1、Designation: D 5406 93 (Reapproved 2006)Standard Practice forRubberCalculation of Producers Process PerformanceIndexes1This standard is issued under the fixed designation D 5406; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the
2、year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice provides a calculation procedure and aformat for reporting the process performance of a manufac
3、tur-ing operation for a rubber or rubber product.1.2 This practice is specifically designed to be used fortechnically significant properties of the final product.2. Referenced Documents2.1 Quality Assurance for the Chemical and Process Indus-tries, American Society for Quality Control, Chemical andP
4、rocess Industries Division, Chemical Interest Committee,1987.23. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 common cause variationthat residual variation in-herent in any process that (1) is operating in a state of statisticalcontrol, and (2) is operating at some recognized
5、or ascertainedlevel of technological competence.3.1.2 lower specification limit (LSL)the producers mini-mum permissible value of any relevant measured productproperty.3.1.3 Pp8 producers process performance indexthe ratioof the difference (USL LSL) to the total process variation;the index does not c
6、onsider where the process is centered. (See7.4.)3.1.4 Ppk8 producers process performance indextheminimum of two ratios: (1) the ratio of the difference(USL process mean) to one-half of the total process varia-tion, or (2) the ratio of the difference (process mean LSL) toone-half of the total process
7、 variation; the magnitude of theminimum index value, used with the Pp8 index, indicates howwell the process mean is centered. (See 7.5.)3.1.5 special cause variationthat variation attributable tocertain specific or assignable sources that have been (or maybe) discovered through an investigation of t
8、he process.3.1.6 target valuethe aiming point of the process; this isoften (USL + LSL)/2.3.1.7 total process variationa range, along the measuredproperty scale, defined as six times the standard deviation(determined under specified process conditions); the variationmay contain either common or combi
9、ned common and specialcause sources.3.1.8 upper specification limit (USL)the producers maxi-mum permissible value of any relevant measured productproperty.4. Summary of Practice4.1 During the production of any product, certain physicalor chemical properties, or both, are normally measured tocontrol
10、the properties of the final product. When enough datahave been accumulated to form a sufficient database, it ispossible to determine the centering (mean) and variation (rangeor standard deviation) of the process property distribution.These results may be informally compared to the desired targetand
11、specification limits to determine if the process is producingan acceptable product.4.2 On a more formal basis, the two process performanceparameters, the “process mean” and the “standard deviation,”are used to calculate two Producers Process PerformanceIndexes designated as Pp8 and Ppk8. These index
12、es allow astandardized comparison of an actual process performance tothe general specifications, the comparison of different pro-cesses for producing the same product, or comparison of thesame process at different times.5. Significance and Use5.1 This practice is used to evaluate the conformance of
13、aproduction process to specifications when (1) special causes ofvariation may be present, and (2) the process may not be in astate of statistical control. This evaluation may also be used tocompare different manufacturing operations for conformanceto specifications.6. Background and Precautions6.1 A
14、 process is said to be in a state of statistical controlwhen there are only common causes of variation present (noassignable causes).Astate of statistical control is a requirementto perform a process capability calculation which can be used1This practice is under the jurisdiction ofASTM Committee D1
15、1 on Rubber andis the direct responsibility of Subcommittee D11.16 on Application of StatisticalMethods.Current edition approved Oct. 1, 2006. Published November 2006. Originallyapproved in 1993. Last previous edition approved in 2002 as D 5406 93 (2002).2Available from American Society for Quality
16、Control, 310 W. Wisconsin Ave.,Milwaukee, WI 53203.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.for prediction. A state of statistical control is not required toperform the process performance calculations covered by thispractice.
