New Bounds for All Types of Multi-state Consecutive <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Out-of-<inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-From-<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>: F System Reliability
A multi-state consecutive k-out-of-r-from-n: F system (named MS C(k,r,n:F)) comprises of n linearly ordered components. The MS C(k,r,n:F) and its components have more than 2 states: 0, 1,<sub>⋯</sub>,H. The state of MS C(k, r, n:F) is less than j if any r consecutive component...
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8915841/ |
| _version_ | 1818621655549739008 |
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| author | Taha Radwan |
| author_facet | Taha Radwan |
| author_sort | Taha Radwan |
| collection | DOAJ |
| description | A multi-state consecutive k-out-of-r-from-n: F system (named MS C(k,r,n:F)) comprises of n linearly ordered components. The MS C(k,r,n:F) and its components have more than 2 states: 0, 1,<sub>⋯</sub>,H. The state of MS C(k, r, n:F) is less than j if any r consecutive components contains k<sub>l</sub> or more, for all j ≤ l ≤ H. This system is a model for a large number of applications. The existing methods for system-reliability evaluation are suitable for some special cases only. In this paper, we suggest bounds for MS C(k, r, n:F) reliability. These bounds are suitable for all system types whether in case of equal or unequal components probabilities. The suggested bounds are examined by previously published examples, when available. Also, illustration examples for the new bounds and system modelling are presented. Furthermore, we studied the cases that make the proposed bounds are sharp. |
| first_indexed | 2024-12-16T18:12:44Z |
| format | Article |
| id | doaj.art-806a95b929ab4f69b46e07224d09bfb6 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T18:12:44Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-806a95b929ab4f69b46e07224d09bfb62022-12-21T22:21:43ZengIEEEIEEE Access2169-35362019-01-01717256217257010.1109/ACCESS.2019.29562928915841New Bounds for All Types of Multi-state Consecutive <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Out-of-<inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-From-<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>: F System ReliabilityTaha Radwan0https://orcid.org/0000-0003-1466-8821Department of Mathematics, College of Sciences and Arts at Al-Rass, Qassim University, Buraydah, Saudi ArabiaA multi-state consecutive k-out-of-r-from-n: F system (named MS C(k,r,n:F)) comprises of n linearly ordered components. The MS C(k,r,n:F) and its components have more than 2 states: 0, 1,<sub>⋯</sub>,H. The state of MS C(k, r, n:F) is less than j if any r consecutive components contains k<sub>l</sub> or more, for all j ≤ l ≤ H. This system is a model for a large number of applications. The existing methods for system-reliability evaluation are suitable for some special cases only. In this paper, we suggest bounds for MS C(k, r, n:F) reliability. These bounds are suitable for all system types whether in case of equal or unequal components probabilities. The suggested bounds are examined by previously published examples, when available. Also, illustration examples for the new bounds and system modelling are presented. Furthermore, we studied the cases that make the proposed bounds are sharp.https://ieeexplore.ieee.org/document/8915841/Boole-Bonferroni boundsupper bound of hunter-worsleymulti-state consecutive <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">k</italic>-out-of-<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">r</italic>-from-<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">n</italic>: F systemsystem reliability |
| spellingShingle | Taha Radwan New Bounds for All Types of Multi-state Consecutive <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Out-of-<inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-From-<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>: F System Reliability IEEE Access Boole-Bonferroni bounds upper bound of hunter-worsley multi-state consecutive <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">k</italic>-out-of-<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">r</italic>-from-<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">n</italic>: F system system reliability |
| title | New Bounds for All Types of Multi-state Consecutive <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Out-of-<inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-From-<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>: F System Reliability |
| title_full | New Bounds for All Types of Multi-state Consecutive <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Out-of-<inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-From-<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>: F System Reliability |
| title_fullStr | New Bounds for All Types of Multi-state Consecutive <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Out-of-<inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-From-<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>: F System Reliability |
| title_full_unstemmed | New Bounds for All Types of Multi-state Consecutive <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Out-of-<inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-From-<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>: F System Reliability |
| title_short | New Bounds for All Types of Multi-state Consecutive <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Out-of-<inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-From-<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>: F System Reliability |
| title_sort | new bounds for all types of multi state consecutive inline formula tex math notation latex k tex math inline formula out of inline formula tex math notation latex r tex math inline formula from inline formula tex math notation latex n tex math inline formula f system reliability |
| topic | Boole-Bonferroni bounds upper bound of hunter-worsley multi-state consecutive <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">k</italic>-out-of-<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">r</italic>-from-<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">n</italic>: F system system reliability |
| url | https://ieeexplore.ieee.org/document/8915841/ |
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