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Two Reliability Acceptance Sampling Plans for Items Subject to Wiener Process of Degradation

Abstract

Traditionally, in reliability acceptance sampling plans, the decision to accept or reject a lot is made by performing the life tests of items. However, when the item’s deterioration is described by a degradation process, it can be made based on the observed deterioration levels of the items obtained from degradation tests. In this paper, two acceptance sampling plans are developed, based on the observation of the deterioration of the items, accumulated on a given period of time. To model the degradation of the items over time, the Wiener process with positive drift is employed. Algorithms to find the parameters of the proposed sampling plans are suggested. Conditionally on the acceptance in the test, the developed sampling plans are shown to improve the reliability performance of the items in the sense that the lifetimes of the items after the reliability sampling test are stochastically larger than those before the test. Also, we compare the two sampling plans both from a technical and economical points of view.

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Abbreviations

Θ:

the frailty r.v. which represents the reliability characteristic of the population

T 𝜃 :

the lifetime of the item with reliability characteristic 𝜃

\(f_{T_{\theta }}(t)\) :

the pdf (probability density function) of T𝜃

{W 𝜃(t), t ≥ 0}:

the conditional degradation process given Θ = 𝜃

{W(t), t ≥ 0}:

the unconditional degradation process

t 0 :

the specified testing duration

{W 1,⋯ .W n}:

the observed degradation levels of the n tested items observed at time t0

κ :

the threshold level of degradation after which the failure of the item occurs

α :

the producer’s risk

β :

the consumer’s risk

(n,c,ξ):

the parameters of Sampling Plan I

\(L_{n,\xi }^{(c)}(\theta )\) :

the lot acceptance probability of Sampling Plan I at 𝜃

(n,ξ):

the parameters of Sampling Plan II

L n,ξ(𝜃):

the lot acceptance probability of Sampling Plan II at 𝜃

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Acknowledgements

The authors thank the reviewer for helpful comments and advices. The work of the first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2019R1A2B5B02069500). The work of the first author was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177).

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Correspondence to Ji Hwan Cha.

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Cha, J.H., Mercier, S. Two Reliability Acceptance Sampling Plans for Items Subject to Wiener Process of Degradation. Methodol Comput Appl Probab (2021). https://doi.org/10.1007/s11009-021-09879-1

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Keywords

  • Quality management
  • Variables sampling plan
  • Degradation test
  • Wiener process
  • Stochastic ordering

Mathematics Subject Classification (2010)

  • 62P30
  • 62N05