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- Vanhatalo, Erik, et al.
(författare)
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Towards improved analysis methods for two-level factorial experiments with time series responses
- 2013
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Ingår i: Quality and Reliability Engineering International. - : Wiley. - 0748-8017 .- 1099-1638. ; 29:5, s. 725-741
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Tidskriftsartikel (refereegranskat)abstract
- Dynamic processes exhibit a time delay between the disturbances and the resulting process response. Therefore, one has to acknowledge process dynamics, such as transition times, when planning and analyzing experiments in dynamic processes. In this article, we explore, discuss, and compare different methods to estimate location effects for two-level factorial experiments where the responses are represented by time series. Particularly, we outline the use of intervention-noise modeling to estimate the effects and to compare this method by using the averages of the response observations in each run as the single response. The comparisons are made by simulated experiments using a dynamic continuous process model. The results show that the effect estimates for the different analysis methods are similar. Using the average of the response in each run, but removing the transition time, is found to be a competitive, robust, and straightforward method, whereas intervention-noise models are found to be more comprehensive, render slightly fewer spurious effects, find more of the active effects for unreplicated experiments and provide the possibility to model effect dynamics. Copyright © 2012 John Wiley & Sons, Ltd. Copyright © 2012 John Wiley & Sons, Ltd.
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| 2. |
- Tano, Ingrid, 1968-, et al.
(författare)
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Comparing Confidence Intervals for Multivariate Process capability Indices
- 2012
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Ingår i: Quality and Reliability Engineering International. - : Wiley. - 0748-8017 .- 1099-1638. ; 28:4, s. 481-495
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Tidskriftsartikel (refereegranskat)abstract
- Multivariate process capability indices (MPCIs) are needed for process capability analysis when the quality of a process is determined by several univariate quality characteristics that are correlated. There are several different MPCIs described in the literature, but confidence intervals have been derived for only a handful of these. In practice, the conclusion about process capability must be drawn from a random sample. Hence, confidence intervals or tests for MPCIs are important. With a case study as a start and under the assumption of multivariate normality, we review and compare four different available methods for calculating confidence intervals of MPCIs that generalize the univariate index Cp. Two of the methods are based on the ratio of a tolerance region to a process region, and two are based on the principal component analysis. For two of the methods, we derive approximate confidence intervals, which are easy to calculate and can be used for moderate sample sizes. We discuss issues that need to be solved before the studied methods can be applied more generally in practice. For instance, three of the methods have approximate confidence levels only, but no investigation has been carried out on how good these approximations are. Furthermore, we highlight the problem with the correspondence between the index value and the probability of nonconformance. We also elucidate a major drawback with the existing MPCIs on the basis of the principal component analysis. Our investigation shows the need for more research to obtain an MPCI with confidence interval such that conclusions about the process capability can be drawn at a known confidence level and that a stated value of the MPCI limits the probability of nonconformance in a known way.
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| 3. |
- Vännman, Kerstin, et al.
(författare)
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Matematisk statistik
- 2020. - Tredje
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Bok (populärvet., debatt m.m.)abstract
- Denna bok är en omarbetning av Kerstin Vännmans tidigare bok Matematisk statistik från 2002. Boken syftar till att träna det statistiska tänkandet så att man kan förstå och använda några ofta förekommande statistiska metoder. Den är uppbyggd kring ett stort antal exempel och nya begrepp introduceras och motiveras med hjälp av inledande exempel.I boken behandlas bland annat enkla sannolikhetsresonemang, några vanligt förekommande fördelningar, till exempel binomial-, Poisson-, normal- och exponential-fördelningen, samt olika läges- och spridningsmått. Vidare behandlas punktskattningar, konfidensintervall (även jämförande situationer) och test. Den största förändringen jämfört med den tidigare boken är att regressionsanalys (både enkel och multipel) och flerdimensionella stokastiska variabler behandlas i denna bok. I regressionsanalysen ligger fokus på tillämpning med hjälp av statistisk programvara och tolkning av resultat.Boken vänder sig i första hand till studenter inom utbildningarna för civil- och högskoleingenjörer, men den är även lämplig för annan högskoleutbildning eller för självstudier. Till varje kapitel finns ett stort antal övningsuppgifter med svar. Dessutom finns ett separat kapitel med blandade övningar av varierande svårighetsgrad.
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| 8. |
- 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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