A Unified Approach for Modeling and Designing Attribute Sampling Plans for Monitoring Dependent Production Processes

Vellaisamy, P.; Sankar, Sivaneswaran

doi:10.1007/s11009-005-4519-7

Cited by 7 publications

(2 citation statements)

References 12 publications

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“…[9] considered a conditional probability model and established a weak law of large numbers and a central limit theorem. [21] proposed a conditional model where Bernoulli random variables depend on several previous observations. [12] established strong limit theorems for a conditional model.…”

Section: Introductionmentioning

confidence: 99%

Limit theorems for a higher order time dependent Markov chain model

Kokoszka,

Kutta,

Singh

et al. 2023

PMS

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The paper establishes a strong law of large numbers and a central limit theorem for a sequence of dependent Bernoulli random variables modeled as a higher order Markov chain. The model under consideration is motivated by problems in quality control where acceptability of an item depends on the past k acceptability scores. Moreover, the model introduces dependence that may evolve over time and thus advances the theory for models with time invariant dependence. We establish explicit assumptions that incorporate this dynamic dependence and show how it enters into the limits describing long-term behavior of the system.

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Section: Introductionmentioning

confidence: 99%

Limit theorems for a higher order time dependent Markov chain model

Kokoszka,

Kutta,

Singh

et al. 2023

PMS

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show abstract

“…Also, such models arise in the study of shock models in reliability theory. Vellaisamy and Sankar (2005) used a rather general dependent model for monitoring a continuous production process, where the classical assumption of iid quality characteristic is not appropriate.…”

Section: Introductionmentioning

confidence: 99%

Some Intrinsic Properties of the Gamma Distribution

Vellaisamy

Sreehari²

2010

JJSS

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Let {Yn} be a sequence of nonnegative random variables (rvs), and Sn = n j=1 Yj, n ≥ 1. It is first shown that independence of S k−1 and Y k , for all 2 ≤ k ≤ n, does not imply the independence of Y1, Y2, . . . , Yn. When Yj's are identically distributed exponential Exp(α) variables, we show that the independence of S k−1 andIt is shown by a counterexample that the converse is not true. We show that if X is a non-negative integer valued rv, then there exists, under certain conditions, a rvwhere {N (t)} is a standard (homogeneous) Poisson process, and obtain the Laplace-Stieltjes transform of Y . This leads to a new characterization for the gamma distribution. It is also shown that a G(α, k) distribution may arise as the distribution of S k , where the components are not necessarily exponential. Several typical examples are discussed.

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Optimal Design of Reliability Acceptance Sampling Plans for Multi-stage Production Process

Kumar

2022

Springer Series in Reliability Engineering

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A Unified Approach for Modeling and Designing Attribute Sampling Plans for Monitoring Dependent Production Processes

Cited by 7 publications

References 12 publications

Limit theorems for a higher order time dependent Markov chain model

Limit theorems for a higher order time dependent Markov chain model

Some Intrinsic Properties of the Gamma Distribution

Optimal Design of Reliability Acceptance Sampling Plans for Multi-stage Production Process

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