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Albing, Malin

Open this publication in new window or tab >>Elliptical safety region plots for Cpk### Albing, Malin

### Vännman, Kerstin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_some",{id:"formSmash:j_idt191:0:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_otherAuthors",{id:"formSmash:j_idt191:0:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_otherAuthors",multiple:true}); 2011 (English)In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 38, no 6, p. 1169-1187Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistic
##### Identifiers

urn:nbn:se:ltu:diva-4824 (URN)10.1080/02664763.2010.491858 (DOI)000288670000005 ()2-s2.0-79952951300 (Scopus ID)2d0af12b-5af8-4586-9a52-46c641c5f54d (Local ID)2d0af12b-5af8-4586-9a52-46c641c5f54d (Archive number)2d0af12b-5af8-4586-9a52-46c641c5f54d (OAI)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_j_idt366",{id:"formSmash:j_idt191:0:j_idt195:j_idt366",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_j_idt366",multiple:true});
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##### Note

Validerad; 2011; 20110408 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

The process capability index Cpk 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. Cpk4/3. 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 Cpk. 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

Open this publication in new window or tab >>Process capability indices for Weibull distributions and upper specification limits### Albing, Malin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_some",{id:"formSmash:j_idt191:1:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_otherAuthors",{id:"formSmash:j_idt191:1:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_otherAuthors",multiple:true}); 2009 (English)In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 25, no 3, p. 317-334Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistic
##### Identifiers

urn:nbn:se:ltu:diva-13302 (URN)10.1002/qre.972 (DOI)000264644600005 ()2-s2.0-63449131737 (Scopus ID)c7f92340-79c3-11dd-b356-000ea68e967b (Local ID)c7f92340-79c3-11dd-b356-000ea68e967b (Archive number)c7f92340-79c3-11dd-b356-000ea68e967b (OAI)
#####

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#####

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#####

##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

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.

Validerad; 2009; 20080903 (malina)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approvedOpen this publication in new window or tab >>Skewed zero-bound distributions and process capability indices for upper specifications### Albing, Malin

### Vännman, Kerstin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_some",{id:"formSmash:j_idt191:2:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_otherAuthors",{id:"formSmash:j_idt191:2:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_otherAuthors",multiple:true}); 2009 (English)In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 36, no 2, p. 205-221Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistic
##### Identifiers

urn:nbn:se:ltu:diva-12942 (URN)10.1080/02664760802443954 (DOI)000261738300006 ()2-s2.0-57949109145 (Scopus ID)c1716d10-79c4-11dd-b356-000ea68e967b (Local ID)c1716d10-79c4-11dd-b356-000ea68e967b (Archive number)c1716d10-79c4-11dd-b356-000ea68e967b (OAI)
#####

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#####

##### Note

Validerad; 2009; 20080903 (malina)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

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.

Open this publication in new window or tab >>Contributions to process capability indices and plots### Albing, Malin

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_some",{id:"formSmash:j_idt191:3:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_otherAuthors",{id:"formSmash:j_idt191:3:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_otherAuthors",multiple:true}); 2008 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Luleå: Luleå tekniska universitet, 2008. p. 44
##### Series

Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544 ; 2008:63
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistic
##### Identifiers

urn:nbn:se:ltu:diva-18127 (URN)70146350-b484-11dd-a6f7-000ea68e967b (Local ID)70146350-b484-11dd-a6f7-000ea68e967b (Archive number)70146350-b484-11dd-a6f7-000ea68e967b (OAI)
#####

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#####

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#####

##### Note

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.

Godkänd; 2008; 20081117 (ysko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-27Bibliographically approvedOpen this publication in new window or tab >>Elliptical Safety Region Plots for Cpk, Cpu and Cpl### Albing, Malin

### Vännman, Kerstin

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_some",{id:"formSmash:j_idt191:4:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_otherAuthors",{id:"formSmash:j_idt191:4:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_otherAuthors",multiple:true}); 2008 (English)Report (Other academic)
##### Place, publisher, year, edition, pages

Luleå: Department of Mathematics, Luleå University of Technology, 2008. p. 30
##### Series

Gula serien, ISSN 1400-4003 ; 2008:07
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistic
##### Identifiers

urn:nbn:se:ltu:diva-24819 (URN)ca24ce2d-dbe5-423d-b8f9-6ac8e3aa35e8 (Local ID)ca24ce2d-dbe5-423d-b8f9-6ac8e3aa35e8 (Archive number)ca24ce2d-dbe5-423d-b8f9-6ac8e3aa35e8 (OAI)
#####

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#####

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##### Note

Godkänd; 2008; 20120417 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

Open this publication in new window or tab >>Process capability indices for Weibull distributions and upper specification limits### Albing, Malin

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_some",{id:"formSmash:j_idt191:5:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_otherAuthors",{id:"formSmash:j_idt191:5:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_otherAuthors",multiple:true}); 2008 (English)Report (Other academic)
##### Place, publisher, year, edition, pages

Luleå: Department of Mathematics, Luleå University of Technology, 2008. p. 25
##### Series

