1、Designation: D4583 95 (Reapproved 2015)Standard Practice forCarbon BlackCalculation of Process Indexes From anAnalysis of Process Control Data1This standard is issued under the fixed designation D4583; the number immediately following the designation indicates the year oforiginal adoption or, in the
2、 case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers (1) a statistical procedure foranalyzing the test data generated i
3、n the statistical processcontrol of a carbon black manufacturing process; (2) a formatfor reporting process capability determined from the analysisof control chart data of an individual production run, and (3)aformat for reporting process performance determined from theanalysis of control chart data
4、 of an individual production run.1.2 This practice specifically applies to the analysis ofpelleted carbon black samples taken during the manufacturingprocess prior to storage. This practice does not apply toshipment samples taken from hopper cars or other containers orpackages.1.3 This practice is s
5、pecifically designed to be used forthose test methods given in Classification D1765 which specifytarget values. However, these techniques are applicable to othertest methods on carbon black.1.4 This practice describes the calculation for two methodsof determining capability factors from an analysis
6、of processcontrol data.1.4.1 Process capability (Cp) is a measurement of variationcalculated from the process control chart data with the use ofan estimated standard deviation () from the mean value of themoving range (R) chart. The calculation of the process capa-bility (Cp and Cpk) indexes can be
7、used as historical informa-tion or to predict future performance of the process, but areonly valid when the process is in a state of statistical control.1.4.2 Process performance (Pp) is a measurement of varia-tion calculated from the process control chart data usingsample standard deviation(s). The
8、 calculation of the processperformance (Pp and Ppk) indexes are used for a historicalreference of a process performance and does not require astate of statistical control.2. Referenced Documents2.1 ASTM Standards:2D1765 Classification System for Carbon Blacks Used inRubber Products3. Terminology3.1
9、Definitions of Terms Specific to This Standard:,43.1.1 average moving range R!the arithmetic mean of nmoving ranges, R5(R/n.3.1.2 Cpk indexan index that indicates how well thecommon cause process variability is actually contained withinthe specifications. (See 6.4.)3.1.3 moving range (R)the absolute
10、 difference betweenconsecutive, individual test values.3.1.4 Ppk indexindicates how well the common andspecial cause process variability is actually contained withinthe specifications. (See 6.6.)3.1.5 process capability index (Cp)an index that comparesthe magnitude of common cause process variabilit
11、y to therange of upper and lower specification limits (USL and LSL)without regard to where the process is centered; Cp in-dex=(USL LSL)/(6). (See 6.3.)3.1.6 process performance index(Pp)an index that com-pares the magnitude of common and special cause processvariability to the range of the upper and
12、 lower specificationlimits (USL and LSL) without regard to where the process iscentered; Pp index = (USL LSL)/(6s). (See 6.5.)4. Significance and Use4.1 This practice will provide the following: (1) a statisticalsummary of individual production run data plotted on a control1This practice is under th
13、e jurisdiction of ASTM Committee D24 on CarbonBlackand is the direct responsibility of Subcommittee D24.61 on Carbon BlackSampling and Statistical Analysis.Current edition approved Jan. 1, 2015. Published February 2015. Originallyapproved in 1986. Last previous edition approved in 2009 as D4583 95 (
14、2009).DOI: 10.1520/D4583-95R15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Manual on Presentation of Dat
15、a and Control Chart Analysis, STP 15D, ASTMInternational, 1976.4Ford Motor Company Manual on “Process Capability and Continuing ProcessControl,” Publication No. 80-01-251. Available in packs of five from Ford MotorCompany, Statistical Methods Publications, P.O. Box 1000, Plymouth, MI 48170.Copyright
16、 ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1chart; (2) a statistical summary of data from multiple produc-tion runs; (3) a procedure to relate the average and variation ofthese data groups to specification limits, and (4) indexes forcompar
