Very superstitious? A preliminary investigation of pigeons’ body position during a matching-to-sample task under differential and common outcome conditions.

The delayed matching-to-sample (DMS) task is widely employed to assess memory in a range of non-human animals. On the standard “common outcomes” (CO) DMS task, correct performance following either sample stimulus results in reinforcement. In contrast, on a “differential outcomes” (DO) DMS task, the outcome following either sample stimulus is different. One of the most consistent findings in the comparative literature is that performance under a DO condition is superior to that under a CO condition. The superior performance is attributed to the fact the DO condition enhances memory for the sample stimulus by tagging each sample with a discrete reward. Here, we investigate an alternative possibility, that pigeons use positional mediation during the delay under DO, but not CO, conditions. To test this, we tracked the head position of pigeons performing a DO (n = 4) or CO (n = 4) task. Consistent with the positional mediation account, all subjects in the DO condition displayed evidence of positional mediation. Surprisingly, positional mediation was not unique to subjects in the DO condition, with subjects in the CO condition also displaying evidence of mediation.&nbsp

Decline and repair, and covariate effects

The failure processes of repairable systems may be impacted by operational and environmental stress factors. To accommodate such factors, reliability can be modelled using a multiplicative intensity function. In the proportional intensity model, the failure intensity is the product of the failure intensity function of the baseline system that quantifies intrinsic factors and a function of covariates that quantify extrinsic factors. The existing literature has extensively studied the failure processes of repairable systems using general repair concepts such as age-reduction when no covariate effects are considered. This paper investigates different approaches for modelling the failure and repair process of repairable systems in the presence of time-dependent covariates. We derive statistical properties of the failure processes for such systems

Two new stochastic models of the failure process of a series system

Consider a series system consisting of sockets into each of which a component is inserted: if a component fails, it is replaced with a new identical one immediately and system operation resumes. An interesting question is: how to model the failure process of the system as a whole when the lifetime distribution of each component is unknown? This paper attempts to answer this question by developing two new models, for the cases of a specified and an unspecified number of sockets, respectively. It introduces the concept of a virtual component, and in this sense, we suppose that the effect of repair corresponds to replacement of the most reliable component in the system. It then discusses the probabilistic properties of the models and methods for parameter estimation. Based on six datasets of artificially generated system failures and a real-world dataset, the paper compares the performance of the proposed models with four other commonly used models: the renewal process, the geometric process, Kijima's generalised renewal process, and the power law process. The results show that the proposed models outperform these comparators on the datasets, based on the Akaike information criterion

On skill and chance in sport

This work studies outcome uncertainty and competitive balance from a broad perspective. It considers four sports with varying scoring rates, from soccer with typically three goals per match to netball with one hundred goals per match. Within a general modelling framework for a two-competitor contest, we argue that outcome uncertainty, the extent to which the outcome of a contest is unpredictable, depends on scoring rate, on strength variation and on score dependence. Score dependence is essentially the tendency for scores to alternate because possession alternates and possession is advantageous. We regard competitive balance as lack of variation in strength or skill, so that when strength variation is large competitive balance is low and vice versa. Thus, we argue that the outcome of a contest depends on skill, scoring rate, score dependence and chance. This description of outcome is useful because it informs policy-making in sport about the design of scoring systems and the control of competitive imbalance. Broadly, we find that: soccer is relatively competitively unbalanced but outcomes are uncertain because the scoring rate is low; the Australian football league is competitively balanced and so outcomes are uncertain in spite of the high scoring rate in this sport; international rugby matches are relatively neither competitive nor uncertain so that little is left to chance; and netball matches have uncertain outcomes because scores are positively dependent

Planning the restoration of membranes in RO desalination using a digital twin

This paper describes the development of a decision support system (DSS) for evaluating membrane restoration strategy. The engine of the DSS is a digital twin (DT), a virtual representation of wear (degradation) and restoration of membrane elements in a reverse osmosis (RO) pressure vessel. The basis of the DT is a mathematical model that describes an RO vessel as a novel multi-component system in which the wear-states of individual elements (components) are quantified and elements can be swapped or replaced. This contrasts with the contemporary presentation in the literature of a membrane system as a single system. We estimate the parameters of the model using statistical methods. We describe our approach in the context of a case study on the Carlsbad Desalination Plant in California, which suffers from biofouling due to seasonal algae blooms. Our results show a good fit between the observed and the modelled wear-states. Competing policies are compared based on risk, cost, downtime, and number of stoppages. Projections indicate that a significant cost-saving can be achieved while not compromising the integrity of plant

Modified age-based replacement

The maintenance policy of age-based replacement (ABR) is widely specified in OEM instructions. The practical application of ABR raises concerns about ensuring consistent adherence to prescribed replacement schedules for extended periods. ABR lacks periodicity, resulting in scheduling asynchrony with designated time slots, while alternative policies such as block replacement (BR) provide periodicity at the expense of efficiency. Additionally, scepticism about ABR is based on its simplicity and restrictive assumptions, which include ideal replacements and the one-component system assumption. The task of estimating component lifetime distributions and defining critical parameters such as cost of failure, which is an average cost with varying downtime, presents significant challenges. We study “modified age-based replacement” (MABR) in response to the limitation of periodicity, so that preventive replacements exhibit quasi-periodic behaviour. We quantify the cost-inefficiency of MABR compared to ABR, thus informing the practical implications of introducing periodicity into the ABR policy and highlighting the need to incorporate real-world constraints, such as time slots for maintenance actions. The findings indicate that MABR and a special case are reasonably efficient provided the slot-interval is not too large. This is a useful insight for practical application of ABR type policies for scheduling preventive maintenance

Planning maintenance when resources are limited: a study of periodic opportunistic replacement

We study an aged-based replacement policy with two control limits. The first triggers opportunistic replacement and the second triggers a guaranteed replacement. The policy is novel because: the instances for component replacement are restricted to instances of time, which we call slots, that arise periodically; and a slot provides an opportunity for replacement with a particular probability. The policy models contexts in which maintenance is periodic, and resources are limited or execution of maintenance is not guaranteed. The policy is important for practice because it is simple and reflects the common reality of time-based maintenance planning. Long-run cost per unit time and average availability are calculated in a renewal-reward framework. Numerical study indicates that, if opportunities are rare, guaranteed replacement is beneficial and opportunities should be taken early in the life of a system. Using the policy, a maintainer can evaluate the cost-benefit of investing more resources to reduce the time between slots. Specific analysis and policy comparisons can be carried out using a web-application developed by the authors

Joint maintenance-inventory optimisation of parallel production systems

We model a joint inspection and spare parts inventory policy for maintaining machines in a parallel system, where simultaneous downtime seriously impacts upon production performance and has a significant financial consequence. This dependency between system components means that analysis of realistic maintenance models is intractable. Therefore we use simulation and a numerical optimisation tool to study the cost-optimality of several policies. Inspection maintenance is modelled using the delay-time concept. Critical spare parts replenishment is considered using several variants of a periodic review policy. In particular, our results indicate that the cost-optimal policy is characterised by equal frequencies of inspection and replenishment, and delivery of spare parts that coincides with maintenance intervention. In general, our model provides a framework for studying the interaction of spare parts ordering with maintenance scheduling. The sensitivity analysis that we present offers insights for the effective management of such parallel systems, not only in a paper-making plant, which motivates our modelling development, but also in other manufacturing contexts

Sprint data

Data for modelling strategy in the track sprint. Numerical coding of videos of the track sprint, and derived data. Analysis published in Moffatt and Scarf (2016) "Sequential regression measurement error models with application", <i>Statistical Modelling (in press).</i