Gula serien, ISSN 1400-4003 ; 2008:01
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistic
##### Identifiers

urn:nbn:se:ltu:diva-23333 (URN)68919b7c-8007-4323-8a6d-88e9c34a8a42 (Local ID)68919b7c-8007-4323-8a6d-88e9c34a8a42 (Archive number)68919b7c-8007-4323-8a6d-88e9c34a8a42 (OAI)
#####

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##### Note

Godkänd; 2008; 20120417 (andbra)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-27Bibliographically approvedOpen this publication in new window or tab >>Process capability indices for one-sided specification intervals and skewed distributions### Vännman, Kerstin

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Albing, Malin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_some",{id:"formSmash:j_idt191:6:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_otherAuthors",{id:"formSmash:j_idt191:6:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_otherAuthors",multiple:true}); 2007 (English)In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 23, no 6, p. 755-765Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistic
##### Identifiers

urn:nbn:se:ltu:diva-15463 (URN)10.1002/qre.877 (DOI)000250237300011 ()2-s2.0-36749103223 (Scopus ID)ef94aa20-80ac-11dc-965a-000ea68e967b (Local ID)ef94aa20-80ac-11dc-965a-000ea68e967b (Archive number)ef94aa20-80ac-11dc-965a-000ea68e967b (OAI)
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_j_idt372",{id:"formSmash:j_idt191:6:j_idt195:j_idt372",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_j_idt372",multiple:true});
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##### Note

Validerad; 2007; 20071022 (malina)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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.

Open this publication in new window or tab >>Process capability plots for one-sided specification limits### Vännman, Kerstin

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Albing, Malin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_some",{id:"formSmash:j_idt191:7:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_otherAuthors",{id:"formSmash:j_idt191:7:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_otherAuthors",multiple:true}); 2007 (English)In: Quality Technology & Quantitative Management, ISSN 1684-3703, E-ISSN 1811-4857, Vol. 4, no 4, p. 569-590Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistics
##### Identifiers

urn:nbn:se:ltu:diva-9719 (URN)10.1080/16843703.2007.11673171 (DOI)863da1d0-6b3f-11dc-9e58-000ea68e967b (Local ID)863da1d0-6b3f-11dc-9e58-000ea68e967b (Archive number)863da1d0-6b3f-11dc-9e58-000ea68e967b (OAI)
#####

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_j_idt372",{id:"formSmash:j_idt191:7:j_idt195:j_idt372",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_j_idt372",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_j_idt378",{id:"formSmash:j_idt191:7:j_idt195:j_idt378",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_j_idt378",multiple:true});
#####

##### Note

We extend the idea of process capability plots from the case of two-sided specification intervals to derive a graphical method useful when doing capability analysis having one-sided specification limits. The derived process capability plots are based on existing capability indices for one-sided specification limits. Both the cases with and without a target value are investigated. Under the assumption of normality we suggest estimated process capability plots to be used to assess process capability at a given significance level. Theoretical results are given for determining the significance level as well as power for the method. 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. Examples are presented.

Validerad; 2007; 20070925 (malina)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2020-04-27Bibliographically approvedOpen this publication in new window or tab >>Process capability analysis with focus on indices for one-sided specification limits### Albing, Malin

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_some",{id:"formSmash:j_idt191:8:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_otherAuthors",{id:"formSmash:j_idt191:8:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_otherAuthors",multiple:true}); 2006 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Luleå: Luleå tekniska universitet, 2006. p. 100
##### Series

Licentiate thesis / Luleå University of Technology, ISSN 1402-1757 ; 2006:71
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistic
##### Identifiers

urn:nbn:se:ltu:diva-18016 (URN)66176f60-8145-11db-aabe-000ea68e967b (Local ID)66176f60-8145-11db-aabe-000ea68e967b (Archive number)66176f60-8145-11db-aabe-000ea68e967b (OAI)
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##### Note

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.

Godkänd; 2006; 20061201 (haneit)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-27Bibliographically approvedOpen this publication in new window or tab >>Process capability indices for one-sided specifications and skew zero-bound distributions### Albing, Malin

### Vännman, Kerstin

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_some",{id:"formSmash:j_idt191:9:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_otherAuthors",{id:"formSmash:j_idt191:9:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_otherAuthors",multiple:true}); 2006 (English)Report (Other academic)
##### Place, publisher, year, edition, pages

Luleå: Department of Mathematics, Luleå University of Technology, 2006. p. 24
##### Series

Gula serien, ISSN 1400-4003 ; 2006:11
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics with special emphasis on Industrial Statistic
##### Identifiers

urn:nbn:se:ltu:diva-22127 (URN)1a3ff5a7-313c-4595-aecb-8ec0be4878a6 (Local ID)1a3ff5a7-313c-4595-aecb-8ec0be4878a6 (Archive number)1a3ff5a7-313c-4595-aecb-8ec0be4878a6 (OAI)
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##### Note

Godkänd; 2006; 20120822 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved