Martin Newby

Optimal non-periodic inspection for a multivariate degradation model

We address the problem of determining inspection and maintenance strategy for a system whose state is described by a multivariate stochastic process. We relax and extend the usual approaches. The system state is a multivariate stochastic process, decisions are based on a performance measure defined by the values of a functional on the process, and the replacement decision is based on the crossings of a critical levels. The critical levels are defined for the performance measure itself and also as the probability of never returning to a satisfactory level of performance. The inspection times are determined by a deterministic function of the system state. A non-periodic policy is developed by evaluating the expected lifetime costs and the optimal policy by an optimal choice of inspection function. The model thus gives a guaranteed level of reliability throughout the life of the project. In the particular case studied here, the underlying process is a multivariate Wiener process, the performance measure is the l2 norm, and the last exit time from a critical set rather than the first hitting time determines the policy.

Bivariate constant stress degradation model: LED lighting system reliability estimation with two-stage modelling

Light-emitting diode (LED) lamp has received great attention as a potential replacement for the more commercially available lighting technology, such as incandescence and fluorescence lamps. LED which is the main component of LED lamp has a very long lifetime. This means that no or very few failures are expected during LED lamp testing. Therefore, degradation testing and modelling are needed. Because the complexity of modern lighting system is increasing, it is possible that more than one degradation failures dominate the system reliability. If degradation paths of the systems performance characteristics (PCs) tend to be comonotone there is a likely dependence between the PCs because of the systems common usage history. In this paper, a bivariate constant stress degradation data model is proposed. The model accommodates assumptions of dependency between PCs and allows the use of different marginal degradation distribution functions. Consequently, a better system reliability estimation can be expected from this model than from a model with independent PCs assumption. The proposed model is applied to an actual LED lamps experiment data. Copyright

Guidelines for corrective replacement based on low stochastic structure assumptions

This paper presents corrective replacement decisions, e.g. for machines in a production process or other technical systems. In an attempt to base decisions on observed failure times only, some guidelines are provided for replacing failed machines. The method does not provide an optimal strategy in all situations, indicating that sometimes more information or assumptions are needed. The optimal policy indicates how to act if the low assumptions model recommends action. If the model does not strongly indicate an action, more data need to be collected or more sophisticated modelling is needed. Further modelling would require additional assumptions or input from expert judgements, and could be an expensive exercise. A method that gives clear guidelines if the data are strongly indicative may save time and money. This paper presents the model in an elementary form and is intended as a first step towards modelling more realistic maintenance situations.

Perspective on Weibull proportional-hazards models

This note uses a paper of Elsayed & Chan (1990) to illustrate some of the advantages and some of the limitations of the proportional hazards approach. The role of proportional hazards as one of several tools for exploratory data analysis is described. The emphasis is on exploratory techniques as a way of: (1) measuring the importance of factors influencing system behavior; and (2) determining the form of the model. The semi-parametric version of proportional hazards shows the relative importance of explanatory factors in determining the failure behavior regardless of whether the model is strictly correct. Thus the relative chance of failure can be assessed, but not the absolute chance. The advantage of proportional hazards is that it always yields a quantitative measure of importance for each influence factor. Although Elsayed & Chan clearly establish the importance of temperature as the most critical factor in thin-oxide breakdown, the other analysis technique indicates that more needs to be done to validate a particular model of system behavior. In this case, the failure mechanism remains open, and the use of accelerated test data to predict performance under usual conditions needs further investigation. >

Moments and generating functions for the absortion distribution and its negative binomial analogue

The moments of the absorption are difficult to obtain. The generating functions are basic hypergeometric functions. This paper shows how to define two shift operators that allow elementary arguments to be used to develop recursions for the expected values of general functions. The exact moments of the distribution follow. The generating function for the negative binomial analogue gives the moments directly.

Accelerated failure time models for reliability data analysis

Abstract Despite the popularity of the proportional hazards model (PHM) in analysing many kinds of reliability data, there are situations in which it is not appropriate. The accelerated failure time model (AFT) then provides an alternative. In this paper, a unified treatment of the accelerated failure time model is outlined for the standard reliability distributions (Weibull, log-normal, inverse Gaussian, gamma). The problem of choosing between the accelerated failure time models and proportional hazard models is discussed and effects of misspecification are reported. The techniques are illustrated in the analysis of data from a fatigue crack growth experiment.

Markov models for fatigue crack growth

Abstract A review of several statistical and probabilistic approaches to the problem of fatigue crack growth shows that many Markov models are equivalent in that they express the probability density of the crack length at time t as solutions of the Kolmogorov, or Fokker-Plank, equations. Further, it is shown that the solution of the problem of the distribution of initial crack lengths is available from the Kolmogorov backward equations.

Maintenance scheduling of a manufacturing system subject to deterioration

Abstract This paper presents an integrated model for the joint determination of both optimal inspection strategy and optimal repair policy for a manufacturing system whose resulting output is subject to system state. An appropriate maintenance strategy is essential to optimize revenue from a manufacturing system which is in continuous operation and subject to deterioration. The optimum policy balances the amount of maintenance required to increase availability against the loss of revenue arising from the down time: insufficient maintenance leads to an increase in the number of defective items, low profit and low maintenance cost; excessive maintenance results in a reduction in the proportion of defective items, high profit and high maintenance cost. In this paper, an intensity control model adapted to partial information provides an optimal inspection intensity and repair degree of the system as an optimal control process to yield maximum revenue. The solution is obtained through formulating an equivalent deterministic Hamilton–Jacobi equation. A numerical example is provided to illustrate the behavior of the optimal control process. The optimal control process determines a solution to both optimum inspection frequency and optimal replacement policy which results in an optimal production run length of the system.

Estimating the size of the outbreak of new‐variant CJD

Despite the small numbers of New‐Variant Creutzfeldt‐Jakob Disease (vCJD) observed, sufficient human data have now accrued to allow statistical estimation of all three of the important parameters: the mean period between infection and death (the “mortality period”), its variance and the size of the outbreak. The mean mortality period is estimated to lie in the range six to 16 years, with low variances associated with the lower values of mean mortality period (< ten years) that are indicated as most likely. If BSE is indeed the cause of vCJD, then the number of human victims of vCJD is predicted not to exceed a few hundred, and is most likely to be a hundred or less. The study suggests that, while there may be a continuing, small number of deaths from vCJD for some years to come, exposure to the disease from BSE in the UK has more or less ceased at the time of writing.

Monitoring and maintenance of spares and one shot devices

Many one shot devices are kept in storage and taken into use when required. This paper examines the deterioration of the devices when in storage. For a complex device limited non-destructive testing and repair is possible short of using it in a destructive test. The tests are not perfect and can give false positive and false negative results. When a fault is indicated a minimal repair is carried out. The objective is to establish levels of reliability of individual components which together with the inspection regime give a particular level of reliability in the delivered components. Assuming a general distribution for the time to fail in storage the likelihood is developed and used to estimate the parameters of the model. The estimated model can then be used to explore different inspection and repair policies.