scholarly journals Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1997
Author(s):  
Vlad Stefan Barbu ◽  
Guglielmo D’Amico ◽  
Thomas Gkelsinis
Keyword(s):  
Discrete Time ◽  
Reliability Function ◽  
Asymptotic Result ◽  
Repairable Systems ◽  
Time Intervals ◽  
Reliability Measure ◽  
Interval Reliability ◽  
Transient Case ◽  
Limiting Behaviour ◽  
Recurrent Type

In this paper, a new reliability measure, named sequential interval reliability, is introduced for homogeneous semi-Markov repairable systems in discrete time. This measure is the probability that the system is working in a given sequence of non-overlapping time intervals. Many reliability measures are particular cases of this new reliability measure that we propose; this is the case for the interval reliability, the reliability function and the availability function. A recurrent-type formula is established for the calculation in the transient case and an asymptotic result determines its limiting behaviour. The results are illustrated by means of a numerical example which illustrates the possible application of the measure to real systems.

Performance Management

2009 ◽  
Author(s):  
Gary P. Latham ◽  
Lorne M. Sulsky ◽  
Heather MacDonald
Keyword(s):  
Job Performance ◽  
Performance Management ◽  
Performance Appraisal ◽  
Discrete Time ◽  
Time Intervals ◽  
Management Performance ◽  
Appraisal Process ◽  
Ongoing Process ◽  
Time Period ◽  
Or Team

A distinguishing feature of performance management relative to performance appraisal is that the former is an ongoing process whereas the latter is done at discrete time intervals (e.g. annually). Ongoing coaching is an integral aspect of performance management. Performance appraisal is the time period in which to summarize the overall progress that an individual or team has made as a result of being coached, and to agree on the new goals that should be set. Common to the performance management/appraisal process are the four following steps. First, desired job performance must be defined. Second, an individual's performance on the job must be observed. Is the person or team's performance excellent, superior, satisfactory, or unacceptable? Third, feedback is provided and specific challenging goals are set as to what the person or team should start doing, stop doing, or be doing differently. Fourth, a decision is made regarding retaining, rewarding, training, transferring, promoting, demoting, or terminating the employmemt of an individual.

CHAOS OF DYNAMICAL SYSTEMS ON GENERAL TIME DOMAINS

2009 ◽  
Vol 19 (11) ◽  
pp. 3829-3832
Author(s):  
ABRAHAM BOYARSKY ◽  
PAWEŁ GÓRA
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Chaotic Map ◽  
Discrete Time System ◽  
Combined System ◽  
Time Intervals ◽  
Time Dynamics ◽  
Time Component ◽  
Time Domains

We consider dynamical systems on time domains that alternate between continuous time intervals and discrete time intervals. The dynamics on the continuous portions may represent species growth when there is population overlap and are governed by differential or partial differential equations. The dynamics across the discrete time intervals are governed by a chaotic map and may represent population growth which is seasonal. We study the long term dynamics of this combined system. We study various conditions on the continuous time dynamics and discrete time dynamics that produce chaos and alternatively nonchaos for the combined system. When the discrete system alone is chaotic we provide a condition on the continuous dynamical component such that the combined system behaves chaotically. We also provide a condition that ensures that if the discrete time system has an absolutely continuous invariant measure so will the combined system. An example based on the logistic continuous time and logistic discrete time component is worked out.

The Reliability Analysis of Multi-Operation State Repairable System

2012 ◽  
Vol 184-185 ◽  
pp. 1608-1612
Author(s):  
Rui Meng Luo ◽  
Jin Yong Yao
Keyword(s):  
Steady State ◽  
Normal State ◽  
Mathematic Model ◽  
Inspection Time ◽  
Repairable Systems ◽  
Time Intervals ◽  
Abnormal State ◽  
Inspection Strategy ◽  
Fault State ◽  
Process Method

To describe precisely the performance characteristics of Markov repairable systems, the model of Markov repairable systems with multi-operating state was introduced. There are three kinds of states of the system: normal, abnormal and fault state. The system works when it is in the normal state and abnormal state, it stops to be mended till it is inspected and diagnosed in abnormal state or something wrong happens in it. Inspect it at intervals after it begins to work in the normal state until it is inspected and diagnosed in abnormal state or it fails. The life of the system, inspection time intervals and repairing time follow exponential distribution, we build the Markov mathematic model to the system. The steady-state reliability and the expression of steady-state yield are derived by using the Markov process method. The study of numerical examples has shown that optimal inspection strategy can increase the system economic effectiveness.

