TNG CC TIU CHUN O LNG CHT LNG

TRUNG TM NNG SUT VIT NAM

TI LIU O TO

QUN L CHT LNG BNG CNG C THNG K

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Mc lc

PHN I: QUN L CHT LNG BNG CC CNG C THNG K 5I. Gii thiu chung v cc cng c SQC 5II. Qun l cht lng bng cc cng c thng k 6

Yu cu i vi o to nhn lc trong vic p dng SQC 6Yu cu ca ISO 9000 lin quan ti vic qun l cht lng da trn d liu thc t 6

PHN II: PHNG PHP THU THP D LIU 7I. Cc khi nim 7

1. Cc d liu cn thu thp 7D liu dng bin s 7Gi tr ri rc (d liu nguyn) 8

II. PHIU KIM TRA (Checksheet) 81. Nguyn tc 82. Cc loi d liu cn ghi 83. V d v phiu kim tra thu thp d liu 9

III. BIU PARETO 101. Khi nim 102. ngha 103. Cc bc xy dng biu Pareto 104. V d xy dng biu Pareto 115. S dng biu Pareto 14IV. LU (FLOW PROCESS CHART) 14V. BIU NHN QU 16

1. Khi nim 162. Xy dng biu nhn qu 16

2.1 Hnh dng ca mt biu nhn qu 162.2 Phng php pht hin cc yu t ca biu nhn qu 17

3. S dng biu nhn qu 184. V d biu nhn qu 18

VI. BIU PHN B (Histogram Biu ct) 191. S bin ng v phn b 192. Tng th v mu 193. Yu cu trong vic ly mu 204. Biu phn b 214.1. Cc thng s thng k 214.2. Xy dng biu phn b 234.2.1. Thit lp bng tn sut 234.2.2. V biu phn b 244.3. V d v v biu phn b 254.4. S dng biu phn b 28

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4.5. Phn tch hnh dng biu phn b 284.6. Xc nh v phn tch nng lc qu trnh 29Ch s nng lc qu trnh 29

VII. BIU PHN TN (Scatter diagram) 311. Biu phn tn 312. H s tng quan 313. Phng trnh hi qui 314. Xy dng biu phn tn 325. S dng biu phn tn 33VIII. BIU KIM SOT 361. Khi nim biu kim sot 362. ngha 373. Cc nh ngha 373.1. Cc ng kim sot 373.2. Cc c tnh kim sot (cc gi tr) 373.3. Cc bin lin tc hay d liu lin tc 383.4. Cc gi tr ri rc hay d liu m c 383.5. Nhm nh (mu) 384. Cc loi biu kim sot 384.1. Biu kim sot cho cc d liu dng bin s 38

4.1.1. Biu kim sot RX 384.1.2. Biu kim sot SX 394.1.3. Biu kim sot X -Rs 394.1.4. La chn loi biu 394.1.5. Thu thp d liu cho biu kim sot (d liu dng bin s): 404.2. Biu kim sot cho d liu nguyn: 434.2.1. Biu kim sot np 434.3. Biu kim sot p 434.4. Biu kim sot c 444.5. Biu kim sot u 455. La chn biu kim sot d liu dng nguyn 466. Thu thp d liu cho biu kim sot (d liu dng nguyn) 467. Cng thc tnh 478. Xy dng biu kim sot 49

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8.1. Cc bc xy dng biu x - R 498.2. Xy dng cc biu khc 499. Phn tch biu kim sot 5010. V d 51

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PHN I: QUN L CHT LNG BNG CC CNG C THNG K

I. Gii thiu chung v cc cng c SQC

Hin nay, cc cng c kim sot cht lng da trn phn tch s liu c chia thnh hai nhm:

Nhm 1: Gm 7 cng c truyn thng hay cn gi l 7 cng c kim sot cht lng (7 QC tools). Cc cng c ny c p dng mt cch hiu qu t nhng nm ca thp nin 60 v c ngi Nht p dng rt thnh cng. C s ca cc cng c ny l l thuyt thng k. Cc cng c bao gm:

