### Abstract

This paper seeks to analyze the imprecision associated with the statistical modelling method employed in devising a predictive maintenance framework on a plasma etching chamber. During operations, the plasma etching chamber may fail due to contamination as a result of a high number of particles that is present. Based on a study done, the particle count is observed to follow a Negative Binomial distribution model and it is also used to model the probability of failure of the chamber. Using this model, an optimum threshold failure probability is determined in which maintenance is scheduled once this value is reached during the operation of the chamber and that the maintenance cost incurred is the lowest. One problem however is that the parameter(s) used to define the Negative Binomial distribution may have uncertainties associated with it in reality and this eventually gives rise to uncertainty in deciding the optimum threshold failure probability. To address this, the paper adopts the use of Confidence structures (or C-boxes) in quantifying the uncertainty of the optimum threshold failure probability. This is achieved by introducing some variations in the p-parameter of the Negative Binomial distribution and then plotting a series of Cost-rate vs threshold failure probability curves. Using the information provided in these curves, empirical cumulative distribution functions are constructed for the possible upper and lower bounds of the threshold failure probability and from there, the confidence interval for the aforementioned quantity will be determined at 50%, 80%, and 95% confidence level.

Original language | English |
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Title of host publication | Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019 |

Editors | M. Papadrakakis, V. Papadopoulos, G. Stefanou |

Place of Publication | Athens |

Pages | 620-628 |

Number of pages | 9 |

DOIs | |

Publication status | Published - 24 Jun 2019 |

Event | 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering - Crete, Greece Duration: 24 Jun 2019 → 26 Jun 2019 |

### Conference

Conference | 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering |
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Abbreviated title | UNCECOMP 2019 |

Country | Greece |

City | Crete |

Period | 24/06/19 → 26/06/19 |

### Keywords

- confidence structures
- maintenance cost
- negative binomial distribution
- optimization
- plasma etching
- predictive maintenance
- uncertainty quantification

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## Cite this

*Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019*(pp. 620-628). https://doi.org/10.7712/120219.6364.18502