# ASTM F1503-02 (Reapproved 2012)

Designation: F1503 − 02 (Reapproved 2012)Standard Practice forMachine/Process Capability Study Procedure1This standard is issued under the fixed designation F1503; the number immediately following the designation indicates the year oforiginal adoption or, in the 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. Scope*1.1 This practice covers provision of a proper method fordetermining process capability for new or existing machineprocesses. It is recommended that available statistical softwarebe used for the calculation of the descriptive statistics requiredfor decision making when using this practice. Where softwareis not available, Section 8 and Tables 1 and 2 are provided formanual calculations.2. Referenced Documents2.1 ASTM Standards:2F1469 Guide for Conducting a Repeatability and Reproduc-ibility Study on Test Equipment for Nondestructive Test-ing3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 bilateral specifications—specifications that have bothupper and lower values.3.1.2 Cp—an index that indicates the variability of theprocess with respect to tolerance.3.1.3 Cpk—an index of process variability and centering.This is a widely-used index which considers the process mean,range, and its relation to the specification nominal.3.1.4 inspection plan—a set of instructions defining productcharacteristics, specifications, frequency of inspection, accep-tance criteria, and methods of inspection for product at aspecified operation.3.1.5 process parameters—combination of people,equipment, materials, methods, and environment that produceoutput.3.1.6 unilateral specifications—specifications that haveonly upper or lower values.3.1.7 σ—an estimate of the standard deviation of a processcharacteristic.4. Summary of Practice4.1 A machine/process capability (MPC) study is conductedto provide a level of confidence in the ability of a machine/process to meet engineering specification requirements. This isaccomplished through statistical process control techniques asdefined in this practice.4.2 For new equipment purchases, the purchaser’s manufac-turing engineering department, or equivalent discipline, shallhave primary responsibility for ensuring that the requirementsof this practice are met. The purchaser’s quality assurancedepartment shall be available to assist on an as-requested basis.4.3 New machines/processes will not be accepted for use inproduction with Cpvalues less than 1.67. If a manufacturingprocess must be conditionally accepted, a processimprovement/product control plan shall be developed.4.3.1 The machine/process control plan shall identify spe-cific process improvement activities, which will be imple-mented to make the process more capable as well as an interiminspection plan to ensure that nonconforming product is notshipped to a customer.4.4 Product Specifications:4.4.1 Prior to any MPC study, the product specifications(nominal dimension and tolerances) must be identified, and anappropriate method of variables type inspection selected.4.4.2 This practice is limited to bilateral specificationswhose distributions can be expected to approximate a normalcurve. This practice should not be applied to unilateral speci-fications (flatness, concentricity, minimum tensile, maximumhardness, etc.).4.5 Gage Capability Analysis:4.5.1 All gaging systems used to evaluate product involvedin the study must have documentation for a gage repeatabilityand reproducibility study in accordance with Guide F1469before the machine/capability study is conducted.4.5.1.1 Gaging systems which consume ≤10 % of the appli-cable product tolerance are considered acceptable.4.5.1.2 Gaging systems which consume over 10 to 30 % ofthe applicable product tolerance are generally considered to beunacceptable. However, users of this guide may authorize their1This practice is under the jurisdiction of ASTM Committee F16 on Fastenersand is the direct responsibility of Subcommittee F16.93 on Quality AssuranceProvisions for Fasteners.Current edition approved Oct. 1, 2012. Published November 2012. Originallyapproved in 1994. Last previous edition approved in 2007 as F1503 – 02(2007).DOI: 10.1520/F1503-02R12.