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- Albing, Malin
(författare)
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Contributions to process capability indices and plots
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis presents contributions within the field of process capability analysis. Process capability analysis deals with how to assess the capability of processes. Based on process capability analysis one can determine how the process performs relative to its product requirements or specifications. An important part within process capability analysis is the use of process capability indices. This thesis focuses on process capability indices and process capability plots. The thesis consists of six papers and a summary. The summary gives a background to the research area, a short overview of the six papers, and some suggestions for future research. The thesis summary also consists of some new results, not presented in any of the appended papers. In paper I, the frequency and use of process capability analysis, together with statistical process control and design of experiments, within Swedish companies hiring alumni students are investigated. We also investigate what motivates organisations to implement or not implement these statistical methods, and what is needed to increase the use. In papers II-III we generalize the ideas with process capability plots and propose two graphical methods, for deeming a process capable at a given significance level, when the studied quality characteristic is assumed to be normally distributed. In paper II we derive estimated process capability plots for the case when the specification interval is one-sided. In paper III we derive elliptical safety region plots for the process capability index Cpk and its one-sided correspondences. The proposed graphical methods are helpful to determine if it is the variability, the deviation from target, or both that need to be reduced to improve the capability. In papers IV-VI we propose a new class of process capability indices designed for the situation with an upper specification limit, a target value zero, and where the studied quality characteristic has a skewed, zero- bound distribution with a long tail towards large values. The proposed class of indices is simple and possesses properties desirable for process capability indices. The results in papers IV-VI are also valid for the situation with a target value, not equal to zero but equal to a natural lower limit of the quality characteristic. Three estimators of the proposed class of indices are studied and the asymptotic distributions of these estimators are derived. We also consider decision procedures, based on the estimated indices, suitable for deeming the process capability at a given significance level. The new results in the summary combines the ideas from paper II with the results in papers IV-VI and a graphical method for the class of indices proposed in IV-VI are derived.
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| 2. |
- Albing, Malin, et al.
(författare)
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Elliptical safety region plots for Cpk
- 2011
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Ingår i: Journal of Applied Statistics. - : Informa UK Limited. - 0266-4763 .- 1360-0532. ; 38:6, s. 1169-1187
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Tidskriftsartikel (refereegranskat)abstract
- The process capability index C pk is widely used when measuring the capability of a manufacturing process. A process is defined to be capable if the capability index exceeds a stated threshold value, e.g. C pk >4/3. This inequality can be expressed graphically using a process capability plot, which is a plot in the plane defined by the process mean and the process standard deviation, showing the region for a capable process. In the process capability plot, a safety region can be plotted to obtain a simple graphical decision rule to assess process capability at a given significance level. We consider safety regions to be used for the index C pk . Under the assumption of normality, we derive elliptical safety regions so that, using a random sample, conclusions about the process capability can be drawn at a given significance level. This simple graphical tool is helpful when trying to understand whether it is the variability, the deviation from target, or both that need to be reduced to improve the capability. Furthermore, using safety regions, several characteristics with different specification limits and different sample sizes can be monitored in the same plot. The proposed graphical decision rule is also investigated with respect to power.
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| 3. |
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| 4. |
- Albing, Malin
(författare)
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Process capability analysis with focus on indices for one-sided specification limits
- 2006
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis some aspects of process capability analysis are considered. Process capability analysis deals with how to assess the capability of manufacturing processes. Based on the process capability analysis one can determine how the process performs relative to its product requirements or specifications. An important part within process capability analysis is the use of process capability indices. This thesis focuses on process capability indices in the situation when the specification limits are one- sided. The thesis consists of a summary and three papers, of which one is already published in an international journal. The summary gives a background to the research area, a short overview of the three papers, and some suggestions for future research. In Paper I, the frequency and use of process capability analysis together with statistical process control and design of experiments, within Swedish companies hiring alumni students are investigated. We also investigate what motivates organisations to implement or not implement these statistical methods, if there are differences in use that can be related to organisational types and what will be needed to increase the use. One conclusion drawn from the results is that the students employed in the Swedish industrial sector witness a modest use of these statistical methods and use in other sectors hiring the alumni is uncommon. In Paper II we present a graphical method useful when doing capability analysis having one-sided specification limits. This is an extension of the process capability plots previously developed for two-sided specification intervals. Under the assumption of normality we suggest estimated process capability plots to be used to assess process capability at a given significance level. The presented graphical approach is helpful to determine if it is the variability, the deviation from target, or both that need to be reduced to improve the capability. In Paper III the situation with non-negative process data having a skew distribution with a long tail towards large values are considered, when an upper specification limit only exists and the target value is 0. No proper indices exist for this specific situation, which is common in practice. We contribute to this area by proposing a new class of indices designed for skew, zero-bound distributions when an upper specification only exists and the target value is 0. This new class of indices is simple and possesses properties desirable for process capability indices. Two estimators of the proposed index are studied and the asymptotic distributions of these estimators are derived. Furthermore, we consider decision procedures, based on the estimated indices, suitable for deeming the process capability or not.
