Improvement on Start-up Demonstration Test

Yue, Panxiang; Cui, Lirong; Wang, Liying

doi:10.1109/icece.2010.932

Cited by 3 publications

(5 citation statements)

References 8 publications

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“…Ind. 2014, 30 373-413 385 correspond to the cases when one of the two termination criteria have been met and are of a similar form to those used by Yue et al [37]. The resulting transition probability matrix is again of the form (9), which along with the relations…”

Section: Inferential Issuesmentioning

confidence: 94%

“…Yue et al , in addition to studying the TSCSTF model, also introduced three more models as follows: CSTFCF: An equipment will be accepted if a number of consecutive successes (say c 1 ) occur prior to a total number of failures (say d ) and a number of consecutive failures (say c 2 ); otherwise, the equipment will be rejected; TSTFCF: An equipment will be accepted if a total number of successes (say d 1 ) occur prior to a total number of failures (say d 2 ) and a number of consecutive failures (say c ); otherwise, the equipment will be rejected; TSCSCF: An equipment will be accepted if a total number of successes (say d ) or a number of consecutive successes (say c 1 ) occur prior to a number of consecutive failures (say c 2 ); otherwise, the equipment will be rejected.…”

Section: Binary Start‐up Demonstration Tests Based On Successes and Fmentioning

confidence: 99%

“…binary trials. Specifically, the state space of the auxiliary Markov chain Y t , t = 0,1, … , in this case is

\begin{matrix} leftalign-star \\ rightalign-odd Ω = MathClass-open{MathClass-open(r, s, w, v MathClass-close) : 0 ⩽ r < c_{1}, 0 ⩽ s < d_{1}, 0 ⩽ w < c_{2}, 0 ⩽ v < d_{2} MathClass-close} \cup MathClass-open{ab s_{1}, ab s_{2} MathClass-close}, & align-even & rightalign-label \end{matrix}

where Y t = ( r , s , w , v ) if after the t ‐th trial, there are r consecutive successes on the last trials, s successes on the whole sequence of trials, w consecutive failures on the last trials and a total number of v failures; the absorbing states { abs 1 , abs 2 } correspond to the cases when one of the two termination criteria have been met and are of a similar form to those used by Yue et al . The resulting transition probability matrix is again of the form , which along with the relations

\begin{matrix} leftalign-star \\ rightalign-odd & align-even P MathClass-open(Y_{t} = MathClass-open(r + 1, s + 1, 0, v MathClass-close) | Y_{t - 1} = MathClass-open(r, s, w, v MathClass-close) MathClass-close) = p, if r < c_{1} - 1 and s < d_{1} - 1, & rightalign-label & align-label \\ rightalign-odd & align-even P MathClass-open(Y_{t} = MathClass-open(0 <...> \end{matrix}

…”

Section: Binary Start‐up Demonstration Tests Based On Successes and Fmentioning

confidence: 99%

“…Yue et al [37], in addition to studying the TSCSTF model, also introduced three more models as follows:…”

Section: Inferential Issuesmentioning

confidence: 99%

“…Then, the expected value of the test length, its probability mass function or the probability of acceptance is readily expressed by formulas similar to those in (10) and (11). Yue et al [37] studied similarly the characteristics of the other models as well.…”

Section: Inferential Issuesmentioning

confidence: 99%

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Start‐up demonstration tests: models, methods and applications, with some unifications

Koutras

Milienos

2014

Appl Stoch Models Bus & Ind

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Start‐up demonstration tests were first discussed in the quality/reliability literature about three decades ago. Since then, many variations of these tests have been introduced, and the corresponding distributional characteristics and inferential methods have also been studied. All these developments, based on independent and identically distributed binary trials, have been further generalized to some other forms of trials such as Markov‐dependent trials, exchangeable trials and multistate trials. In this paper, we provide a comprehensive review of all these results and highlight some unifications of the results. We also describe a general estimation method and then present several numerical examples to illustrate some of the models and methods described here. Finally, a number of open issues in this area of research are pointed out. Copyright © 2014 John Wiley & Sons, Ltd.

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Section: Inferential Issuesmentioning

confidence: 94%

Section: Binary Start‐up Demonstration Tests Based On Successes and Fmentioning

confidence: 99%

“…binary trials. Specifically, the state space of the auxiliary Markov chain Y t , t = 0,1, … , in this case is

\begin{matrix} leftalign-star \\ rightalign-odd Ω = MathClass-open{MathClass-open(r, s, w, v MathClass-close) : 0 ⩽ r < c_{1}, 0 ⩽ s < d_{1}, 0 ⩽ w < c_{2}, 0 ⩽ v < d_{2} MathClass-close} \cup MathClass-open{ab s_{1}, ab s_{2} MathClass-close}, & align-even & rightalign-label \end{matrix}

\begin{matrix} leftalign-star \\ rightalign-odd & align-even P MathClass-open(Y_{t} = MathClass-open(r + 1, s + 1, 0, v MathClass-close) | Y_{t - 1} = MathClass-open(r, s, w, v MathClass-close) MathClass-close) = p, if r < c_{1} - 1 and s < d_{1} - 1, & rightalign-label & align-label \\ rightalign-odd & align-even P MathClass-open(Y_{t} = MathClass-open(0 <...> \end{matrix}

…”

Section: Binary Start‐up Demonstration Tests Based On Successes and Fmentioning

confidence: 99%

“…Yue et al [37], in addition to studying the TSCSTF model, also introduced three more models as follows:…”

Section: Inferential Issuesmentioning

confidence: 99%

Section: Inferential Issuesmentioning

confidence: 99%

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Start‐up demonstration tests: models, methods and applications, with some unifications

Koutras

Milienos

2014

Appl Stoch Models Bus & Ind

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Binary State Start‐Up Demonstration Tests

Griffith¹,

Smith²

2019

Wiley StatsRef: Statistics Reference Online

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Start‐up demonstration tests are used to determine the acceptability of equipment. These have been employed in a variety of situations including, among others, power generation equipment, emergency power systems, and security systems. This article discusses the various types of binary state start‐up demonstration tests that have been discussed in the literature. The structure of the tests varies based on the pattern of total or consecutive start‐ups required for acceptance or rejection of the equipment being tested. The assumptions on the start‐ups also vary as to whether they are considered as independent and identically distributed Bernoulli trials or have a more complex dependence structure. Start‐up demonstrations tests that utilize multiple stages and inspectors are also discussed.

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On the identifiability of start-up demonstration mixture models

Koutras

Milienos

2016

Ann Inst Stat Math

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Improvement on Start-up Demonstration Test

Cited by 3 publications

References 8 publications

Start‐up demonstration tests: models, methods and applications, with some unifications

Start‐up demonstration tests: models, methods and applications, with some unifications

Binary State Start‐Up Demonstration Tests

On the identifiability of start-up demonstration mixture models

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