The step-stress tampered failure rate model under interval monitoring

Bobotas, Panayiotis; Kateri, Maria

doi:10.1016/j.stamet.2015.06.002

Cited by 11 publications

(9 citation statements)

References 42 publications

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“…As in the works of Kateri and Kamps and Bobotas and Kateri, the cdf of the lifetime of a test unit under the FR‐based SSALT model, type‐I censored at τ s , takes the form

G false(t false) = ({, \begin{matrix} array 1 - \exp \{- g_{1} (t) / ϑ_{1}\}, 0 < t \leq τ_{1}, \\ array 1 - \exp \{\sum_{i = 1}^{k - 1} (\frac{g_{i + 1} (τ_{i})}{ϑ_{i + 1}} - \frac{g_{i} (τ_{i})}{ϑ_{i}})\} \exp {- g_{k} (t) / ϑ_{k}}, \\ array τ_{k - 1} < t \leq τ_{k}, 2 \leq k \leq s . \end{matrix})

Under the distributional assumption , the hazard rate at the i th stress level is

h_{i} false(t false) = {sans-serifg}_{i} false(t false) false/ ϑ_{i}

. Thus, model reduces to the TFR model if the function

{sans-serifg}_{i}

is the same over all stress levels, ie,

{sans-serifg}_{i} = sans-serifg

, i = 1,…, s .…”

Section: The Interval Monitored Fr‐based Step‐stress Modelmentioning

confidence: 99%

“…Following the work of Bobotas and Kateri and using the notation

\begin{matrix} alignleft \\ align-1 u_{10} : = & align-2 v_{10} : = w_{10} : = 0, \\ align-1 u_{i j} : = & align-2 u_{i j} (β_{0}, β_{1}) : = \sum_{k = 1}^{i - 1} \frac{g_{k} (τ_{k}) - g_{k} (τ_{k - 1})}{\exp (β_{0} + β_{1} x_{k})} + \frac{g_{i} (τ_{i j}) - g_{i} (τ_{i - 1})}{\exp (β_{0} + β_{1} x_{i})}, \end{matrix}

we have

1 - G (τ_{i j}) = \exp (- u_{i j} (β_{0}, β_{1})) for all i = 1, …, s,

and

p_{i j} : = P (τ_{i, j - 1} < T \leq τ_{}

…”

Section: Non‐conjugate Bayesian Analysismentioning

confidence: 99%

“…In addition, we assume to know that the data follow the exponential distribution on each stress level. Under this setup, the ML estimates (MLEs) of ϑ 1 and ϑ 2 as well as the corresponding exact 95% confidence intervals (CIs) under continuous and interval monitoring (without intermediate inspection points) are derived in the work of Bobotas and Kateri and given in Table , along with summary results of our Bayesian analysis under the same interval monitoring scheme.…”

Section: Examplesmentioning

confidence: 99%

“…The lifetimes are from a general class of life distributions, that includes exponential and Weibull as special cases. For an extended discussion on the model and the related literature, we refer to the work of Bobotas and Kateri . Here, the more general progressively type‐I censoring scheme is considered, whereas the Bayesian approach is adopted.…”

Section: Introductionmentioning

confidence: 99%

“…Here, the more general progressively type‐I censoring scheme is considered, whereas the Bayesian approach is adopted. For the role of progressive censoring in SSALT experiments and associated designs, we refer to the works of Gouno et al, Fan et al, and Shen et al Furthermore, note that, in the work of Bobotas and Kateri, the shape parameters of the underlying lifetime distributions at each stress level were assumed to be known while they can be estimated here as well. Moreover, the shape parameter may not be necessarily constant over all stress levels, as is usually assumed.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bayesian analysis for step‐stress accelerated life testing under progressive interval censoring

Kohl

Kateri

2019

Appl Stoch Models Bus & Ind

Self Cite

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A step‐stress accelerated life testing model is considered for progressive type‐I censored experiments when the tested items are not monitored continuously but inspected at prespecified time points, producing thus grouped data. The underlying lifetime distributions belong to a general scale family of distributions. The points of stress‐level change are simultaneously inspection points as well while there is the option of assigning additional inspection points in between the stress‐level change points. In a Bayesian framework, the posterior distributions of the parameters of the model are derived for characteristic choices of prior distributions, as conjugate‐like and normal priors; vague or noninformative. The developed approach is illustrated on a simulated example and on a real data set, both known from the literature. The results are compared to previous analyses; frequentist or Bayes.

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“…As in the works of Kateri and Kamps and Bobotas and Kateri, the cdf of the lifetime of a test unit under the FR‐based SSALT model, type‐I censored at τ s , takes the form

G false(t false) = ({, \begin{matrix} array 1 - \exp \{- g_{1} (t) / ϑ_{1}\}, 0 < t \leq τ_{1}, \\ array 1 - \exp \{\sum_{i = 1}^{k - 1} (\frac{g_{i + 1} (τ_{i})}{ϑ_{i + 1}} - \frac{g_{i} (τ_{i})}{ϑ_{i}})\} \exp {- g_{k} (t) / ϑ_{k}}, \\ array τ_{k - 1} < t \leq τ_{k}, 2 \leq k \leq s . \end{matrix})

Under the distributional assumption , the hazard rate at the i th stress level is

h_{i} false(t false) = {sans-serifg}_{i} false(t false) false/ ϑ_{i}

. Thus, model reduces to the TFR model if the function

{sans-serifg}_{i}

is the same over all stress levels, ie,

{sans-serifg}_{i} = sans-serifg

, i = 1,…, s .…”

Section: The Interval Monitored Fr‐based Step‐stress Modelmentioning

confidence: 99%

“…Following the work of Bobotas and Kateri and using the notation

\begin{matrix} alignleft \\ align-1 u_{10} : = & align-2 v_{10} : = w_{10} : = 0, \\ align-1 u_{i j} : = & align-2 u_{i j} (β_{0}, β_{1}) : = \sum_{k = 1}^{i - 1} \frac{g_{k} (τ_{k}) - g_{k} (τ_{k - 1})}{\exp (β_{0} + β_{1} x_{k})} + \frac{g_{i} (τ_{i j}) - g_{i} (τ_{i - 1})}{\exp (β_{0} + β_{1} x_{i})}, \end{matrix}

we have

1 - G (τ_{i j}) = \exp (- u_{i j} (β_{0}, β_{1})) for all i = 1, …, s,

and

p_{i j} : = P (τ_{i, j - 1} < T \leq τ_{}

…”

Section: Non‐conjugate Bayesian Analysismentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bayesian analysis for step‐stress accelerated life testing under progressive interval censoring

Kohl

Kateri

2019

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

show abstract

Modeling Chronic Disease Mortality by Methods From Accelerated Life Testing

Zamsheva,

Kluttig,

Wienke

et al. 2024

Statistics in Medicine

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We propose a parametric model for describing chronic disease mortality from cohort data and illustrate its use for Type 2 diabetes. The model uses ideas from accelerated life testing in reliability theory and conceptualizes the occurrence of a chronic disease as putting the observational unit to an enhanced stress level, which is supposed to shorten its lifetime. It further addresses the issue of semi‐competing risk, that is, the asymmetry of death and diagnosis of disease, where the disease can be diagnosed before death, but not after. With respect to the cohort structure of the data, late entry into the cohort is taken into account and prevalent as well as incident cases inform the analysis. We finally give an extension of the model that allows age at disease diagnosis to be observed not exactly, but only partially within an interval. Model parameters can be straightforwardly estimated by Maximum Likelihood, using the assumption of a Gompertz distribution we show in a small simulation study that this works well. Data of the Cardiovascular Disease, Living and Ageing in Halle (CARLA) study, a population‐based cohort in the city of Halle (Saale) in the eastern part of Germany, are used for illustration.

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Optimal Designs for Step-Stress Models Under Interval Censoring

Bobotas

Kateri

2019

J Stat Theory Pract

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The step-stress tampered failure rate model under interval monitoring

Cited by 11 publications

References 42 publications

Bayesian analysis for step‐stress accelerated life testing under progressive interval censoring

Bayesian analysis for step‐stress accelerated life testing under progressive interval censoring

Modeling Chronic Disease Mortality by Methods From Accelerated Life Testing

Optimal Designs for Step-Stress Models Under Interval Censoring

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