1. Phiu kim tra (Check sheet)

2. Biu Pareto (Pareto chart)

3. Biu nhn qu (Cause-effect diagram)

4. Biu phn b (Histogram)

5. Biu kim sot (Control chart)

6. Biu phn tn (Scatter diagram)

7. Lu (Flow chart)

Phng php xy dng v ng dng cc biu ny s c trnh by chi tit trong phn sau. Nhm 2: Gm 7 cng c hay cn gi l 7 cng c mi (7 new tools) c pht trin v s dng t nhng nm u ca thp nin 80. Cc cng c ny h tr rt c lc cho qu trnh phn tch tm ra nguyn nhn gy ra cht lng km cng nh tm gii php ci tin cht lng. 7 cng c ny bao gm:

8. Biu tng ng (Affinity diagram): Phn tch vn da trn cm gic

9. Biu quan h (Relation diagram): Phn tch vn da trn logic

10. Biu ma trn (Matrix diagram): Pht hin mi quan h gia mc tiu v chin lc, gia gii php ra v kh nng thc hin

11. Phn tch d liu theo phng php ma trn: Tm ra mc u tin cho cc gii php ra

12. Biu cy (Tree diagram): chia mt mc tiu thnh cc mc tiu nh hay mt phng n thnh cc phng n chi tit c th thc hin c trong thc t. Biu ny cng c th s dng phn tch nguyn nhn tng t nh biu nhn qu

13. Biu mi tn (Arrow diagram): S dng xc nh r cc s kin, cc nguyn nhn ca vn nhm tng hiu qu hoch nh gii php

14. S qu trnh ra quyt nh (PDPC): Cng c lp k hoch ngu nhin v d bo s khng chc chn qua vic phi hp thng tin ti mi giai on ca qu trnh.

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II. Qun l cht lng bng cc cng c thng k

Qun l bng d liu, qun l da trn thc t c xem nh k thut qun l quan trng ca qun l thng ngy. Kim sot cht lng thng k (SQC) c xem l cng c nm bt thc t to trn c s cc d liu s.

Trong nn kinh t th trng, mi trng kinh doanh khng ngng thay i, do cc cng ty phi khng ngng ci tin qui trnh hot ng v cht lng ca sn phm v dch v tng li nhun, khng ch duy tr v kim sot cht lng hin thi ca sn phm trn th trng m cn phi duy tr v kim sot qu trnh to ra sn phm. Thm vo , tng ny c lin tng ti Ngi ph hp nht, ngi m c th theo di cht lng sn phm hng ngy l ngi gn nht, ngi lun lun bn cnh sn phm Con ngi y l cng nhn, ngi iu hnh phn xng, ngi trc tip tham gia vo qu trnh to ra sn phm v cung cp dch v. Nu nhng ngi c th tham gia vo qu trnh kim sot v qun l, th y s l c s khuyn khch ci tin hiu qu nht v l cch t tn km nht m bo cht lng sn phm.

Tm li, nn tng ca thc hin kim sot cht lng da trn d liu thc t l s tham gia ca tt c mi ngi, c bit l nhng nhng ngi trc tip tham gia vo qu trnh sn xut v cung cp dch v.

Yu cu i vi o to nhn lc trong vic p dng SQC

m bo vic thc hin tt SQC, cn b cng nhn vin cn phi c o to hp l cc mc khc nhau tu mc ch s dng. C th:

- Cn b qun l v cc gim st vin phi quen thuc vi cc cng c kim sot cht lng v hiu r c s ca phng php thng k oc s dng trong qun l cht lng. H cng phi c o to y hng dn nhn vin p dng ng cc k thut thng k

- T trng t dch v hoc phn xng sn xut phi c o to v cc phng php thng k c th p dng ca 7 cng c qun l cht lng truyn thng v 7 cng c qun l cht lng mi. H phi c kh nng p dng cc k thut thng k ci tin vic kim sot cht lng cng nh cc cng vic hng ngy.

