Stochastically ordered subpopulations and optimal burn-in procedure

Burn-in is a widely used engineering method which is adopted to eliminate defective items before they are shipped to customers or put into the field operation. In the studies of burn-in, the assumption of bathtub shaped failure rate function is usually employed and optimal burn-in procedures are investigated. In this paper, however, we assume that the population is composed of two ordered subpopulations and optimal burn-in procedures are studied in this context. Two types of risks are defined and an optimal burn-in procedure, which minimizes the weighted risks is studied. The joint optimal solutions for the optimal burn-in procedure, which minimizes the mean number of repairs during the field operation, are also investigated.

Optimal Burn-in Time and Imperfect Maintenance Strategy for a Warranted Product with Bathtub Shaped Failure Rate

‘Burn-in/preventive maintenance’ programme is an efficient approach used to minimise the warranty servicing cost of a product with bathtub shaped failure rate. Burn-in is a widely used method to improve the quality of product during its ‘infant mortality’ period and preventive maintenance is a scheduled necessary activity carried out during its ‘wear-out’ period. In this paper, an optimisation model is developed to determine the optimal burn-in time and optimal imperfect preventive maintenance strategy that minimises the total mean servicing cost of a warranted product with an age-dependent repair cost. We provide a numerical study to illustrate our results

Operations and Maintenance Optimization of Stochastic Systems: Three Essays

This dissertation presents three essays on topics related to optimally operating and maintaining systems that evolve randomly over time. Two primary areas are considered: (i) joint staffing and pricing strategies for call centers that use co-sourcing to improve service operations and reduce costs; and (ii) optimally maintaining stochastically degrading systems when either multiple systems are associated via a common environment, or when a single-unit system is maintained using a population of heterogeneous spare parts. First we present a queueing and stochastic programming framework for optimally staffing a call center utilizing co-sourced service capacity. The interplay between the call center and external service provider is modeled as a leader-follower game in which the call center, acting as the follower, solves a two-stage stochastic integer program. The problem is reformulated as a quadratically-constrained linear program to obtain the optimal contract prices and the optimal staffing problem yields a closed-form solution. Numerically we demonstrate that significant cost reductions can be achieved, even in the presence of imperfect and asymmetric information. Second the problem of optimally replacing multiple stochastically degrading systems using condition-based maintenance is considered. Properties of the optimal value function and policy motivate a tractable, approximate model with state- and action-space transformations and a basis-function approximation of the action-value function. It is demonstrated that near optimal policies are attainable and significantly outperform heuristics. Finally, we consider the problem of optimally maintaining a stochastically degrading system using spares of varying quality. Conditions are provided under which the optimal value function exhibits monotonicity and the optimal policy is characterized. Numerically we demonstrate the utility of our proposed framework, and provide insights into the optimal policy as an exploration-exploitation type policy

Maintenance of systems with critical components. Prevention of early failures and wear-out

We present a model for inspection and maintenance of a system under two types of failures. Early failures (type I), affecting only a proportion p of systems, are due to a weak critical component detected by inspection. Type II failures are the result of the system ageing and preventive maintenance is used against them. The two novelties of this model are: (1) the use of a defective distribution to model strong components free of defects and thus immune to early failures. (2) the removal of the weak critical part once it is detected with no other type of rejuvenation of the system which constitutes an alternative to the minimal repair. We study the conditions under which this model outperforms, from a cost viewpoint, other two classical age-replacement models. The analysis reveals that inspection is advantageous if the system can function with the critical component in the defective state for a long enough time. The proportion of weak units and the quality of inspections also determine the optimum policy. The results about the range of application of the model are useful for decision making in actual maintenance. A case study concerning the timing belt of a four-stroke engine illustrates the model

Optimal Burn-In under Complex Failure Processes: Some New Perspectives

Ph.DDOCTOR OF PHILOSOPH

Robust Parameter Estimation for the Mixed Weibull (Seven Parameter) Including the Method of Minimum Likelihood and the Method of Minimum Distance

