Control Charts. Introduction. Purpose and benefit: UCL (upper control limit) UWL (upper warning limit) Quality feature

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Tyler Fowler
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1 Qality featre Cotrol Charts Itrodctio A Cotrol Chart shows the time corse of a process characteristic. For this prpose, data ca be take cotiosly or i periodic samples. The prereqisite is that the process capability has previosly bee cofirmed. The Cotrol Chart is also well kow as Statistical Process Cotrol SPC. There are cotrol charts for cotiig qatitative measrads ad for attribtive characteristics (test with cots). The sole represetatio of a cotiig measrad is defied as a sigle measremet chart. Cotiig measremets Sigle measremet chart (oly measrad o its ow) x /s - cotrol chart (additioally with scatter distribtio) Attribtive characteristics p-chart proportio of defective its p-chart mber of defective its x /R - cotrol chart (additioally with distribtio of rage) -chart Nmber of errors per it for mltiple possible errors Prpose ad beefit: The qality cotrol chart helps i recogizig systematic ifleces of a process, as well as distrbace variables ad evirometal ifleces. I the SPC, warig ad cotrol limits calclated statistically from the process data are determied ad etered. A itervetio is oly reqired if the cotrol limits are exceeded, leadig to a more stable process (see illstratio): UCL (pper cotrol limit) UWL (pper warig limit) Cetral lie (mea vale) Nomial vale LWL (lower warig limit) LCL (lower cotrol limit) Time scale If oe or more vales of a radom sample is/are otside the cotrol limits, this defect mst be idetified ad rectified as qickly as possible before the process exceeds the tolerace limits. Note: The tolerace is ormally ot show i the cotrol chart. 1

Cotrol Charts Frther itervetios mst be made if the followig coditios are met: Oe poit otside 3s 6 poits i sccessio risig or fallig ot of 3 poits i sccessio otside s 9 poits i sccessio o the same side

2 Cotrol Charts Frther itervetios mst be made if the followig coditios are met: Oe poit otside 3s 6 poits i sccessio risig or fallig ot of 3 poits i sccessio otside s 9 poits i sccessio o the same side 4 ot of 5 poits i sccessio otside 1s 14 poits i sccessio alteratig above ad below the midlie 8 poits i sccessio otside 1s A expasio to 8 rles is also referred to the so called "Wester Electric Rles". The cases of these deviatios mst be ascertaied. Measres carried ot i a correspodig way are oted o the SPC. The prodctio qatity sice the last radom sample was take mst be traced. Basics ad examples x - Qality cotrol chart I the followig illstratio, the legth of a trasverse member was moitored sig the SPC: UCL OE G OWG UWL Prodktm erkm al mea Mittel LWL UWG LCL UE G Absolte Häfigkeit lafede Nm m er

3 Cotrol Charts What are referred to as the lower/pper warig limits LWL/UWL ad cotrol limits LCL/UCL are show o the right. LWL - UWL % Average vale ± s LCL - UCL % Average vale ±3 s The areas ± s ad ±3s correspod to a probability rage of 95.45% ad 99.73%. (Note: I sorces from the Germa literatre, warig ad cotrol limits above 95% ad 99% probability are ofte defied). These limits do ot reflect the tolerace rage, bt rather oly the observed freqecy distribtio (histogram o the left i the previos illstratio) of the particlar radom sample parameter that is beig moitored. The tolerace limits are ever specified o the process cotrol chart. The collected process data does however form the basis for the process capability ivestigatio i relatio to the tolerace (see Cp/Cpk). The warig ad cotrol limits are calclated periodically based o the most recet process data. Itervetio of correctio of the process oly takes place oce the cotrol limits have bee dershot or exceeded. x/s - Qality cotrol chart I the x /s - qality cotrol chart acc. to Shewhart, the data is sbdivided ito radom samples. Withi these radom samples, it is possible to create a stadard deviatio for each, the profile of which is represeted alogside the average vale. The warig ad cotrol limits for the average vales are broght ito relatio with a sbdivided sample size here (stadard grop size = 5): LWL - UWL % Average vale LCL - UCL % Average vale s' / ' 3s' / ' Warig ad cotrol limits for the stadard deviatio are calclated here sig the ²-distribtio: LWL s 0,075, ' 1 ' 1 UWL s 0,9775, ' 1 ' 1 LCL s 0,00135, ' 1 ' 1 UCL s 0,99865, ' 1 ' 1 The stadard deviatio shold always be as small as possible, so the LWL ad LCL are ot sed as a rle. Qality cotrol charts for qalitative featres Qalitative featres are derstood to be evets sch as falty/good, yes/o or missig/ot missig, etc. I this case, large sample rages are reqired so that defects ca be detected. If there are very low defect probabilities, coseqetly, the samples mst be take over a log period ad this ca be a disadvatage. The followig differetiatio is made: 3

4 Cotrol Charts p-card -card The proportio of falty its i the sample is etered here Here, the mber of defects per it i the sample is etered p-card The sample rages do ot have to be costat, althogh a flctatio of more tha 5% is ot recommeded. The relative proportio of falty its is: p ' * ' p ' Depedig o whether the relative defect proportio (p-card) or the absolte defects are oted o the cotrol chart, there is also what is referred to as the p-card for the latter case. I the p-card, the radom sample rage is costat. The average defect proportio i several radom samples is the: 1 p tot m i1 * i The cotrol limits are calclated by way of approximatio to the ormal distribtio where: LCL 3 Here too, LCL is geerally ot reqired, particlarly sice egative vales are mathematically possible. -card I the -card, the radom samples mst cosist of its with several compoets or defect possibilities. The sample size ca be differet, bt shold ot flctate by more tha 5%. The mber of defects per it is: c ' p : relative defect proportio * : mber of falty its : sample rage (falty ad itact its) : mber of defects per radom sample m : mber of radom samples tot : mber of total its c : mber of defects i the radom sample : sample rage Aalogosly to the -card, there is also the c-card, i which the absolte mber of defects is show here. The radom sample rage is costat. I the -card, the average mber of defects is: 1 tot m i1 c i The cotrol limits are calclated as follows: * i UCL 3 c i : mber of defects per radom sample m : mber of radom samples tot : mber of total its : Mea sample size UEG 3 OEG 3 : Mea sample size LCL, however, is sally ot sed ad ca also be egative. 4

5 Cotrol Charts Usig Visal-XSel All cotrol charts are available as templates. Click to the ico i the mai gide or se me File / Templates 5

Cotrol Charts Use the Paste lik for yor data i the clipboard,

After data trasfere start the macro The the charts o the right

6 Cotrol Charts Use the Paste lik for yor data i the clipboard, which has to be copied before (e.g. from Excel). After data trasfere start the macro The the charts o the right mai widow has pdate with the ew data I case of the Cotrol_Chart_x_s.vxg o the d page the "Wester Electric Rles" will be show, if relevat coditios where met here. The example has at poit 17 oe poit is otside ± 3s 6

Statistical Fundamentals and Control Charts

Statistical Fundamentals and Control Charts Statistical Fudametals ad Cotrol Charts 1. Statistical Process Cotrol Basics Chace causes of variatio uavoidable causes of variatios Assigable causes of variatio large variatios related to machies, materials,