Yu cu ca ISO 9000 lin quan ti vic qun l cht lng da trn d liu thc t

Bng 1 di y cho thy mi lin quan gia yu cu ca ISO 9000 vi qun l cht lng da trn d liu thc t

Bng 1 : Yu cu ISO 9000 vi vic phn tch d liu

Phn tch d liu ISO 9000:1994 ISO 9000:2008

Yu cu trong tiu chun

4.20 8.2.1, 8.2.3, 8.2.4, 8.4

Mc ch kim sot v xc nhn kh nng ca qu trnh sn xut v c tnh ca sn phm

m bo s ph hp ca sn phm v t c cc kt qu ci tin

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Cc chc nng ch yu

nh gi nng lc qu trnh v c tnh ca sn phm

nh gi s tho mn khch hng

S ph hp ca sn phm c tnh xu th ca qu trnh,

sn phm

Nh cung ng Yu cu p dng Tu chn, ph thuc vo

doanh nghip Bt buc

Cc hot ng ch yu

Khng qui nh c th Thu thp v phn tch d liu

Cc k thut p dng

Hng dn trong ISO 9004 Hng dn trong ISO 9004

Cch dn gii yu cu

L mt yu cu c lp Nm trong yu cu gim st & o lng

Yu cu v vn bn ho

Phi xy dng v duy tr vn bn th tc

Phi lp k hoch

PHN II: PHNG PHP THU THP D LIU I. Cc khi nim

1. Cc d liu cn thu thp

L cc d liu v c tnh cht lng dng thng tin bng s (hoc thng tin c th c trnh by bng cc s liu) ca cc thc t khch quan. Vic kim sot cht lng c tin hnh vi 2 loi d liu: d liu v kt qu ca c tnh cht lng v d liu v qu trnh ch ra nguyn nhn ca c tnh cht lng.

D liu v c tnh cht lng cn phn nh cc iu kin cht lng ca qu trnh. Cc d liu c s dng kim tra xem sn phm c c ph hp vi cc c tnh cht lng yu cu nh tiu chun hoc yu cu k thut hay khng hoc xc nh phn vt qu c tnh cht lng bin ng vi mc tiu.

V d: c tnh cht lng ca gch men: bn (N/cm2), m.

D liu v iu kin qu trnh cng ch ra iu kin thc t p dng i vi qu trnh v iu kin trong chng c lp v duy tr.

V d c tnh ca qu trnh nung: nhit l ( C)

D liu dng bin s

Gi tr ca cc c tnh cht lng m c th o c nh mt i lng lin tc (JIS Z 8101)

V d: Chiu di ca chi tit (1,2m, 1,3m, 1,4m)

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Gi tr ri rc (d liu nguyn)

Gi tr ca c tnh cht lng c th m c nh l s cc khuyt tt hoc s sn phm khuyt tt.

V d : 3 sn phm khuyt tt/ 1000 sn phm c kim tra

II. PHIU KIM TRA (Checksheet)

Phiu kim tra l mt trong by cng c truyn thng thng c s dng cho vic thu thp d liu. D liu thu c t phiu kim tra l u vo cho cc cng c phn tch d liu khc, do y bc quan trng quyt nh hiu qu s dng ca cc cng c khc.

1. Nguyn tc

- Ghi chp li cc d liu vo mu ghi h s tiu chun - Ghi chp li mi d liu cn thit - Ghi chp cc d liu i vi cc loi hnh cng vic, my mc v thi gian khc

nhau.

- Cc d liu cn phi chnh xc v y vi cc ni dung tin cy dng cc con s c ngha phc v cho mc ch kim tra.

- Trnh ghi chp khng chnh xc, b st, vit khng ng quy nh, ghi chp sai ni dung hoc khc phc sai

- Trnh phiu ghi chp cho cn b qun l c trch nhim th nghim ng thi hn tho nh quy trnh m t

- Phiu ghi chp cn phi c nh du xc nhn v nhn xt bi nhng ngi c trch nhim kim tra, ngy lp h s v cc nhn xt cn thit hoc hng dn vin

- Trong cc trng hp m t khng ng, khng chnh xc, khng r rng hoc cc h s cng vic m khng p ng tiu chun, cn b qun l chu trch nhim lp h s, xc nhn ni dung v ban hnh vn bn hng dn hnh ng khc phc.

