A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment ξ^*:={ξ1,x∈N,x∈ X}is a random field. We study the dependence relations between th...A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment ξ^*:={ξ1,x∈N,x∈ X}is a random field. We study the dependence relations between the environment and the original chain, especially the "feedback". Some equivalence theorems and law of large numbers are obtained.展开更多
Suppose {Xn} is a random walk in time-random environment with state space Z^d, |Xn| approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the r...Suppose {Xn} is a random walk in time-random environment with state space Z^d, |Xn| approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.展开更多
We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic accor...We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to supk,θmk,θ1, mk,θn→1 as k →∞, n→∞, infk,θmk,θ1.展开更多
After defining generating functions,this paper discusses their properties,and then provides a sufFcient and necessary condition for a finite property of the moments of first entrance time distributions of Markov chain...After defining generating functions,this paper discusses their properties,and then provides a sufFcient and necessary condition for a finite property of the moments of first entrance time distributions of Markov chains in random environments by generating functions.Finally,the paper obtains relevant conclusions of the moments of first entrance time distributions.展开更多
BACKGROUND: Disease recurrence is a main challenge in treatment of hepatocellular carcinoma (HCC). There is no generally accepted method for preventing recurrence of HCC after resection. OBJECTIVE: To compare the ...BACKGROUND: Disease recurrence is a main challenge in treatment of hepatocellular carcinoma (HCC). There is no generally accepted method for preventing recurrence of HCC after resection. OBJECTIVE: To compare the efficacy of a traditional herbal medicine (THM) regimen and transarterial chemoembolization (TACE) in preventing recurrence in post-resection patients with small HCC. DESIGN, SETTING, PARTICIPANTS AND INTERVENTIONS: This is a multicenter, open- label, randomized, controlled study, which was undertaken in five centers of China. A total of 379 patients who met the eligibility criteria and underwent randomization were enrolled in this trial. One hundred and eighty-eight patients were assigned to the THM group and received Cinobufacini injection and Jiedu Granule, and the other 191 patients were assigned to the TACE group and received one single course of TACE. MAIN OUTCOME MEASURES: Primary outcome measures were the annual recurrence rate and the time to recurrence. Incidence of adverse events was regarded as the secondary outcome measure. RESULTS: Among the 364 patients who were included in the intention-to-treat analysis, 67 patients of the THM group and 87 of the TACE group had recurrence, with a hazard ratio of 0.695 (P = 0.048). Median recurrence-free survival of the patients in the THM and TACE groups was 46.89 and 34.49 months, respectively. Recurrence rates at 1, 2 and 3 years were 17.7%, 33.0% and 43.5% for the THM group, and 28.8%, 42.5% and 54.0% for the TACE group, respectively (P = 0.026). Multivariate analysis indicated that the THM regimen had a big advantage for prolonging the recurrence-free survival. Adverse events were mild and abnormality of laboratory indices of the two groups were similar. CONCLUSION: In comparison with TACE therapy, the THM regimen was associated with diminished risk of recurrence of small-sized HCC after resection, with comparable adverse events. TRIAL REGISTRTION IDENTIFIER: This trial was registered in the Chinese Clinical Trial Registry with the identifier ChiCTR-TRC-07000033.展开更多
In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTR...In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...展开更多
The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary an...The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.展开更多
The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introd...The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment (CMBCRE) and multitype Markov branching chain in random environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.展开更多
To review the preventive approaches for recurrence after curative resection of hepatic metastases from colorectal carcinoma, we have summarized all available publications reporting randomized control trials (RCTs) cov...To review the preventive approaches for recurrence after curative resection of hepatic metastases from colorectal carcinoma, we have summarized all available publications reporting randomized control trials (RCTs) covered in PubMed. The treatment approaches presented above include adjuvant intrahepatic arterial infusion chemotherapy, systemic chemotherapy, neoadjuvant chemotherapy, and immunotherapy. Although no standard treatment has been established, several approaches present promising results, which are both effective and tolerable in post-hepatectomy patients. Intrahepatic arterial infusion chemotherapy should be regarded as effective and tolerable and it increases overall survival (OS) and disease free survival (DFS) of patients, while 5-fluorouracil-based systemic chemotherapy has not shown any significant survival benefit. Fortunately chemotherapy combined with hepatic arterial infusion and intravenous infusion has shown OS and DFS benefit in many researches. Few neoadjuvant RCT studies have been conducted to evaluate its effect on prolonging survivals although many retrospective studies and case reports are published in which unresectable colorectal liver metastases are downstaged and made resectable with neoadjuvant chemotherapy. Liver resection supplemented with immunotherapy is associated with optimal results; however, it is also questioned by others. In conclusion, several adjuvant approaches have been studied for their efficacy on recurrence after hepatectomy for liver metastases from colorectal cancer (CRC), but multi-centric RCT is still needed for further evaluation on their efficacy and systemic or local toxicities. In addition, new adjuvant treatment should be investigated to provide more effective and tolerable methods for the patients with resectable hepatic metastases from CRC.展开更多
