We provide a detailed, introductory exposition of the Metropolis-Hastings algorithm, a powerful Markov chain method to simulate multivariate distributions. A simple, intuitive derivation of this method is given along with guidance on implementation. Also discussed are two applications of the algorithm, one for implementing acceptance-rejection sampling when a blanketing function is not available and the other for implementing the algorithm with block-at-a-time scans. In the latter situation, many different algorithms, including the Gibbs sampler, are shown to be special cases of the Metropolis-Hastings algorithm. The methods are illustrated with examples.

/pdf/understanding-the-metropolis-hastings-algorithm-43977vycuo.pdf

Understanding the Metropolis-Hastings Algorithm

A survey of maintenance policies of deteriorating systems

An introduction to survival and event history analysis.- Stochastic processes in event history analysis.- Nonparametric analysis of survival and event history data.- Regression models.- Parametric counting process models.- Unobserved heterogeneity: The odd effects of frailty.- Multivariate frailty models.- Marginal and dynamic models for recurrent events and clustered survival data.- Causality.- First passage time models: Understanding the shape of the hazard rate.- Diffusion and L#x00E9 vy process models for dynamic frailty.

https://www.springer.com/productFlyer_978-0-387-20287-7.pdf?SGWID=0-0-1297-52088484-0

Survival and Event History Analysis: A Process Point of View

Invited reviewImperfect maintenance

New product warranty: A literature review

We consider a component which undergoes instantaneous general repairs on failure. Suppose that V i = Φ(V i-l + Y i ), where V i is the virtual age immediately after the ith failure, Y i is the time between the (i - 1)th and ith failures, Φ(.) is a specified repair functional, and V 0 =s. We derive integral equations for the repair density, and also for the joint density of repairs with respect to chronological age and virtual age on failure. In the asymptotic case, approximations are obtained for the mean and variance of virtual age on failure, virtual age after repair, and time between failures. Two policies are then considered. The first, an upgraded repair strategy employs minimal repairs until the component reaches a specified age, thereafter repairs restore the virtual age to that prescribed level. The second policy considered is the Kijima Type 2 model which is not amenable to the usual g-renewal analysis that is used in the Type 1 model. The repair density is obtained by numerical solution of the relevant integral equation. Finally, approximations for the asymptotic moments are found to be in close agreement with simulated results.

Renewal-type equations for a general repair process

(1982). Formulation of a Multi Item Single Supplier Inventory Problem. Journal of the Operational Research Society: Vol. 33, No. 3, pp. 285-286.

Formulation of a Multi Item Single Supplier Inventory Problem

The number of COVID-19 deaths reported from European countries has varied more than 100-fold In terms of coronavirus transmission, the relatively low death rates in some countries could be due to 

https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.201726

The scale and dynamics of COVID-19 epidemics across Europe

We consider a general repair process where the virtual age V i after the ith repair is given by V i = O(V i-1 + X i ), O(.) is a specified repair functional, and X i is the time between the (i - 1)th and ith repair. Some monotonicity and dominance properties are derived, and an equilibrium process is considered. A computational method for evaluating the expected number/density of repairs is described together with an approximation method for obtaining some parameters of the equilibrium process.

Some properties and computational results for a general repair process

The high cost of maintenance in the processing industry implies the need for optimal planning of maintenance strategy. In order to achieve this there is a need to understand the underlying failure processes, which are often very complex. In this paper, a new semi-parametric approach, combining Cox regression with density kernal smoothing, is introduced to estimate the underlying performance. The approach has been applied to several processes and it allowed insight into each process, which would not have been achieved if traditional approaches had been used. Particularly, the refurbishment of processes had a significant impact on the rate failure. This paper concludes by assessing this impact of refurbishment on the maintenance programme.

John Dagpunar

Papers

Renewal-type equations for a general repair process

Formulation of a Multi Item Single Supplier Inventory Problem

The scale and dynamics of COVID-19 epidemics across Europe

Some properties and computational results for a general repair process

Analysing maintenance data to gain insight into systems performance