- Sau khi xc nhn h s ng n, cn b qun l c trch nhim kim tra cn k hoc nh du vo ct c th chng minh s ph duyt. Khi s dng cc d liu cn xem xt tnh khch quan v tin cy.

2. Cc loi d liu cn ghi

Cc h s cn phi m t ng v cc thit b o, ngi kim tra, thit b kim tra, phng php kim tra. Cc d liu c th c trong phiu kim tra bao gm:

- Tn v s hiu sn phm

- Thi gian

- Tn qu trnh

- Tn thit b

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- Tn cng vic

- Tn ngi vn hnh

- Tn ngi ghi h s

- S hiu l trong qu trnh trc

- S hiu l ca nguyn vt liu

- D liu v iu kin qu trnh (nhit , tc , p sut, nng , ni dung, thi gian v cc thng tin khc)

- Tn v s hiu ca cc dng c v g

- Tn v s hiu ca cc thit b o

- iu kin ly mu th nghim v tn s kim tra.

- Cc d liu v c tnh cht lng, chp nhn hay loi b.

- Khuyt tt, m t chi tit, bo co v hnh ng khc phc.

3. V d v phiu kim tra thu thp d liu

Bng 2 - Phiu kim tra iu tra khuyt tt ca my copy

BM 01-02-01 Phiu ghi s c thit b

Sn phm My copy Thi gian iu tra

1-6 thng 6

S hiu sn phm FX-124 B phn B phn tng hp

Ngy mua Thng 4/ 1999 Ngi ghi h s

Thnh vin nhm: Nguyn Vn A

Ngy thng

Loi khuyt tt

6/1 6/2 6/3 6/4 6/5 6/6 Tng

Qu ti ///// ///// / ///// // ///// / ///// /// ///// 37

Qu m ///// ///// ///// ///// ///// // ///// ///// / ///// / 44

Bn /// /// //// ///// ///// // ///// 27

Sai v tr // / ///// // /// /// 16

Sai c / / /// // // /// 12

Kt giy // / / // // / 9

Cc li khc / // / / // // 9

Tng 24 19 26 25 35 25 154

S bn copy 1.808 1.615 1.720 1.900 2.010 1.345 10.398

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Bng d liu thu thp c cho thy loi khuyt tt qu m xy ra nhiu nht v thng xuyn nht. S dng cc cng c thng k nh biu nhn qu, biu pareto x l v phn tch cc s liu thu c s gp phn tm ra gii php nng cao cht lng bn copy v gim s lng khuyt tt.

III. BIU PARETO

1. Khi nim

Biu Pareto c Loren xy dng da trn hc thuyt Pareto (tn ca mt nh kinh t hc ngi ), l phn ln ca ci ca x hi nm trong tay mt s t ngi. Tin s Juran (M) ng dng phng php ny vo lnh vc qun l cht lng theo phn lot cc vn v cht lng thnh vn trng yu v th yu. ng ch ra rng phn ln cc khuyt tt v chi ph cht lng cho cc khuyt tt ny xut pht t mt s t nguyn nhn trong s nhiu nguyn nhn.

Biu Pareto s dng cc ct minh ho cc hin tng v nguyn nhn, nhm li cc dng nh l cc khuyt tt, ti sn xut, sa cha, khiu ni, tai nn v hng hc. Cc ng gp khc c thm vo ch ra tn sut tch lu (hnh 1).

2. ngha

Biu Pareto sp xp cc dng khuyt tt trn trc x theo tn s v s cc khuyt tt hoc tng sai li v tng tch lu ca chng trn trc y t ra hiu qu trong vic ch trng vo cc vn ln, tp trung ch khng phi nhiu vn nh nhng tn mn. Biu Pareto c s dng rng ri la chn cc vn v cc i tng nghin cu v kho st ti giai on lp k hoch ca gii quyt vn v cht lng v xc nhn kt qu ca hot ng khc phc khi cc hnh ng ny c thc hin.