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| 5. |
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| 6. |
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| 7. |
- Albing, Malin
(författare)
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Process capability indices for Weibull distributions and upper specification limits
- 2009
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Ingår i: Quality and Reliability Engineering International. - : Wiley. - 0748-8017 .- 1099-1638. ; 25:3, s. 317-334
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Tidskriftsartikel (refereegranskat)abstract
- We consider a previously proposed class of capability indices that are useful when the quality characteristic of interest has a skewed, zero-bound distribution with a long tail towards large values and there is an upper specification with a pre-specified target value, T = 0. We investigate this class of process capability indices when the underlying distribution is a Weibull distribution and focus on the situation when the Weibull distribution is highly skewed. We propose an estimator of the index in the studied class, based on the maximum likelihood estimators of the parameters in the Weibull distribution, and derive the asymptotic distribution for this estimator. Furthermore, we suggest a decision rule based on the estimated index and its asymptotic distribution, and presents a power comparison between the proposed estimator and a previously studied estimator. A simulation study is also performed to investigate the true significance level when the sample size is small or moderate. An example from a Swedish industry is presented.
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| 8. |
- Albing, Malin, et al.
(författare)
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Skewed zero-bound distributions and process capability indices for upper specifications
- 2009
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Ingår i: Journal of Applied Statistics. - : Informa UK Limited. - 0266-4763 .- 1360-0532. ; 36:2, s. 205-221
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Tidskriftsartikel (refereegranskat)abstract
- A common practical situation in process capability analysis, which is not well developed theoretically, is when the quality characteristic of interest has a skewed distribution with a long tail towards relatively large values and an upper specification limit only exists. In such situations it is not uncommon that the smallest possible value of the characteristic is 0 and this also is the best value to obtain. Hence a target value 0 is assumed to exist. We investigate a new class of process capability indices for this situation. Two estimators of the proposed index are studied and the asymptotic distributions of these estimators are derived. Furthermore we suggest a decision procedure useful when drawing conclusions about the capability at a given significance level, based on the estimated indices and their asymptotic distributions. A simulation study is also performed, assuming that the quality characteristic is Weibull distributed, to investigate the true significance level when the sample size is finite.
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| 9. |
- Bergquist, Bjarne, et al.
(författare)
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Statistical methods - does anyone really use them?
- 2006
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Ingår i: Total Quality Management and Business Excellence. - : Informa UK Limited. - 1478-3363 .- 1478-3371. ; 17:8, s. 961-972
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Tidskriftsartikel (refereegranskat)abstract
- Students taking courses in quality management at Luleå University of Technology receive extensive education in statistical methods. To improve the education and to understand what kind of competence students need when they graduate, a survey was preformed examining how and to what extent the methods Statistical Process Control, Capability Analysis and Design of Experiments are used by organisations hiring the alumni. The result shows that the students employed in the Swedish industrial sector witness a modest use of statistical methods, while use of statistical methods in other sectors hiring the alumni is uncommon. Lack of competence and resources within the organizations are stated as hindrances to expanded use. Conclusions from the study are that implementation techniques must be emphasized in the curriculum and that different types of courses should be given - practical, hands-on courses for engineers, managers and others working in organizations. Furthermore, courses offered at universities must have a strong focus on practical problems such as difficulties randomizing experiments and that graphical methods should be favoured.
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| 10. |
- Vännman, Kerstin, et al.
(författare)
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Process capability indices for one-sided specification intervals and skewed distributions
- 2007
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Ingår i: Quality and Reliability Engineering International. - : Wiley. - 0748-8017 .- 1099-1638. ; 23:6, s. 755-765
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Tidskriftsartikel (refereegranskat)abstract
- One-sided specification intervals are frequent in industry, but the process capability analysis is not well developed theoretically for this case. Most of the published articles about process capability focus on the case when the specification interval is two-sided. Furthermore, usually the assumption of normality is necessary. However, a common practical situation is process capability analysis when the studied characteristic has a skewed distribution with a long tail towards large values and an upper specification limit only exists. In such situations it is not uncommon that the smallest possible value of the characteristic is 0 and that this also is the best value to obtain. We propose a new class of indices for such a situation with an upper specification limit, a target value zero, and where the studied characteristic has a skewed, zero-bound distribution with a long tail towards large values. A confidence interval for an index in the proposed class, as well as a decision procedure for deeming a process as capable or not, is discussed. These results are based on large sample properties of the distribution of a suggested estimator of the index. A simulation study is performed, assuming the quality characteristic is Weibull distributed, to investigate the properties of the suggested decision procedure.
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