This article is a continuation of[9].Based on the discussion of random Kolmogorov forward(backward)equations,for any given q-matrix in random environment, Q(θ)=(q(θ;x,y),x,y∈X),an infinite class of q-proces...This article is a continuation of[9].Based on the discussion of random Kolmogorov forward(backward)equations,for any given q-matrix in random environment, Q(θ)=(q(θ;x,y),x,y∈X),an infinite class of q-processes in random environments satisfying the random Kolmogorov forward(backward)equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward(backward)equation are constructed.展开更多
For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuo...For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.展开更多
The concepts of random Markov matrix, Markov branching chain in randomenvironment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE)are introduced. The properties of LFMBCRE and t...The concepts of random Markov matrix, Markov branching chain in randomenvironment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE)are introduced. The properties of LFMBCRE and the explicit formulas of momentsof MBCRE are given.展开更多
Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) ...Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) and describe the decay rates of the n-step transition probabilities.As applications,a large deviation principle for the sequence log Z_(n) is established,and related large deviations are also studied.展开更多
First of all, we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible, the relationship of recurrent and positive recurrent between two states is stu...First of all, we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible, the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible, for any two states in x, they have the same period.展开更多
In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with...In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.展开更多
The concepts of π-irreduciblity, recurrence and transience are introduced into the research field of Markov chains in random environments.That a π-irreducible chain must be either recurrent or transient is proved, a...The concepts of π-irreduciblity, recurrence and transience are introduced into the research field of Markov chains in random environments.That a π-irreducible chain must be either recurrent or transient is proved, a criterion is shown for recurrent Markov chains in double-infinite random environments, the existence of invariant measure of π-irreducible chains in double-infinite environments is discussed,and then Orey's open-questions are partially answered.展开更多
We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random env...We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.展开更多
We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the proce...We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξ n ) on ?+, and reproduce independently new particles according to a probability law p(ξ n ) on ?. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean E ξ Z(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.展开更多
This study proposed a new real-time manufacturing process monitoring method to monitor and detect process shifts in manufacturing operations.Since real-time production process monitoring is critical in today’s smart ...This study proposed a new real-time manufacturing process monitoring method to monitor and detect process shifts in manufacturing operations.Since real-time production process monitoring is critical in today’s smart manufacturing.The more robust the monitoring model,the more reliable a process is to be under control.In the past,many researchers have developed real-time monitoring methods to detect process shifts early.However,thesemethods have limitations in detecting process shifts as quickly as possible and handling various data volumes and varieties.In this paper,a robust monitoring model combining Gated Recurrent Unit(GRU)and Random Forest(RF)with Real-Time Contrast(RTC)called GRU-RF-RTC was proposed to detect process shifts rapidly.The effectiveness of the proposed GRU-RF-RTC model is first evaluated using multivariate normal and nonnormal distribution datasets.Then,to prove the applicability of the proposed model in a realmanufacturing setting,the model was evaluated using real-world normal and non-normal problems.The results demonstrate that the proposed GRU-RF-RTC outperforms other methods in detecting process shifts quickly with the lowest average out-of-control run length(ARL1)in all synthesis and real-world problems under normal and non-normal cases.The experiment results on real-world problems highlight the significance of the proposed GRU-RF-RTC model in modern manufacturing process monitoring applications.The result reveals that the proposed method improves the shift detection capability by 42.14%in normal and 43.64%in gamma distribution problems.展开更多
In this paper, we consider a bisexual Galton-Watson branching process whose offspring probability distribution is controlled by a random environment proccss. Some results for the probability generating functions assoc...In this paper, we consider a bisexual Galton-Watson branching process whose offspring probability distribution is controlled by a random environment proccss. Some results for the probability generating functions associated with the process are obtained and sufficient conditions for certain extinction and for non-certain extinction are established.展开更多
基金Supported by the National Natural Science Foundation of China (10371092)
文摘A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment ξ^*:={ξ1,x∈N,x∈ X}is a random field. We study the dependence relations between the environment and the original chain, especially the "feedback". Some equivalence theorems and law of large numbers are obtained.
