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Statistical Process Control in Count Time Series Models : 계수 시계열 모형에서 통계적 공정 관리
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 이상열 | - |
| dc.contributor.author | 김한울 | - |
| dc.date.accessioned | 2018-11-12T01:00:12Z | - |
| dc.date.available | 2018-11-12T01:00:12Z | - |
| dc.date.issued | 2018-08 | - |
| dc.identifier.other | 000000151978 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/143272 | - |
| dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 자연과학대학 통계학과, 2018. 8. 이상열. | - |
| dc.description.abstract | This thesis consider cumulative sum (CUSUM) charts based statistical process control (SPC) in count time series. Time series of counts have gained much attention in recent years in diverse fields such as manufacturing process, communication, queueing systems, medical science, crime and insurance. First, we considers the first-order integer-valued autoregressive (INAR) process with Katz family innovations to include a broad class of INAR(1) processes featuring equi-, over-, and under-dispersion. Its probabilistic properties such as ergodicity and stationarity are investigated. Further, a SPC procedure based on the CUSUM control chart is considered to monitor autocorrelated count processes. The CUSUM-type test statistic with conditional least square (CLS) and squared difference (SD) estimator for the PINAR(1) model and its application to the diagnostic of control chart are also investigated. Also, we propose an upper one-sided CUSUM-type chart based on the considered CUSUM statistic for an effective detection and a change point estimation. For enhanced monitoring Markov counting process with excessive zeros. we consider three control charts, namely cumulative sum (CUSUM) chart with a delay rule (CUSUM-DR), conforming run length (CRL)-CUSUM chart, and the combined Shewhart CRL-CUSUM chart. Moreover, for an easy implementation of the attribute
fixed sampling interval (FSI) and variable sampling internal (VSI) CUSUM control charts, an R package, attrCUSUM, is developed. | - |
| dc.description.tableofcontents | 1 Introduction 1
2 Reviews 7 2.1 Integer-valued autoregressive (INAR) models 7 2.2 CUSUM control chart 10 3 On First-order Integer-valued Autoregressive Process with Katz Family Innovations 13 3.1 Introduction 13 3.2 INAR(1) process with Katz innovations 14 3.3 Parameter estimation and real example 19 3.4 CUSUM chart to monitor a mean increase 24 3.5 Proofs 32 3.6 Concluding remarks 37 4 Improved CUSUM monitoring of Markov counting process with frequent zeros 38 4.1 Introduction 38 4.2 Modeling zero-inflated Markov counting process 40 4.2.1 Zero-inflated Poisson INAR(1) model 40 4.2.2 Zero-inflated Poisson INARCH(1) model 43 4.2.3 Some commonly required properties 44 4.3 Control chart for zero-inflated Markov counting process 47 4.4 Performance evaluation 52 4.5 A real data example 62 4.6 Concluding remarks 65 4.7 Appendix A. ARL computation for CUSUM-DR chart 68 4.8 Appendix B. ATS computation for CRL-CUSUM chart 69 5 Monitoring Mean Shift in INAR(1)s Processes based on CLSE-CUSUM Procedure 74 5.1 Introduction 74 5.2 Higher moments and CLSE-based CUSUM test 76 5.3 Monitoring mean shift using CLSE-CUSUM scheme 81 5.4 Performance comparison 85 5.5 A real data example 90 5.6 Proof of Proposition 5.2.1 93 5.7 Concluding remarks 94 6 On Residual CUSUM Statistic for PINAR(1) Model in Statistical Design and Diagnostic of Control Chart 95 6.1 Introduction 95 6.2 PINAR(1) process 97 6.3 Change point test based on SD estimator 100 6.4 Anomaly detection and post-signal diagnostic 107 6.5 Proofs 121 6.6 Concluding remarks 126 7 On the VSI CUSUM Chart for Count Processes and its Implementation with R Package attrCUSUM 128 7.1 Introduction 128 7.2 The zero-inflated model for count data 130 7.3 FSI and VSI control scheme for ZIB process 132 7.3.1 CUSUM control statistic for ZIB process 132 7.3.2 The Markov chain approach for CUSUM control chart 137 7.4 Effects of the VSI CUSUM control scheme in ZIB process 140 7.5 Software 144 7.5.1 Examples of usage with zero inflated binomial process 144 7.5.2 Other count models 148 7.6 Concluding remarks 152 | - |
| dc.language.iso | en | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject.ddc | 519.5 | - |
| dc.title | Statistical Process Control in Count Time Series Models | - |
| dc.title.alternative | 계수 시계열 모형에서 통계적 공정 관리 | - |
| dc.type | Thesis | - |
| dc.contributor.AlternativeAuthor | Hanwool Kim | - |
| dc.description.degree | Doctor | - |
| dc.contributor.affiliation | 자연과학대학 통계학과 | - |
| dc.date.awarded | 2018-08 | - |
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