T biu Pareto, cho thy:

1) Hng mc no quan trng nht,

2) Hiu c mc quan trng

3) nhn ra t l mt s hng mc trong s cc hng mc

4) T l ci tin c th thy c sau khi ci tin cc hng mc,

5) ln ca vn d dng thuyt phc khi nhn thong qua.

3. Cc bc xy dng biu Pareto

Bc 1. Xc nh nghin cu vn g v cch thu thp d liu.

(1) Xc nh vn cn nghin cu.

V d: Cc hng mc khuyt tt, tn tht bng tin hoc tn sut xut hin ri ro.

(2) Xc nh nhng d liu cn phn loi chng.

V d: Dng khuyt tt, v tr, qua trnh, my mc, cng nhn, v phng php.

Ghi ch: Tp hp cc hng mc t khi xut hin vo mc "Cc dng khc"

(3) Xc nh phng php thu thp d liu v thi gian thu thp d liu

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Bc 2. Sp xp bng d liu theo cc hng mc.

Bc 3. in vo bng tnh d liu v tnh ton tng s.

Bc 4. Lp bng d liu cho biu Pareto theo cc hng mc, tng s tng hng mc, tng s tch lu, phn trm tng th v phn trm tch lu.

Bc 5. Sp xp cc hng mc theo s lng khuyt tt gim dn v in vo bng d liu.

Ghi ch: Hng mc khuyt tt dng khc phi t cui dng mc d s lng khuyt tt ln.

Bc 6. V trc tung v trc honh.

(1) Trc tung

(a) Bn tri trc tung: nh du vo trc, chia t 0 n tng s cc khuyt tt

(b) Bn phi trc tung: nh du vo trc, chia t 0% n 100%.

(2) Trc honh

Chia trc honh thnh cc khong theo s cc loi khuyt tt c phn loi.

Bc 7. Xy dng biu ct.

Bc 8. V ng cong tch lu (ng cong Pareto).

nh du cc gi tr tch lu (tng tch lu hay phn trm tch lu) pha trn bn phi khong cch ca mi mt hng mc, ni cc im bng mt ng thng.

Bc 9. Vit cc chi tit cn thit trn biu .

(1) Cc chi tit lin quan ti biu : Tiu , cc con s quan trng, n v, tn ngi v biu .

(2) Cc hng mc lin quan ti d liu: thi gian thu thp d liu, ch v a im nghin cu, tng s d liu.

4. V d xy dng biu Pareto

Bc 1. Vn cn nghin cu: Sn phm c b li

- D liu cn phn loi chng: Cc loi khuyt tt ca sn phm c

- Phng php thu thp d liu v thi gian thu thp d liu: Kim tra 100% bng mt trong thi gian 3 thng : 4, 5, 6.

Bc 2. Sp xp bng d liu theo cc hng mc (dng khuyt tt)- Ct u, bng 4.1

Bc 3. in d liu thu thp c qua cc ln kim tra vo ct 2 bng 4.1 v tnh ton tng s, ghi kt qu vo ct th 3. Tnh tng s khuyt tt cc loi v ghi vo hng cui cng

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Bng 3-1: Bng d liu khuyt tt ca sn phm c

Dng khuyt tt

im s Tng s

(1) (2) (3)

St, m //// //// 10

Xc //// //// //// ////........//// // 42

Bn //// 6

Sc cng //// //// //// //// ////.....................//// //// 104

K h //// 4

L hng //// //// //// //// 20

Dng khc //// //// //// 14

Tng s 200

Bc 4. Lp bng d liu cho biu Pareto theo cc hng mc, tng s tng hng mc, tng s tch lu, phn trm tng th v phn trm tch lu- bng 4-2.

Bc 5. Sp xp cc dng khuyt tt trong bng 4-1 vo bng 4-2 theo s lng khuyt tt gim dn. Tnh tng tch lu, phn trm tng th v phn trm tch lu cho tng hng v in vo bng d liu.

