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One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations
Joint Authors
Shongwe, S. C.
Malela-Majika, J.-C.
Rapoo, E. M.
Source
Journal of Probability and Statistics
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-02-19
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
The one-sided and two-sided Shewhart w-of-w standard and improved runs-rules monitoring schemes to monitor the mean of normally distributed observations from independent and identically distributed (iid) samples are investigated from an overall performance perspective, i.e., the expected weighted run-length (EWRL), for every possible positive integer value of w.
The main objective of this work is to use the Markov chain methodology to formulate a theoretical unified approach of designing and evaluating Shewhart w-of-w standard and improved runs-rules for one-sided and two-sided X- schemes in both the zero-state and steady-state modes.
Consequently, the main findings of this paper are as follows: (i) the zero-state and steady-state ARL and initial probability vectors of some of the one-sided and two-sided Shewhart w-of-w standard and improved runs-rules schemes are theoretically similar in design; however, their empirical performances are different and (ii) unlike previous studies that use ARL only, we base our recommendations using the zero-state and steady-state EWRL metrics and we observe that the steady-state improved runs-rules schemes tend to yield better performance than the other considered competing schemes, separately, for one-sided and two-sided schemes.
Finally, the zero-state and steady-state unified approach run-length equations derived here can easily be used to evaluate other monitoring schemes based on a variety of parametric and nonparametric distributions.
American Psychological Association (APA)
Shongwe, S. C.& Malela-Majika, J.-C.& Rapoo, E. M.. 2019. One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations. Journal of Probability and Statistics،Vol. 2019, no. 2019, pp.1-20.
https://search.emarefa.net/detail/BIM-1186856
Modern Language Association (MLA)
Shongwe, S. C.…[et al.]. One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations. Journal of Probability and Statistics No. 2019 (2019), pp.1-20.
https://search.emarefa.net/detail/BIM-1186856
American Medical Association (AMA)
Shongwe, S. C.& Malela-Majika, J.-C.& Rapoo, E. M.. One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations. Journal of Probability and Statistics. 2019. Vol. 2019, no. 2019, pp.1-20.
https://search.emarefa.net/detail/BIM-1186856
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186856