Lektion 4. Sources of variation. Attribute Chapter 6 Attribute control
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1 Lektio Chapter 6 Attribute cotrol Sources of variatio Chace causes (Slupässiga källor) Rado variatio Backgroud oise Statistical cotrol, stable process Assigable causes (Systeatiska källor) There is a cause Out of cotrol Not stable The purpose of SPC is to detect ad eliiate systeatic (assigable) sources of variatio! Attribute Yes/No data. Nuber of defect uits i a batch. Bioial distributio p-diagra p-diagra Couatble data Nuber of defects (a product ca have several) i a batch. Poisso distributio c-diagra u-diagra
2 Defect No-coforig Deviatio fro give specificatios Defective Defective uit Ca have oe or ore o-coforaties. I this chapter: No-coforig Classificatio Deerit systes page 3 Class A Very Serious The uit is either copletely ufit for service, or will fail i service i such a aer that caot be easily corrected i the field, or will cause persoalijury or property daage. Class B -- Serious Class C Moderately Serious Class D Defects -- Mior Fractio ocoforig Nuber of ocoforig divided with the toal uber of uits i the populatio. A uit ca have ultiple characteristics. If at least oe characteristics differs fro specificatios the uit is judged as ocoforig. Give as percetage. 2
3 Model for fractio ocoforities. Assue that the process is stable ad that the uits are idepedet of eachother. Let saple size p fractio ocoforig. Duber of defects i the batch. D is the Bioially distributed ad D pˆ x x P( D x) p ( p), x,,, x µ pˆ p 2 p( p) σ pˆ Cotrol liits for bioial data. Phase I uber saple groups uder phase I. Di pˆ i, i,, pˆ p i i i D i Cotrol liits: p( p) UCL p + 3 CL p p( p) LCL p 3 UCL CL LCL Tid, provuer Exact Bioial Cotrol liits Bioial data Probability liits D UCL Decide UCL: P UCL α 2 D LCL Decide LCL: P LCL α 2 α Matlab : UCL / bioiv(,, p) 2 Poisso approxiatio ( p) D D x x p p ( p) e i x i x! Noral approxiatio x For sall values o p the probability liits should be used. 3
4 Exepel 6- Apelsi juice boxes Estiate process average 3 5 p D i i.233 Cotrol liits ( p) UCL p + 3 p.42 CL p ( p) p LCL p Exepel 6-, Iitial Phase.5 Adele avvikade, p Försöks UCL.42 Two alar! Idetify the cause! New liits?. Försöks LCL Provuer 4
5 Adele avvikade, p Reviderad UCL.3893 Reviderad LCL.47 Exepel 6-, Iitial Phase New Material New Operator Caot fid cause to poit 2. - Keep it! The Process stabil The level too high! Iproveets ad adjustets Provuer.5 Exepel 6-, Iitial Phase New Operator New Material Adele avvikade, p.4 UCL Maskijusterigar Process is stable! Process see to be better! Is it?. LCL Provuer p p2 Is the adjusted process better? Test hypothesis H : p p2 H : p > p2 Saple statistics (oral approx.): pˆ pˆ 2 Z N(,) pˆ ( pˆ ) + 2 ˆ ˆ p + 2 p2 pˆ + 2 pˆ.25 pˆ 2.8 pˆ z > z We reject H o level α.5. Aswer: Yes. There is a differece! 5
6 .5 New Operator New Material Exepel 6-, Phase II Adele avvikade, p.4 UCL LCL.47 UCL.244 LCL Provuer Further iproveet eed aageet support ad oey. Exepel 6- Cotrol liits (Noral approx) ( p) p UCL p ( p) p LCL p Cotrol liits (Bioial) UCL.26 LCL Wider liits! saple size saple frequecy Desig of p-diagra width of cotrol liits (α) 6
7 How large saple size ()? Choose such that P( D, p).95 Exeple p. P( D ) p ( p) ( p).5 log(.5) 298 log( p) We wat for Ex. 6- that LCL> p( p) LCL p L > p.8 > L p OC-curva β P( pˆ < UCL p) P( pˆ < LCL p) P( D< UCL p) P( D< LCL p) ARL α ARL β p-diagra Valid for all proportios ocoforig if Failure frequecy is costat. Data are idepedet. Warig for Cluster Depedecies 7
8 p-diagra Cotrol the uber of defect istead of proportio. Clearer! UCL p + 3 p( p) CL p LCL p 3 p( p) Choose itegers as liits as Cotrol chart for ocoforities A uit ca have ay ocoforities. Nuber of defects is iportat. Nuber of defects per uit. Defects per car Nuber of defects per area, legth Defects per of pipelie Nuber of piholes per 2 o plastic fil Poisso distributio D Poi ( c) c x e c p( x) P( D x), x,, x! c> the paraeter of Poisso distributio Not syetrical! Exeple holes i fil 8
9 Poisso cotrol chart Estiate c with Di i cˆ Cotrol liits becoes UCL c + 3 c CL c LCL c 3 c Out of cotrol pla (OCAP) ust be writte. Classify defects. Pareto diagra Cause ad effects diagra Refer to Table 6-9 for occurrece of defect type by type of prited circuit board (part uber)` Aalyse the defects! 9
10 u-diagra Saple size Nuber of defects i saple D D u Di i uˆ Cotrol liits u UCL u + 3 CL u u LCL u 3 Proble with Poisso odel Cluster Bacteria Nuber of defects per car Copoud Poisso distributio To choose betwee variable ad attribute diagra? Attribute: The su of ay defects collected i oe diagra. Variable: More kowledge about the pheoeo. x R diagra larar! p diagra larar! LSL µ µ 2 µ 3 USL
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