Reliability analysis of complex repairable systems by means of marked point processes

1980 ◽  
Vol 17 (1) ◽  
pp. 154-167 ◽  
Author(s):  
Peter Franken ◽  
Arnfried Streller
Keyword(s):  
Reliability Analysis ◽  
Point Processes ◽  
Marked Point ◽  
Regenerative Process ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
Repairable Systems ◽  
Interval Reliability ◽  
Repair Facility ◽  
Markovian Systems

Starting from the theory of point processes the concept of a process with an embedded marked point process is defined. It is shown that the known formula expressing the relation between the stationary and synchronous version of a regenerative process remains valid without the assumption of independence of cycles. General formulae for stationary availability and interval reliability of complex systems with repair are also obtained. In this way generalizations of Keilson's results for Markovian systems and Ross's results for systems with separately maintained elements are presented. The formulae are applied to a two-unit parallel system with a single repair facility.

Discretizors and Interpolators for Five-Axis CNC Machines

1999 ◽  
Vol 122 (1) ◽  
pp. 191-197 ◽  
Author(s):  
Radha Sarma ◽  
Aarthi Rao
Keyword(s):  
Discrete Time ◽  
Sampling Period ◽  
Cnc Machine ◽  
Time Intervals ◽  
New Techniques ◽  
Cnc Machines ◽  
Complex Curves ◽  
Computer Numerically Controlled ◽  
Five Axis

Discretization and interpolation of curves are two frequently adopted practices when machining complex curves using computer numerically controlled (CNC) machines. Both practices stem from the need to sample curves at discrete time intervals corresponding to the sampling period of the CNC machine. This paper proposes new techniques for discretization and interpolation that account for the change of tool orientations in five-axis machining. First, the method for discretization proposed in this paper is based on sampling the curves such that specified contour, feedrate, and orientation errors are not exceeded. Second, the interpolator proposed in this paper will be able to avoid excessive angular speeds arising from sampling the curves based on the feedrate alone. [S1087-1357(00)01401-5]

scholarly journals On the Embedding Problem for Discrete-Time Markov Chains

2013 ◽  
Vol 50 (04) ◽  
pp. 918-930 ◽  
Author(s):  
Marie-Anne Guerry
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Transition Matrix ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Embedding Problem ◽  
Time Intervals ◽  
Square Roots ◽  
Probability Matrices

When a discrete-time homogenous Markov chain is observed at time intervals that correspond to its time unit, then the transition probabilities of the chain can be estimated using known maximum likelihood estimators. In this paper we consider a situation when a Markov chain is observed on time intervals with length equal to twice the time unit of the Markov chain. The issue then arises of characterizing probability matrices whose square root(s) are also probability matrices. This characterization is referred to in the literature as the embedding problem for discrete time Markov chains. The probability matrix which has probability root(s) is called embeddable. In this paper for two-state Markov chains, necessary and sufficient conditions for embeddability are formulated and the probability square roots of the transition matrix are presented in analytic form. In finding conditions for the existence of probability square roots for (k x k) transition matrices, properties of row-normalized matrices are examined. Besides the existence of probability square roots, the uniqueness of these solutions is discussed: In the case of nonuniqueness, a procedure is introduced to identify a transition matrix that takes into account the specificity of the concrete context. In the case of nonexistence of a probability root, the concept of an approximate probability root is introduced as a solution of an optimization problem related to approximate nonnegative matrix factorization.

scholarly journals A Sensitivity-Based Approach for Reliability Analysis of Randomly Excited Structures With Interval Axial Stiffness

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Alba Sofi ◽  
Giuseppe Muscolino ◽  
Filippo Giunta
Keyword(s):  
Reliability Analysis ◽  
Interval Analysis ◽  
Structural Reliability ◽  
Reliability Function ◽  
Extreme Value ◽  
Axial Stiffness ◽  
Engineering Practice ◽  
Stress Process ◽  
Rational Series ◽  
Interval Reliability

Abstract Reliability assessment of linear discretized structures with interval parameters subjected to stationary Gaussian multicorrelated random excitation is addressed. The interval reliability function for the extreme value stress process is evaluated under the Poisson assumption of independent up-crossing of a critical threshold. Within the interval framework, the range of stress-related quantities may be significantly overestimated as a consequence of the so-called dependency phenomenon, which arises due to the inability of the classical interval analysis to treat multiple occurrences of the same interval variables as dependent ones. To limit undesirable conservatism in the context of interval reliability analysis, a novel sensitivity-based procedure relying on a combination of the interval rational series expansion and the improved interval analysis via extra unitary interval is proposed. This procedure allows us to detect suitable combinations of the endpoints of the uncertain parameters which yield accurate estimates of the lower bound and upper bound of the interval reliability function for the extreme value stress process. Furthermore, sensitivity analysis enables to identify the most influential parameters on structural reliability. A numerical application is presented to demonstrate the accuracy and efficiency of the proposed method as well as its usefulness in view of decision-making in engineering practice.

