The effect of skewness on estimates of some process capability indices |
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| Affiliation: | 1. Department of Obstetrics and Gynecology, Strasbourg Teaching Hospital, France;2. UMR-S 1121 Inserm, “Biomatériaux et Bioingénierie”, Strasbourg, France;3. Department of Pediatrics, Strasbourg Teaching Hospital, France;4. Department of Obstetrics and Gynecology, Hospital of Haguenau, France;5. Department of Pediatrics, Hospital of Haguenau, France;6. Department of Public Health, Strasbourg Teaching Hospital, France;7. Department of Obstetrics and Gynecology, Toulouse Teaching Hospital, France;1. Service de chirurgie plastique centre hospitalier Saint-Joseph-Saint-Luc, 20, Quai-Claude-Bernard, 69365 Lyon cedex 7, France;2. Laboratoire d’anatomie de l’université Claude-Bernard Lyon 1, 8, avenue Rockefeller, 69008 Lyon, France;3. Department of Plastic-Reconstructive and Aesthetic Surgery, University of Lyon UCBL1, hospices civils de Lyon, 103, grand rue de la Croix-Rousse, 69004 Lyon, France;1. Department of Neurological Surgery, University of Virginia, Charlottesville, Virginia;2. Department of Radiation Oncology, University of Virginia, Charlottesville, Virginia;3. Department of Internal Medicine, University of Virginia, Charlottesville, Virginia;4. Division of Neuropathology, University of Virginia, Charlottesville, Virginia;1. University of Oxford and Retired Consultant Maxillofacial Surgeon, UK;2. Evidence-Based Practice Research Centre (EPRC), Faculty of Health, Edge Hill University, St Helens Road, Ormskirk, L39 4QP, UK;3. Consultant Regional Maxillofacial Unit, University Hospital Aintree, Liverpool, L9 1AE, UK;4. Nuffield Department of Primary Care Health Sciences, University of Oxford, UK |
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| Abstract: | The use of process capability indices, which are statistical measures of process capability, is based on several assumptions. For instance, the process monitored is supposed to be stable and the process output should be approximately normally distributed. These assumptions are not always fulfilled in practice. This article focuses on the problem when the process monitored has an output which is non-normally distributed. After presenting a short literature review on research concerning process capability indices and non-normal distributions, the effect of skewness on estimates of process capability indices is studied using a simulation study based on lognormally distributed process outputs. It is found that the effect of skewness is relatively systematic. From the study it is clear that the effect of skewness on estimates of process capability indices is so severe that it has to be considered when studying the capability of a process. Otherwise, erroneous decisions might be made when improving the process studied. It is suggested that further research, for instance, focusing on correction-factors to use when the process output has different skew shapes might be meaningful. However, research focusing on totally new ways of estimating process capability is primarily encouraged. |
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