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1use depending on factors such as the criticality of the specifi-cation in question, the cost of alternative gaging systems, andso forth.4.5.1.3 Gaging systems which consume more than 30 % ofthe product tolerance are unacceptable and must not be used.4.5.2 All gaging systems must be certified as accurate usingstandards traceable to NIST, other recognized standardsorganizations, or the equivalent manufacturer’s standard.4.6 Process Parameter Selection :4.6.1 For studies conducted at the equipment vendor’sfacility, all machine/process parameters (for example, infeedrates, coolant, dies, pressures, fixtures, etc.) must be estab-lished and documented prior to the MPC study so the require-ments of 9.5 can be met.4.6.1.1 Machine/process parameters may not be changedonce an MPC study has begun.4.6.1.2 All machine/process adjustments made during theMPC study must be documented and included with informationrequired in Section 10.1 of this practice.NOTE 1—Machine/process adjustments are defined as those adjustmentsmade due to internal machine/process gaging (or other sources offeedback control), or by the operator as part of the normal operation of themachine/process.4.6.2 The selection of machine/process parameters is theresponsibility of the purchaser’s manufacturing engineering orequivalent discipline, or, in some cases, the machine supplierdepending on preestablished contractual agreements.4.6.2.1 The machine/process parameters selected must beconsistent with those intended to be used in production.4.6.3 Machine/process parameters may be systematicallyvaried after a study is completed and additional MPC studiesperformed for optimization purposes.5. Significance and Use5.1 This practice is designed to evaluate a machine orprocess isolated from its normal operating environment. In itsnormal operating environment, there would be many sources ofvariation that may not exist at a machine/process builder’sfacility; or put another way, this study is usually conductedunder ideal conditions. Therefore, it should be recognized thatthe results of this practice are usually a “best case” analysis,and allowances need to be made for sources of variations thatmay exist at the purchaser’s facility.6. Material Selection6.1 Material (for example, steel slugs, bar, wire, prefinishedparts, etc.) used for MPC studies shall be selected at random.The variability of material used for MPC studies should beconsistent with the variability of material the machine is likelyto see in production. However, all selected samples shallconform to their applicable product engineering standards.6.2 Presorting of material is not permissible for machine/process qualification purposes.6.3 In some cases, machine/process capability results maybe influenced by the specific product specifications selected forthe study. The specific product selected for qualifying a newmachine/process should be based on that which will yield themost conservative results. If the relationship between specificproduct specifications and machine/process capability isunknown, two or more distinct studies should be performedwith different products to qualify and accept the new machine/process.7. Procedure-Machine/Process Capability Study7.1 Operate the machine/process for a sufficient period oftime to ensure that the machine/process is stable and all initialsetup adjustments are complete.7.2 Control charting techniques should be utilized to deter-mine the stability and capability of the machine/process.7.2.1 When possible, a standard X¯,Rchart should be usedwith subgroup size n equals 2 through 5.7.2.1.1 Sampling frequencies shall be established to ensurethat all likely sources of variability occur.7.2.1.2 A minimum of 25 subgroups are required to estab-lish control.7.2.2 When the quantity of sample measurements cannot bepractically obtained, it is permissible to utilize a chart forindividuals and moving ranges.7.2.2.1 A minimum of 25 subgroups are required to estab-lish control.7.2.3 After the study is complete, calculate and plot thecontrol limits, X¯and R¯(or MR¯), for each specificationidentified in 4.4.1 (see Table 1). If during the study themachine/process was out of control, the MPC study is notvalid. The root cause(s) of the out-of-control condition(s) mustbe identified and eliminated and the study repeated.7.2.3.1 If the out-of-control condition is associated with nomore than two subgroups on the range chart, one point on theX¯or individuals chart and the root cause of the out-of-controlcondition is identified and corrected, new control limits may becalculated by excluding the out-of-control points. A secondstudy is not required.7.2.3.2 In some instances, control chart analysis may revealout-of-control conditions that are inherent to the machine/process. Trends due to tool wear or grinding wheel wear aretypical examples. If the cause of the out-of-control condition isknown, the out-of-control condition is both repeatable andpredictable, and the condition cannot be eliminated, the