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All Journal Journal of Mathematics and Scientific Computing With Applications
Roder, Klause
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Mathematics

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APPLICATION OF SIX SIGMA METHOD TO REDUCE DEFECT RATE IN BREAD PRODUCTION Ikhsan Nurrobbil, Damar; Roder, Klause
Journal of Mathematics and Scientific Computing With Applications Vol. 5 No. 2 (2024)
Publisher : Pena Cendekia Insani

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.53806/jmscowa.v5i2.983

Abstract

This research discusses the application of the Six Sigma method with the DMAIC approach to reduce the defect rate of bread products at Fadillah Bakery. Through seven days of observation, 248 defective products were found from 2.100 samples with an average Defect Per Million Opportunities (DPMO) of 118.095,2 and asigma level of 2,19. The analysis showed that the factors causing product defects include human error (lack of training and accuracy), non-optimal work methods, and improper roasting machine settings. The proposed improvement measures include increased worker training, scheduling machine maintenance, and stricter supervision. The proposed improvement measures included increased worker training, scheduling machine maintenance, and stricter supervision. The results prove that the implementation of Six Sigma is effective in reducing defect rates, improving product quality, and production process efficiency. Continued implementation is expected to improve Fadillah Bakery's competitiveness and customer satisfaction of Fadillah Bakery.
APPLICATION OF SIX SIGMA METHOD TO REDUCE DEFECT RATE IN BREAD PRODUCTION Ikhsan Nurrobbil, Damar; Roder, Klause
Journal of Mathematics and Scientific Computing With Applications Vol. 5 No. 2 (2024)
Publisher : Pena Cendekia Insani

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.53806/jmscowa.v5i2.983

Abstract

This research discusses the application of the Six Sigma method with the DMAIC approach to reduce the defect rate of bread products at Fadillah Bakery. Through seven days of observation, 248 defective products were found from 2.100 samples with an average Defect Per Million Opportunities (DPMO) of 118.095,2 and asigma level of 2,19. The analysis showed that the factors causing product defects include human error (lack of training and accuracy), non-optimal work methods, and improper roasting machine settings. The proposed improvement measures include increased worker training, scheduling machine maintenance, and stricter supervision. The proposed improvement measures included increased worker training, scheduling machine maintenance, and stricter supervision. The results prove that the implementation of Six Sigma is effective in reducing defect rates, improving product quality, and production process efficiency. Continued implementation is expected to improve Fadillah Bakery's competitiveness and customer satisfaction of Fadillah Bakery.
GRAPH INTERPRETATION OF IRREDUCIBLE, REDUCIBLE, PERIODIC, AND APERIODIC PROPERTIES IN MARKOV CHAINS Suci Rachmadini, Haliza; Muhammad, Faisal; Roder, Klause
Journal of Mathematics and Scientific Computing With Applications Vol. 6 No. 2 (2025)
Publisher : Pena Cendekia Insani

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.53806/jmscowa.v6i2.1331

Abstract

Markov chains are widely used stochastic models for describing dynamic systems whose future states depend only on short-term probabilistic transitions. Key structural properties irreducibility, reducibility, periodicity, and aperiodicity are crucial for understanding long-term behavior, particularly the existence and stability of stationary distributions. Traditionally, these characteristics are determined through analysis of the transition probability matrix; however, this approach can be computationally demanding and difficult to interpret for large systems. This study explores an alternative representation using directed graphs, where each state is modeled as a node and each positive transition probability as a directed edge. The approach connects irreducibility with strong graph connectivity, while reducibility corresponds to the presence of separate communication classes. Periodicity and aperiodicity are identified through the structure of cycles and the greatest common divisor of return path lengths. The results demonstrate that graph-based analysis provides clearer and more intuitive framework for examining structural properties of Markov chains.
Co-Authors Faisal Muhammad, Faisal Ikhsan Nurrobbil, Damar Suci Rachmadini, Haliza