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Evaluating Six Sigma failure rate for inverse Gaussian cycle times

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  • Mustapha Nourelfath
  • Tariq Aldowaisan
  • Jawad Hassan

Abstract

Six Sigma is a quality philosophy and methodology that aims to achieve operational excellence and delighted customers. The cost of poor quality depends on the sigma quality level and its corresponding failure rate. Six Sigma provides a well-defined target of 3.4 defects per million. This failure rate is commonly evaluated under the assumption that the process is normally distributed and its specifications are two-sided. However, these assumptions may lead to implementation of quality-improvement strategies that are based on inaccurate evaluations of quality costs and profits. This paper defines the relationship between failure rate and sigma quality level for inverse Gaussian processes. The inverse Gaussian distribution has considerable applications in describing cycle times, product life, employee service times, and so on. We show that for these processes attaining Six Sigma target failure rate requires higher quality efforts than for normal processes. A generic model is presented to characterise cycle times in manufacturing systems. In this model, the asymptotic production is described by a drifted Brownian motion, and the cycle time is evaluated by using the first passage time theory of a Wiener process to a boundary. The proposed method estimates the right efforts required to reach Six Sigma goals.

Suggested Citation

  • Mustapha Nourelfath & Tariq Aldowaisan & Jawad Hassan, 2016. "Evaluating Six Sigma failure rate for inverse Gaussian cycle times," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6092-6101, October.
  • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:20:p:6092-6101
    DOI: 10.1080/00207543.2016.1190880
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    References listed on IDEAS

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    1. Nourelfath, Mustapha & Hassan, Jawad, 2015. "Six Sigma performance for non-normal processesAuthor-Name: Aldowaisan, Tariq," European Journal of Operational Research, Elsevier, vol. 247(3), pages 968-977.
    2. Chen, Huifen & Chang, Kuo-Hwa & Cheng, Liuying, 2004. "Estimation of means and covariances of inverse-Gaussian order statistics," European Journal of Operational Research, Elsevier, vol. 155(1), pages 154-169, May.
    3. Kumar, U. Dinesh & Nowicki, David & Ramirez-Marquez, Jose Emmanuel & Verma, Dinesh, 2008. "On the optimal selection of process alternatives in a Six Sigma implementation," International Journal of Production Economics, Elsevier, vol. 111(2), pages 456-467, February.
    4. Saghaei, Abbas & Najafi, Hoorieh & Noorossana, Rassoul, 2012. "Enhanced Rolled Throughput Yield: A new six sigma-based performance measure," International Journal of Production Economics, Elsevier, vol. 140(1), pages 368-373.
    5. Hsu, Ya-Chen & Pearn, W.L. & Wu, Pei-Ching, 2008. "Capability adjustment for gamma processes with mean shift consideration in implementing Six Sigma program," European Journal of Operational Research, Elsevier, vol. 191(2), pages 517-529, December.
    6. Nourelfath, Mustapha, 2011. "Service level robustness in stochastic production planning under random machine breakdowns," European Journal of Operational Research, Elsevier, vol. 212(1), pages 81-88, July.
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    Cited by:

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