Capability adjustment for gamma processes with mean shift consideration in implementing Six Sigma program

In the 1980s, Motorola, Inc. introduced its Six Sigma quality program to the world. Some quality practitioners questioned why the Six Sigma advocates claim it is necessary to add a 1.5 σ shift to the process mean when estimating process capability. Bothe [Bothe, D.R., 2002. Statistical reason for th...

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Bibliographic Details
Published in:European journal of operational research 2008-12, Vol.191 (2), p.517-529
Main Authors: Hsu, Ya-Chen, Pearn, W.L., Wu, Pei-Ching
Format: Article
Language:English
Subjects:
Applied sciences
Control charts
Dynamic [formula omitted]
Exact sciences and technology
Firm modelling
Gamma distribution
Inventory control, production control. Distribution
Mean shift
Operational research and scientific management
Operational research. Management science
Operations research
Process capability index
Quality management
Six Sigma
Studies
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Summary:In the 1980s, Motorola, Inc. introduced its Six Sigma quality program to the world. Some quality practitioners questioned why the Six Sigma advocates claim it is necessary to add a 1.5 σ shift to the process mean when estimating process capability. Bothe [Bothe, D.R., 2002. Statistical reason for the 1.5 σ shift. Quality Engineering 14 (3), 479–487] provided a statistical reason for considering such a shift in the process mean for normal processes. In this paper, we consider gamma processes which cover a wide class of applications. For fixed sample size n, the detection power of the control chart can be computed. For small process mean shifts, it is beyond the control chart detection power, which results in overestimating process capability. To resolve the problem, we first examine Bothe’s approach and find the detection power is less than 0.5 when data comes from gamma distribution, showing that Bothe’s adjustments are inadequate when we have gamma processes. We then calculate adjustments under various sample sizes n and gamma parameter N, with power fixed to 0.5. At the end, we adjust the formula of process capability to accommodate those shifts which can not be detected. Consequently, our adjustments provide much more accurate capability calculation for gamma processes. For illustration purpose, an application example is presented.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2007.07.023