Robust parameter estimation is successfully applied to the Mixed Weibull (seven parameter) using the Method of Minimum Distance and the Method of Maximum Likelihood. That is, parameters can now be estimated for a mixture of two Weibull distributions where the true populations are co-located, partially co-located or highly separated. Both techniques provided very robust estimates that were far superior to current parameter estimation techniques. Sample sizes as low as ten with mixing proportions down to 0.1 were investigated. For the MLEs, innovative bounding techniques are presented to allow consistent and correct convergence using any reasonable point estimate. The likelihood function is solved numerically as a non-linear constrained optimization using a quasi-Newton method. Minimum Distance Estimates (over three hundred scenarios investigated) are derived for some variation or combination of the mixing proportion and the location parameter(s), individually and simultaneously (the Anderson-Darling and Cramer-von Mises statistics were used). In tact, the MDE for the mixing proportion was so effective that future researchers should consider some permanent combination Primary measures of success were based on comparison of CDFs. Mean square error (MSE) and integrated absolute difference (LAF) between the estimated and true distributions were measured including confidence intervals

The adaptive designs CONSORT extension (ACE) statement: a checklist with explanation and elaboration guideline for reporting randomised trials that use an adaptive design

Abstract: Adaptive designs (ADs) allow pre-planned changes to an ongoing trial without compromising the validity of conclusions and it is essential to distinguish pre-planned from unplanned changes that may also occur. The reporting of ADs in randomised trials is inconsistent and needs improving. Incompletely reported AD randomised trials are difficult to reproduce and are hard to interpret and synthesise. This consequently hampers their ability to inform practice as well as future research and contributes to research waste. Better transparency and adequate reporting will enable the potential benefits of ADs to be realised. This extension to the Consolidated Standards Of Reporting Trials (CONSORT) 2010 statement was developed to enhance the reporting of randomised AD clinical trials. We developed an Adaptive designs CONSORT Extension (ACE) guideline through a two-stage Delphi process with input from multidisciplinary key stakeholders in clinical trials research in the public and private sectors from 21 countries, followed by a consensus meeting. Members of the CONSORT Group were involved during the development process. The paper presents the ACE checklists for AD randomised trial reports and abstracts, as well as an explanation with examples to aid the application of the guideline. The ACE checklist comprises seven new items, nine modified items, six unchanged items for which additional explanatory text clarifies further considerations for ADs, and 20 unchanged items not requiring further explanatory text. The ACE abstract checklist has one new item, one modified item, one unchanged item with additional explanatory text for ADs, and 15 unchanged items not requiring further explanatory text. The intention is to enhance transparency and improve reporting of AD randomised trials to improve the interpretability of their results and reproducibility of their methods, results and inference. We also hope indirectly to facilitate the much-needed knowledge transfer of innovative trial designs to maximise their potential benefits. In order to encourage its wide dissemination this article is freely accessible on the BMJ and Trials journal websites.“To maximise the benefit to society, you need to not just do research but do it well” Douglas G Altma

Consistent and fast inference in compartmental models of epidemics using Poisson Approximate Likelihoods

Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson Approximate Likelihood (PAL) methods. In contrast to the popular ODE approach to compartmental modelling, in which a large population limit is used to motivate a deterministic model, PALs are derived from approximate filtering equations for finite-population, stochastic compartmental models, and the large population limit drives consistency of maximum PAL estimators. Our theoretical results appear to be the first likelihood-based parameter estimation consistency results which apply to a broad class of partially observed stochastic compartmental models and address the large population limit. PALs are simple to implement, involving only elementary arithmetic operations and no tuning parameters, and fast to evaluate, requiring no simulation from the model and having computational cost independent of population size. Through examples we demonstrate how PALs can be used to: fit an age-structured model of influenza, taking advantage of automatic differentiation in Stan; compare over-dispersion mechanisms in a model of rotavirus by embedding PALs within sequential Monte Carlo; and evaluate the role of unit-specific parameters in a meta-population model of measles