基金Project supported by NNSF of China (10371092)Foundation of Wuhan University
文摘Suppose {Xn} is a random walk in time-random environment with state space Z^d, |Xn| approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.
基金supported by the National Natural Science Foundation of China (10771185,10926036)Zhejiang Provinicial Natural Science Foundation of China (Y6090172)
文摘We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to supk,θmk,θ1, mk,θn→1 as k →∞, n→∞, infk,θmk,θ1.
文摘After defining generating functions,this paper discusses their properties,and then provides a sufFcient and necessary condition for a finite property of the moments of first entrance time distributions of Markov chains in random environments by generating functions.Finally,the paper obtains relevant conclusions of the moments of first entrance time distributions.
基金Supported by a grant from the Ministry of Science and Technology of China (National Key Technology Research & Development Program, No. 2006BAI 04A06)
文摘BACKGROUND: Disease recurrence is a main challenge in treatment of hepatocellular carcinoma (HCC). There is no generally accepted method for preventing recurrence of HCC after resection. OBJECTIVE: To compare the efficacy of a traditional herbal medicine (THM) regimen and transarterial chemoembolization (TACE) in preventing recurrence in post-resection patients with small HCC. DESIGN, SETTING, PARTICIPANTS AND INTERVENTIONS: This is a multicenter, open- label, randomized, controlled study, which was undertaken in five centers of China. A total of 379 patients who met the eligibility criteria and underwent randomization were enrolled in this trial. One hundred and eighty-eight patients were assigned to the THM group and received Cinobufacini injection and Jiedu Granule, and the other 191 patients were assigned to the TACE group and received one single course of TACE. MAIN OUTCOME MEASURES: Primary outcome measures were the annual recurrence rate and the time to recurrence. Incidence of adverse events was regarded as the secondary outcome measure. RESULTS: Among the 364 patients who were included in the intention-to-treat analysis, 67 patients of the THM group and 87 of the TACE group had recurrence, with a hazard ratio of 0.695 (P = 0.048). Median recurrence-free survival of the patients in the THM and TACE groups was 46.89 and 34.49 months, respectively. Recurrence rates at 1, 2 and 3 years were 17.7%, 33.0% and 43.5% for the THM group, and 28.8%, 42.5% and 54.0% for the TACE group, respectively (P = 0.026). Multivariate analysis indicated that the THM regimen had a big advantage for prolonging the recurrence-free survival. Adverse events were mild and abnormality of laboratory indices of the two groups were similar. CONCLUSION: In comparison with TACE therapy, the THM regimen was associated with diminished risk of recurrence of small-sized HCC after resection, with comparable adverse events. TRIAL REGISTRTION IDENTIFIER: This trial was registered in the Chinese Clinical Trial Registry with the identifier ChiCTR-TRC-07000033.
基金Supported by the National Natural Science Foundation of China (10771185 and 10871200)
文摘In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...
文摘The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.
基金Project supported by the National Natural Science Foundation of China and the Foundation of Wuhan University
文摘The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment (CMBCRE) and multitype Markov branching chain in random environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.
文摘To review the preventive approaches for recurrence after curative resection of hepatic metastases from colorectal carcinoma, we have summarized all available publications reporting randomized control trials (RCTs) covered in PubMed. The treatment approaches presented above include adjuvant intrahepatic arterial infusion chemotherapy, systemic chemotherapy, neoadjuvant chemotherapy, and immunotherapy. Although no standard treatment has been established, several approaches present promising results, which are both effective and tolerable in post-hepatectomy patients. Intrahepatic arterial infusion chemotherapy should be regarded as effective and tolerable and it increases overall survival (OS) and disease free survival (DFS) of patients, while 5-fluorouracil-based systemic chemotherapy has not shown any significant survival benefit. Fortunately chemotherapy combined with hepatic arterial infusion and intravenous infusion has shown OS and DFS benefit in many researches. Few neoadjuvant RCT studies have been conducted to evaluate its effect on prolonging survivals although many retrospective studies and case reports are published in which unresectable colorectal liver metastases are downstaged and made resectable with neoadjuvant chemotherapy. Liver resection supplemented with immunotherapy is associated with optimal results; however, it is also questioned by others. In conclusion, several adjuvant approaches have been studied for their efficacy on recurrence after hepatectomy for liver metastases from colorectal cancer (CRC), but multi-centric RCT is still needed for further evaluation on their efficacy and systemic or local toxicities. In addition, new adjuvant treatment should be investigated to provide more effective and tolerable methods for the patients with resectable hepatic metastases from CRC.