scholarly journals Reduction of auditory input improves performance on the heartbeat tracking task, but does not necessarily enhance interoception

2019 ◽  
Author(s):  
Jennifer Todd ◽  
Farah Hina ◽  
Jane E Aspell
Keyword(s):  
Discrete Time ◽  
Repeated Measures ◽  
Tracking Task ◽  
Auditory Input ◽  
Time Intervals ◽  
Non Invasive ◽  
Lower Baseline ◽  
Interoceptive Accuracy

Previous research utilising a between-subjects design has indicated that the use of noise-dampening ear-protectors might enhance interoceptive accuracy (IAcc). In the present study, we further examined this effect using a repeated-measures, within-participants design, and investigated potential mechanisms that might explain the effect. 50 participants completed the heartbeat tracking task (HTT) with and without the use of industrial ear-protectors, in a counter-balanced order. Participants were asked to count the number of heartbeats occurring in five discrete time intervals of 25, 35, 45, 55 and 95 seconds, without feeling for a manual pulse. HTT scores were significantly higher when ear-protectors were worn, and the improvement in performance was greatest for participants with lower baseline IAcc. The ear-protectors were associated with significantly increased self-reported heartbeat audibility, task-related confidence and concentration, and decreased levels of distractibility. Heartbeat audibility was also correlated with HTT performance when the ear-protectors were worn. Because the use of industrial ear defenders resulted in increased heartbeat audibility, this manipulation should not be used to assess causal hypotheses related to changes in IAcc. However, it may serve as a simple, non-invasive manipulation to assess the effects of externalised interoceptive signals.

scholarly journals Adjuvant nivolumab for stage III/IV melanoma: evaluation of safety outcomes and association with recurrence-free survival

2021 ◽  
Vol 9 (8) ◽  
pp. e003188
Author(s):  
Mario Mandalá ◽  
James Larkin ◽  
Paolo A Ascierto ◽  
Michele Del Vecchio ◽  
Helen Gogas ◽  
...  
Keyword(s):  
Discrete Time ◽  
Cox Model ◽  
Disease Recurrence ◽  
Phase Iii ◽  
Recurrence Free Survival ◽  
Time Intervals ◽  
Free Survival ◽  
Registration Number ◽  
First Occurrence ◽  
Resected Stage

BackgroundSeveral therapeutic options are now available in the adjuvant melanoma setting, mandating an understanding of their benefit‒risk profiles in order to make informed treatment decisions. Herein we characterize adjuvant nivolumab select (immune-related) treatment-related adverse events (TRAEs) and evaluate possible associations between safety and recurrence-free survival (RFS) in the phase III CheckMate 238 trial.MethodsPatients with resected stage IIIB–C or IV melanoma received nivolumab 3 mg/kg every 2 weeks (n=452) or ipilimumab 10 mg/kg every 3 weeks for four doses and then every 12 weeks (n=453) for up to 1 year or until disease recurrence, unacceptable toxicity, or consent withdrawal. First-occurrence and all-occurrence select TRAEs were analyzed within discrete time intervals: from 0 to 3 months of treatment, from >3–12 months of treatment, and from the last dose (regardless of early or per-protocol treatment discontinuation) to 100 days after the last dose. Possible associations between select TRAEs and RFS were investigated post randomization in 3-month landmark analyses and in Cox model analyses (including a time-varying covariate of select TRAE), within and between treatment groups.ResultsFrom the first nivolumab dose to 100 days after the last dose, first-occurrence select TRAEs were reported in 67.7% (306/452) of patients. First-occurrence select TRAEs were reported most frequently from 0 to 3 months (48.0%), during which the most common were pruritus (15.5%) and diarrhea (15.3%). Most select TRAEs resolved within 6 months. There was no clear association between the occurrence (or not) of select TRAEs and RFS by landmark analysis or by Cox model analysis within treatment arms or comparing nivolumab to the ipilimumab comparator arm.ConclusionResults of this safety analysis of nivolumab in adjuvant melanoma were consistent with its established safety profile. In the discrete time intervals evaluated, most first-occurrence TRAEs occurred early during treatment and resolved. No association between RFS and select TRAEs was evident.Trial registration numberNCT02388906.

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