MPCstudy may be considered acceptable and Cpand Cpk valuescalculated in accordance with 8.1-8.3, or through the use ofstatistical software.TABLE 1 Machine/Process Average and RangeCalculate the average Range (R¯) and the Process Average X¯For the study period,calculate:R¯5R11R21.1RkkX¯5X¯11X¯21.1X¯kkwhere:k = the number of subgroups,R1= the range and average of the first subgroup,X¯1= the range and average of the first subgroup,R2= from the second subgroup, andX¯2= from the second subgroup, etc.F1503 − 02 (2012)28. Calculating Results8.1 Estimate the process standard deviation as follows:σ 5 R¯/d2(1)where:d2= constants for sample size 2 to 10, see Table 2.8.2 Calculate Cpby dividing the total product tolerance by6 σ.8.3 Calculate Cpk as follows:Cpk 5 minimum of ~USL 2 X¯!/3 σ or ~ X¯2 LSL!/3 σ (2)whereUSL = upper specification limit, andLSL = lower specification limit.9. Analysis of Results9.1 The qualification of a machine/process shall be based ona review of the statistical parameters Cpand Cpk. Cpand Cpkare both numerical indexes that provide a measure of aprocess’s variability relative to predefined product specifica-tions. Cpconsiders the tolerance range only, whereas Cpkconsiders both the tolerance range as well as how close theprocess average was to the nominal specification. Cpand Cpkwill have the same numerical value when the process averageis centered around nominal. As the process average movesaway from nominal, Cpk will decrease.9.2 The decision to accept or qualify a manufacturingprocess shall be based on the following criteria:9.2.1 Accept—Cpk equals 1.67 or greater. Process is capableof consistently producing product within specification, if con-trolled properly, using statistical process control (SPC) tech-niques.9.2.2 Conditional Acceptance—Cpk equals 1.33 to 1.67.Machine/process is marginally capable. SPC techniques maybe used; however, special care must be taken to ensure that themachine/process average is as close to nominal as possible.Occasional 100 % sorting of product may be required.9.2.3 Reject—Cpk equals less than 1.33. Process is incapableof producing product within specification. This will require100 % sorting by the machine/process operator.9.3 A process with Cpk 1.33 may also be accepted if bothof the following conditions exist.9.3.1 Cp≥ 1.67, and9.3.2 The machine/process is such that the machine/processaverage can be controlled by the machine operator throughnormal machine/process adjustments.9.3.3 The requirements identified in 4.3 shall be imposed onany machine/process that receives conditional acceptance.9.4 In many cases, capability may vary depending on thedegree of control exercised during the study (that is, the typeand frequency of adjustments made). The purchaser is respon-sible for reviewing all adjustments made during the study andensuring that the same level of control can/will be used inproduction.9.5 If the original machine/process capability study is con-ducted at the equipment vendor’s facility, a follow-up studymust be performed after the machine/process is set up andrunning in the appropriate manufacturing facility to confirmresults.10. Documentation10.1 It is recommended that documentation of each gagerepeatability/reproducibility study and MPC study conductedbe maintained and used as a benchmark for continuousimprovement of the machine/process.11. Keywords11.1 bilateral specification; capability; Cp; Cpk; fasterners;gage capability; inspection plan; machine capability; machinecapability study; process capability; process capability study;process parameters; sampling; SPC; statistical process control;unilateral specificationSUMMARY OF CHANGESThis section contains the principal changes to the standard that have been incorporated since the last issue(F1503 – 95).(1) Revised the title from Potential to Capability Study, andthroughout the body of the standard to reflect current industrypractices.(2) Changed the capability measure index from Ppand Ppk toCpand Cpk to align the pracice with short-run studies.(3) Removed the figures of variables and individuals controlcharts.TABLE 2 Machine/Process Standard DeviationEstimate the process standard deviation (the estimate is shown as sˆ “sigmahat”).Using the existing sample size calculate:sˆ=R¯/d2Where R¯is the average of the subgroup ranges (for periods with the ranges incontrol) and d2is a constant varying by sample size, as shown in the table below:n2 3 4 5 6 7 8 910d21.13 1.69 2.06 2.33 2.53 2.70 2.85 2.97 3.08F1503 − 02 (2012)3ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. 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