基金the NNSF of China(10371092,10771185,10471148)the Foundation of Wuhan University
文摘This article is a continuation of[9].Based on the discussion of random Kolmogorov forward(backward)equations,for any given q-matrix in random environment, Q(θ)=(q(θ;x,y),x,y∈X),an infinite class of q-processes in random environments satisfying the random Kolmogorov forward(backward)equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward(backward)equation are constructed.
基金supported by the National Natural Science Foundation of China(11531001)
文摘For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.
文摘The concepts of random Markov matrix, Markov branching chain in randomenvironment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE)are introduced. The properties of LFMBCRE and the explicit formulas of momentsof MBCRE are given.
基金partially supported by the National Nature Science Foundation of China(11601286,11501146)。
文摘Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) and describe the decay rates of the n-step transition probabilities.As applications,a large deviation principle for the sequence log Z_(n) is established,and related large deviations are also studied.
基金Supported by the National Natural Science Foundation of China (10371092)the Foundation of Wuhan University
文摘First of all, we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible, the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible, for any two states in x, they have the same period.
文摘In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.
基金the Natural Science Foundation of Hunan Province (Grant No. 99JJY2001) Hunan Provincial Foundation for Young and Middleaged People (Grant No. 00JJEY2141) .
文摘The concepts of π-irreduciblity, recurrence and transience are introduced into the research field of Markov chains in random environments.That a π-irreducible chain must be either recurrent or transient is proved, a criterion is shown for recurrent Markov chains in double-infinite random environments, the existence of invariant measure of π-irreducible chains in double-infinite environments is discussed,and then Orey's open-questions are partially answered.
基金the National Natural Science Foundation of China (Grant Nos. 10271020,10471012)SRF for ROCS, SEM (Grant No. [2005]564)
文摘We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.
基金the National Natural Sciente Foundation of China (Grant Nos. 10771021, 10471012)Scientific Research Foundation for Returned Scholars, Ministry of Education of China (Grant No. [2005]564)
文摘We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξ n ) on ?+, and reproduce independently new particles according to a probability law p(ξ n ) on ?. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean E ξ Z(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.
基金support from the National Science and Technology Council of Taiwan(Contract Nos.111-2221 E-011081 and 111-2622-E-011019)the support from Intelligent Manufacturing Innovation Center(IMIC),National Taiwan University of Science and Technology(NTUST),Taipei,Taiwan,which is a Featured Areas Research Center in Higher Education Sprout Project of Ministry of Education(MOE),Taiwan(since 2023)was appreciatedWe also thank Wang Jhan Yang Charitable Trust Fund(Contract No.WJY 2020-HR-01)for its financial support.
文摘This study proposed a new real-time manufacturing process monitoring method to monitor and detect process shifts in manufacturing operations.Since real-time production process monitoring is critical in today’s smart manufacturing.The more robust the monitoring model,the more reliable a process is to be under control.In the past,many researchers have developed real-time monitoring methods to detect process shifts early.However,thesemethods have limitations in detecting process shifts as quickly as possible and handling various data volumes and varieties.In this paper,a robust monitoring model combining Gated Recurrent Unit(GRU)and Random Forest(RF)with Real-Time Contrast(RTC)called GRU-RF-RTC was proposed to detect process shifts rapidly.The effectiveness of the proposed GRU-RF-RTC model is first evaluated using multivariate normal and nonnormal distribution datasets.Then,to prove the applicability of the proposed model in a realmanufacturing setting,the model was evaluated using real-world normal and non-normal problems.The results demonstrate that the proposed GRU-RF-RTC outperforms other methods in detecting process shifts quickly with the lowest average out-of-control run length(ARL1)in all synthesis and real-world problems under normal and non-normal cases.The experiment results on real-world problems highlight the significance of the proposed GRU-RF-RTC model in modern manufacturing process monitoring applications.The result reveals that the proposed method improves the shift detection capability by 42.14%in normal and 43.64%in gamma distribution problems.
文摘In this paper, we consider a bisexual Galton-Watson branching process whose offspring probability distribution is controlled by a random environment proccss. Some results for the probability generating functions associated with the process are obtained and sufficient conditions for certain extinction and for non-certain extinction are established.