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Optimal Design of ALT under Progressive Type I Interval Censoring with Random Removals

Optimal Design of ALT under Progressive Type I Interval Censoring with Random Removals. Tse, Siu-Keung Department of Management Sciences, City University of Hong Kong, HK Yang, Chunyan (speaker) Department of Statistics, Yunnan University, PRC Ding, Chang

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Optimal Design of ALT under Progressive Type I Interval Censoring with Random Removals

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  1. Optimal Design of ALT under Progressive Type I Interval Censoring with Random Removals Tse, Siu-Keung Department of Management Sciences, City University of Hong Kong, HK Yang, Chunyan (speaker) Department of Statistics, Yunnan University, PRC Ding, Chang Department of Statistics, Yunnan University, PRC

  2. Part I: Motivation

  3. Quality Reliability normal complete Life tests censoring accelerated continuous periodic various types of accelerated life tests (ALT)

  4. ni1 ni2 niki 0 ti1 ti2 tiki ALT under Type I censoring with periodic inspection: Yum & Choi (1989) i=1: low stress level (s1) i=2: high stress level (s2)

  5. ri1 ri2 riki ni1 ni2 niki 0 ti1 ti2 tiki Removal: budget, inspection, test specimen fixed or random? Yuen & Tse (1996) ALT under progressive Type I interval censoring with random removals

  6. Part II: Model Formulation

  7. ri1 ri2 riki (allocation proportion) 3. lifetime 1. constant 2. Xi1 Xi2 Xiki 0 ti1 ti2 tiki Assumptions:

  8. 4. observed data, binomial distribution. such that the qth quantile is estimated accurately (that is, AV( ) minimized). • Optimal design: • Inspection time: {tij, i=1,2,…, m; j=1, 2,…, ki} • The stress level: si, i=1,2,…, m-1. • Allocation of test units: ai , ni= ain

  9. Part III: Optimal Plans

  10. such that the corresponding is minimized. 3.1 Statistically Optimal (SO) Plans (m=2)

  11. 3.2 Equally Spaced (ES) Plan (m=2) The inspection is conducted at the time points with equal space. pre-specified 3.3 Equal Probability (EP) Plan (m=2) The inspection times are selected such that the probability of failure in each interval is the same.

  12. pre-specified 3.4 ES and EP Plans (m=3) provide a mean to check the straight-line relationship assumed

  13. Conclusions: • a. SO plans always produce the smallest AV and stable over k and p. b. the performance of ES and EP are similar to those of SO plans, especially when p = 0. c. EP plans are relatively better than ES plans, especially when p> 0.

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