17、6.2 Although the defining calculation equations for theproducers process performance indexes (Pp8 and Ppk8) givenin 7.4 and 7.5 bear a resemblance to the defining equations forthe process capability indexes (Cp and Cpk), a legitimatecalculation of Cp and Cpk can be made only when a process isin a st
18、ate of statistical control. The symbols Pp8 and Ppk8 havebeen selected to represent the producers process performanceindexes to distinguish them from other capability and processperformance indexes.6.3 The Pp8 and Ppk8 indexes are historical in nature. Theyindicate whether or not the process variati
19、on could have metthe specifications over the time period covered by the data.Since a state of statistical control is not required to do thesecalculations, the indexes can not be used to predict futureperformance.6.4 For the best understanding of the information presented,associated control charts, h
20、istograms, performance, and capa-bility indexes should be reviewed.6.5 The formula for calculating the standard deviation (7.3)will be used for test results which have a normal (Gaussian) ornon-normal distribution. Although possible presence of specialcause variation could also cause the results to
21、be non-normallydistributed, the calculation of Pp8 and Ppk8 indexes from suchnon-normally distributed test results is useful for the purposesof this standard (5.1).6.6 The selection of the time period covered by the data setis critical if the process is known, or suspected, to havetimedependent cycl
22、es or trends. The data should include aperiod long enough to encompass these cycles or trends. If thedata period does not include these cycles or trends, the reportedresults will understate the true process variability.6.6.1 The time period covered in the report should beestablished by mutual agreem
23、ent between the producer andconsumer subject to the precaution given in 6.6. Typically, thisperiod would be for three months, but not less than 30 datapoints.6.7 Individual test results as defined in the appropriate testmethod shall be used for these calculations. Sample averagestend to have a norma
24、l distribution even when they are takenfrom non-normal populations. The use of averages in thecalculations will hide the true individual data distribution. Thestandard deviation of the individual values will be greater thanthe standard deviation of the sample averages. They are relatedby the square
25、root of the number of values averaged:Si5 SA=n (1)where:Si= standard deviation of individual values,SA= standard deviation of averaged values, andn = number of individual values averaged.6.8 For asymmetric two-sided specifications, each portionof the specification range from the target to the limit
26、must becalculated separately as if it were for a one-sided specification.6.9 For one-sided specifications, only the Ppk8 index isapplicable; however, if there is no target value because the goalis to be as low as possible (for example, impurities) or as highas possible (for example, strength), inter
27、pretation of the Ppk8index should not be used to permit intentional contamination ordegradation of the product. See 2.1.6.10 The Ppk8 index is inherently less than or equal to thePp8 index. Maximum performance is achieved when theprocess is perfectly centered on the target and the Ppk8 is equalto th
28、e Pp8.APp8 or a Ppk8 index that steadily increases overtime demonstrates an improvement in the control of, orelimination of, special causes of variation in the process.6.11 A Pp8 or Ppk8 index of less than 1.0 indicates that theprocess did not meet the specifications during the periodcovered by the
29、data. When these indexes are less than 1.0, theprocess or the specification limits, or both, need to be studied.6.12 Nothing in the calculation of these indexes requires orindicates that the process is in a state of statistical control or ispredictable. This practice is not meant to replace statisti
30、calprocess control (SPC) charts or any other statistical tool aimedat controlling or improving the process.7. Calculation7.1 Data used in the statistical calculation shall cover allproducts produced while operating to a single aiming point (ortarget) that went into a finished product area for shipme
31、nt to acustomer. Thus, transition product made while switching fromone product or subproduct to another product or subproductmay be excluded. Any off-specification or out-of-control prod-uct made while producing to a common aiming point must beincluded.7.2 The process mean, x, is calculated as follo
32、ws:X5(i 5 1nxin(2)where:n = number of test results, andxi= individual test result.7.3 The calculation of the process standard deviation shouldbe based on at least 30 test results (see 6.6). The samplestandard deviation, s, is calculated as follows:s 5S1n 2 1D (i 5 1nxi2 x!2(3)where:s = sample standa
33、rd deviation,n = number of test results,xi= individual test result, andx = process mean.7.4 The total process variation is six times the processstandard deviation; that is, 6s. The producers process perfor-mance index, Pp8, is calculated as follows:Pp8 5USL 2 LSL6s(4)where:USL = producers upper spec
34、ification limit, andLSL = producers lower specification limit.D 5406 93 (2006)27.5 The Ppk8 index, when used with the Pp8 index, revealshow well the production process was centered in the specifi-cation range. The minimum value of either (5) or (6) is used fortwo-sided specifications. With one-sided
35、 specifications, either(5) or (6) is used, as appropriate.Ppk8 5 USL 2 x!/3 s (5)orPpk8 5 x 2 LSL!/3s (6)where:x = mean value of process property for the period asspecified in 6.6.7.6 If the process center is outside the specification limits,negative values of Ppk8 will result.7.7 A histogram prepar
36、ed from the individual results willincrease understanding of the nature of the data distribution.increase understanding of the nature of the data distribution.8. Report8.1 The report shall include the following as a minimum:8.1.1 A description of the product and the property beingreported.8.1.2 Time
37、 period of production chosen for analysis.8.1.3 Pp8 (for two-sided specifications only) and Ppk8 in-dexes.8.1.4 Producers USL, LSL, and target value.8.1.5 Mean, standard deviation and number of test results.8.2 If a histogram was prepared, it may be included in thereport.9. Keywords9.1 performance i
38、ndex; Pp8; Ppk8; producers processperformanceASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, an
39、d the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revisi
40、on of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you sh
41、ouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org).D 5406 93 (2006)3
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