scholarly journals A study on continuous inspection of markov processs with a clearance interval

10.26524/cm77 ◽  
2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Govindarajan P ◽  
Jayaraman R
Keyword(s):  
Markov Chain ◽  
Correlation Coefficient ◽  
Serial Correlation ◽  
A Priori ◽  
Sampling Plan ◽  
Continuous Sampling ◽  
Clearance Interval ◽  
Serial Correlation Coefficient

Dodge’s continuous sampling plan-1 (CSP-1) with clearance interval zero may be inefficient if there is serial correlation between successive units which are Markov dependent and a clearance interval greater than zero is appropriate. For such a situation, the average outgoing quality limit (AOQL) expression has been obtained and, when the serial correlation coefficient of the Markov chain is assumed to be known a priori, it is numerically demonstrated that smaller AOQL values are achieved numerically for values of the clearance interval from 1 to 4, by improving the performance of CSP-1.

A queueing system with Markov-dependent arrivals

1985 ◽  
Vol 22 (03) ◽  
pp. 668-677 ◽  
Author(s):  
Pyke Tin
Keyword(s):  
Special Reference ◽  
Correlation Coefficient ◽  
Waiting Time ◽  
Serial Correlation ◽  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Queue Size ◽  
Interarrival Times ◽  
Serial Correlation Coefficient

This paper considers a single-server queueing system with Markov-dependent interarrival times, with special reference to the serial correlation coefficient of the arrival process. The queue size and waiting-time processes are investigated. Both transient and limiting results are given.

On the serial correlation for number in system in the stationary GI/M/1 bulk arrival and GI/Em/1 queues

1992 ◽  
Vol 29 (2) ◽  
pp. 404-417
Author(s):  
D. A. Stanford ◽  
B. Pagurek
Keyword(s):  
Correlation Coefficient ◽  
Generating Functions ◽  
Serial Correlation ◽  
Correlation Coefficients ◽  
Numerical Examples ◽  
Bulk Arrival ◽  
Serial Correlation Coefficient ◽  
Infinite Sum

The generating functions for the serial covariances for number in system in the stationary GI/M/1 bulk arrival queue with fixed bulk sizes, and the GI/Em/1 queue, are derived. Expressions for the infinite sum of the serial correlation coefficients are also presented, as well as the first serial correlation coefficient in the case of the bulk arrival queue. Several numerical examples are considered.

scholarly journals The Continuous Sampling Plan for Two Production Lines: The CSP-2L

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Markov Chain ◽  
Performance Measures ◽  
Sampling Plan ◽  
Production Lines ◽  
Continuous Sampling ◽  
Sampling Inspection ◽  
Sampling Fraction ◽  
Total Fraction ◽  
High Level

This paper presents the CSP-2L continuous sampling plan, which is designed for product inspectionon two independent production lines at the same time. The purpose of the CSP-2L is to improve the CSP-1-2Lin order to reduce the number of defective products that have passed without being inspected during thetemporary inspection stop, so the quality of the products is better. Therefore, if the manufacturer who uses theCSP-2L plan to inspect the production lines then resulting in higher quality of the products than the CSP-1-2L.This presentation includes the product inspection procedures and the formulas for performance measures suchas average total fraction inspected (ATFI), average total outgoing quality (ATOQ), and average total outgoingquality limit (ATOQL) which are carried out using a Markov chain. The formulas for performance measures ofthe CSP-2L have been tested to be accurate. When defined, the probability of a unit produced by the processbeing nonconforming of line 1 and line 2 are equal (p1 = p2 = p = 0.005, 0.015 and 0.035), the clearance numberof line 1 and line 2 are equal (i1 = i2 = 10, 20, 30, 40 and 50), the sampling fraction of line 1 and line 2 are equal(f1 = f2 =12and13) and the number of units to be found when inspection of line 1 and line 2 are in the phaseof sampling inspection at the same time (m = i1 and 2i1). Moreover, the ATOQ values from the CSP-2L and theCSP-1-2L plans were compared. The results showed that, the formulas for performance measures are accurateand in the case of p, the levels are low and moderate, the ATOQ of the CSP-2L are less than those of theCSP-1-2L in all cases. But in the case of p is at a high level, the ATOQ of the CSP-2L is less than those of theCSP-1-2L for some cases of i.

scholarly journals Interspike interval correlations in neuron models with adaptation and correlated noise

2021 ◽  
Vol 17 (8) ◽  
pp. e1009261
Author(s):  
Lukas Ramlow ◽  
Benjamin Lindner
Keyword(s):  
Correlation Coefficient ◽  
Serial Correlation ◽  
Colored Noise ◽  
Interspike Interval ◽  
Correlated Noise ◽  
Spike Frequency Adaptation ◽  
Noise Sources ◽  
Integrate And Fire ◽  
Weak Noise ◽  
Serial Correlation Coefficient

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel’s time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

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