17、ing different manufacturing units for projecting futurecapabilities or as historical reference.5. Procedure5.1 Sampling:5.1.1 In order to provide uniformity and the ability to makevalid comparisons of process capability and process perfor-mance indexes, all samples used for these calculations shall
18、becollected in the same way. Samples that are to be tested forproperties on which capability or performance indexes will becalculated shall be collected as follows:5.1.1.1 All samples shall be taken from the process at thefinished pellet discharge and tested individually. Compositingof samples is no
19、t permitted.5.1.1.2 Samples normally shall be taken every 4 h. Allresults obtained on material that is put into finished productstorage tanks shall be included.5.1.1.3 Averaging of results is not permitted. Each result, asdefined by the appropriate test method, is to be recorded andused in performin
20、g the calculations described in Section 6.5.2 Process Capability:5.2.1 A minimum of 30 test data generated during produc-tion periods in which the process is in statistical control arerecommended for estimating a process capability standarddeviation. In that case, the number (n) of moving rangesaver
21、aged will be 29.5.2.2 Calculate Cp and Cpk as shown in 6.3 and 6.4. The Cpindex and the Cpk index must be greater than 1.00 in order toindicate the capability of the process to meet the establishedspecifications. The Cpk index is inherently less than or equal tothe Cp index (for one-sided specificat
22、ions, only the Cpk indexis applicable).5.2.3 The Cp index indicates whether or not the process iscapable of meeting a specification. Maximum performance isachieved when the process is perfectly centered and the Cpk isequal to the Cp.5.2.4 In comparing one manufacturing unit to another, thelarger Cpk
23、 index demonstrates a greater capability to conformto the specification range of the specified property.5.2.5 A process capability summary can be used to evaluatea production unit over a period of time such as weekly,monthly, or quarterly. (See Fig. 1.) After each production run,or after 30 or so te
24、sts, the values of n, x, 6 difference fromtarget, MR,3, Cp, and Cpk are recorded on the summaryform. At the conclusion of the appropriate time interval, thegrand averagex%!,average difference from target, average Cp, and average Cpkcan be displayed at the foot of the appropriate column.FIG. 1 Sample
25、 Process Capability Summary SheetD4583 95 (2015)2These average values, especially the Cpk, can be used tocompare the quality levels of different manufacturing units.5.3 Process Performance:5.3.1 A minimum of 30 test data are required, withoutregard to the process being in a state of statistical cont
26、rol, whencalculating the standard deviation for process performance. Inthis case, extended production periods such as weeks ormonths can be represented.5.3.2 Calculate Pp and Ppk as shown in 6.5 and 6.6. Boththe Pp index and Ppk index must be greater than 1.0 in orderto indicate that the process mee
27、ts specifications. The Ppk indexis inherently less than or equal to the Pp index (for one-sidedspecifications, only the Ppk is applicable).5.3.3 A process performance summary can be used tosummarize the data generated by the different productionperiods represented in a row of calculated values. (See
28、 Fig. 2.)6. Calculation6.1 Calculate estimated standard deviation () as follows: ! 5Rd2(1)where:d2= 1.128 for n =2.6.2 Calculate sample standard deviation as follows:s 5!(i51nXi2! 2 XS(i51nXiDn 2 1(2)where:s = sample standard deviation,n = number of tests,Xi= individual test results, andX= average o
29、f all test results.6.3 Calculate the Cp index as follows:Cp index 5USL 2 LSL6(3)where:USL = the upper specification limit,LSL = the lower specification limit, and = the process capability estimated standard deviation.6.4 Calculate the Cpk index as follows:Cpk index 5 minimum ratio of: (4)USL 2 X3orX
30、2 LSL3(5)where:X= the process average, and = the estimated standard deviation.6.5 Calculate the Pp index as follows:Pp index 5USL 2 LSL6s(6)6.6 Calculate the Ppk index as follows:Ppk index 5 minimum ratio of: (7)USL 2 X3sorX2 LSL3s(8)where:X= the process average, ands = the sample standard deviation
31、.7. Keywords7.1 carbon black; Cp index; Cpk index; moving range;process capability; process capability from test data; processcontrolPROCESS PERFORMANCE SUMMARYPLANT: _ UNIT: _ GRADE: _ PROPERTY: _ AS OF DATE: _MATERIAL SPEC: _RANGE: _TARGET: _Production Period n XDifference Target 3s Pp PpkFIG. 2 S
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