A Log-Logistic Step-Stress Model

Srivastava, Preeti Wanti; Shukla, Rishikesh

doi:10.1109/tr.2008.928182

Cited by 25 publications

(11 citation statements)

References 10 publications

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“…Chapter The log-logistic distribution is typically applied to the fields of hydrology, reliability and economics (see Ashkar & Mahdi, 2006, Srivastava & Shukla, 2008, Wang, 2008 references therein). Attempts have also been made in fitting the distribution to service time.…”

Section: Log-logistic Distributionmentioning

confidence: 99%

Modelling activities at a neurological rehabilitation unit

Griffiths

Williams

Wood

2013

European Journal of Operational Research

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DeclarationThis work has not previously been accepted in substance for any degree and is not concurrently being submitted in candidature for any degree. Signed:Date: Statement 1This thesis is the result of my own investigations, except where otherwise stated. Other sources are acknowledged by giving explicit references. A bibliography is appended. Signed:Date: Statement 2I hereby give consent for my thesis, if accepted, to be available for photocopying and interlibrary loan, and for the title and summary to be made available to outside organisations. SummaryA queuing model is developed for the neurological rehabilitation unit at Rookwood Hospital in Cardiff. Arrivals at the queuing system are represented by patient referrals and service is represented by patient length of stay (typically five months). Since there are often delays to discharge, length of stay is partitioned into two parts: admission until date ready for discharge (modelled by Coxian phase-type distribution) and date ready for discharge until ultimate discharge (modelled by exponential distribution). The attributes of patients (such as age, gender, diagnosis etc) are taken into account since they affect these distributions. A computer program has been developed to solve this multi-server (21 bed) queuing system to produce steady-state probabilities and various performance measures.However, early on in the project it became apparent that the intensity of treatment received by patients has an effect on the time, from admission, until they are ready for discharge. That is, the service rates of the Coxian distribution are dependent on the amount of therapy received over time. This directly relates to the amount of treatment allocated in the weekly timetables. For the physiotherapy department, these take about eight hours to produce each week by hand. In order to ask the valuable what-if questions that relate to treatment intensity, it is therefore necessary to produce an automated scheduling program that replicates the manual assignment of therapy. The quality of timetables produced using this program was, in fact, considerably better than its alternative and so replaced the by-hand approach. Other benefits are more clinical time (since less employee input is required) and a convenient output of data and performance measures that are required for audit purposes.Once the model is constructed a number of relevant hypothetical scenarios are considered.Such as, what if delays to discharge are reduced by 50%? Also, through the scheduling program, the effect of changes to the composition of staff or therapy sessions can be evaluated, for example, what if the number of therapists is increased by one third? The effects of such measures are analysed by studying performance measures (such as throughput and occupancy) and the associated costs.

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Section: Log-logistic Distributionmentioning

confidence: 99%

Modelling activities at a neurological rehabilitation unit

Griffiths

Williams

Wood

2013

European Journal of Operational Research

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“…Ng et al [21] discussed the problem of specifying the optimal sample size allocation for extreme value distribution. Srivastava and Shukla [22] obtained the optimal plan for simple step-stress ALT under the log-logistic distribution by minimizing the asymptotic variance of the MLE of the median life at a design stress. Srivastava and Shukla [23] extended their results in [22] to the case of censored data.…”

Section: Introductionmentioning

confidence: 99%

“…Srivastava and Shukla [22] obtained the optimal plan for simple step-stress ALT under the log-logistic distribution by minimizing the asymptotic variance of the MLE of the median life at a design stress. Srivastava and Shukla [23] extended their results in [22] to the case of censored data. Srivastava and Mittal [24] developed the results of Srivastava and Shukla [23] for truncated logistic distribution.…”

Section: Introductionmentioning

confidence: 99%

Estimation and Optimal Plans of Multiple Ramp-Stress Accelerated Life Tests for the Generalized Half-Normal Distribution

El-Raheem

2018

Journal of the Egyptian Mathematical Society

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Accelerated life tests are commonly utilized in manufacturing industries to induce early failures of highly reliable products. In this paper, estimation and optimal design issues of multiple ramp-stress accelerated life tests are discussed for the generalized half-normal distribution. Assuming inverse power model as a life-stress relationship, the maximum likelihood estimates of the parameters, as well as Fisher information matrix are derived. In addition, the methods of least square, moments, Bayes are used for estimating the model parameters. The optimal proportion of test units allocated to each stress level is obtained under D and A-optimality criteria. A sensitivity analysis of the optimal allocation to misspecification of the model parameters is carried out. Furthermore, a real data set is used to show the application of the generalized half-normal distribution in reliability studies. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

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“…Many works of various models and optimum designs in SSALT have been studied over the last few decades, (Bai & Chun, 1991;Khamis & Higgins, 1996;Khamis, 1997;Bagdonavicius & et al, 2002;Srivastava & Shukla, 2008), just to name a few. In general, there are a few methods to model SSALT.…”

Section: Introductionmentioning

confidence: 99%

A Bayes Inference for Step-Stress Accelerated Life Testing

Sha¹,

Teng²

2017

IJSP

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In this article, we present a Bayesian analysis with convex tent priors for step-stress accelerated life testing (SSALT) using a proportional hazard (PH) model. As flexible as the cumulative exposure (CE) model in fitting step-stress data and its attractive mathematical properties, the PH model makes Bayesian inference much more accessible than the CE model. Two sampling methods through Markov chain Monte Carlo algorithms are employed for posterior inference of parameters. The performance of the methodology is investigated using both simulated and real data sets.

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A Log-Logistic Step-Stress Model

Cited by 25 publications

References 10 publications

Modelling activities at a neurological rehabilitation unit

Modelling activities at a neurological rehabilitation unit

Estimation and Optimal Plans of Multiple Ramp-Stress Accelerated Life Tests for the Generalized Half-Normal Distribution

A Bayes Inference for Step-Stress Accelerated Life Testing

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