in the RHS is strictly increasing in m and approaches 1 as m approaches I. Thus, the problem is feasible for all m !…”

Section: No Prior Informationmentioning

confidence: 93%

Optimum combined test plans for systems and components

Rajgopal¹,

Mazumdar²,

Majety³

1999

IIE Transactions

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Since mathematical models based on component reliabilities are frequently used for prediction of system reliability, it stands to reason that cost-eective inferences on the reliability of a system could be made on the basis of tests of its constituent components. Prior research in the area of system-based component testing has for the most part addressed the development of plans that test only the components. From a practitioner's point of view, this is an issue of concern since system failures are often caused by imperfect interfaces and other causes that are not directly attributable to component failures. The exclusion of system tests may thus be an erroneous approach. This paper addresses the development of test plans that explicitly consider the possibility of interface failures. The paper analyzes a series system to determine when testing should be performed on the system alone, on the components only, and on both, depending on test costs and interface reliabilities. Optimum test plans are derived by solving a twostage mathematical program.

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Two‐stage component test plans for testing the reliability of a series system

Vellaisamy

Sankar

2002

Naval Research Logistics

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Abstract:A system reliability is often evaluated by individual tests of components that constitute the system. These component test plans have advantages over complete system based tests in terms of time and cost. In this paper, we consider the series system with n components, where the lifetime of the i-th component follows exponential distribution with parameter λi. Assuming test costs for the components are different, we develop an efficient algorithm to design a two-stage component test plan that satisfies the usual probability requirements on the system reliability and in addition minimizes the maximum expected cost. For the case of prior information in the form of upper bounds on λi's, we use the genetic algorithm to solve the associated optimization problems which are otherwise difficult to solve using mathematical programming techniques. The two-stage component test plans are cost effective compared to single-stage plans developed by Rajgopal and Mazumdar. We demonstrate through several numerical examples that our approach has the potential to reduce the overall testing costs significantly.

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Some Properties of the Poisson Distribution with an Application to Reliability Testing

Abstract: Construction of a certain class of component tests for verification of series system reliability requires the use of some properties of the Poisson distribution that are not commonly known or used. This paper states and proves these results.

Cited by 10 publications

References 4 publications

System-Based Component Test Plans for Reliability Inferences

System-Based Component Test Plans for Reliability Inferences

Optimum combined test plans for systems and components

Two‐stage component test plans for testing the reliability of a series system

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