Ghi ch: Hng mc khuyt tt dng khc phi t cui dng mc d s lng khuyt tt ln hn s lng ca dng khuyt tt c th (k h, bn, st m). T l phn trm tng th ca hng mc Khuyt tt khc ny khng nn qu ln (10%-15%)

Bng 3-2: Bng d liu cho biu Pareto

Dng khuyt tt

S lng khuyt

tt

Tng tch lu

Phn trm tng th

Phn trm tch lu

(1) (2) (3) (4) (5)

Sc cng 104 104 52 52

Xc 42 146 21 73

L hng 20 166 10 83

St, m 10 176 5 88

Bn 6 182 3 91

K h 4 186 2 93

Dng khc 14 200 7 100

Tng s 200 - 100 -

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Bc 6. V trc tung v trc honh.

(1) Trc tung

(a) Bn tri trc tung: nh du vo trc, chia t 0 n 200 (tng s cc khuyt tt)

(b) Bn phi trc tung: nh du vo trc, chia t 0% n 100%.

(2) Trc honh

Chia trc honh thnh 7 khong theo s hng mc cc loi khuyt tt c phn loi.

Bc 7. Xy dng biu ct (ly d liu t ct th 2 ca bng 4-2). Biu c th hin trn hnh 1

Bc 8. V ng cong tch lu (ng cong Pareto) bng cch ly d liu t ct 3 hoc ct 5 ca bng 4-2.

nh du cc gi tr tch lu (tng tch lu hay phn trm tch lu) pha trn bn phi khong cch ca mi mt hng mc, ni cc im bng ng thng.

Bc 9. Vit cc chi tit cn thit trn biu .

(3) Cc chi tit lin quan ti biu : Tiu , cc con s quan trng, n v, tn ngi v biu .

(4) Cc hng mc lin quan ti d liu: thi gian thu thp d liu, ch v a im nghin cu, tng s d liu.

Hnh 3-1: Biu Pareto cho cc hng mc khuyt tt

Ph

n tr

m k

huy

t tt

S sn phm kim tra: 5000 Thi gian: 1/4 - 30/6/2013

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5. S dng biu Pareto

Biu Pareto s dng :

1) Quyt nh vn trng yu cn gii quyt,

2) Thy r s khc nhau gia trc khi ci tin v sau khi ci tin,

3) Bo co hay ghi li mt cch d hiu.

Mt s lu khi s dng biu Pareto

(1) Phn loi tn tht theo s lng khuyt tt, t l khuyt tt, s lng khiu ni, chi ph cht lng cho cc loi khuyt tt.

(2) Xc nh khong thi gian theo di ph hp vi mc ch.

(3) Xy dng biu Pareto bng cch thu thp cc d liu c phn vng theo nguyn nhn (yu t) hoc kt qu (c tnh, hin tng). Khng nn ly cc d liu t cc loi khc nhau, mc khc nhau, cc nguyn nhn khc nhau.

(4) Khi s dng biu Pareto theo mt phng php no m khng th phn bit c s khc nhau gia cc thnh phn, th nn thay i phng php phn loi hoc cc c tnh trn trc y xc nh c cc thnh phn quan trng.

IV. LU (FLOW PROCESS CHART)

1. Phn tch qu trnh (process analysis)

Trc khi mun thay i hay ci tin mt qui trnh, phi hiu r qui trnh , c ngha l phi phn tch qui trnh. Lu qui trnh nhm gip tm hiu v phn tch qui trnh.

Lu l mt cng c hu hiu gip vic hiu v phn tch mt qu trnh do cch trnh by n gin, d hiu.

2. Xy dng lu

Mt lu qui trnh c xy dng tt lm sng t cc tng quan trong qui trnh ng thi cc lu qui trnh l cng c rt c gi tr gip nhn nh c cc khu vc c ph phm, lp li v sai lm.

Tuy nhin, thng th mt ngi n c khng th thu hiu ton th mt qui trnh. Ngay c mt t son tho qui trnh cng c th mi ngi hiu mt cch. Mt th nghim cho thy, sau khi son tho mt qui trnh c th, mi ngi trong t son tho c yu cu t xy dng lu ring cho qui trnh. Kt qu cho thy, cc biu trn u khc nhau. L do ca s khc nhau nh sau:

- Mi ngi nhn qui trnh theo quan im ca mnh. Th d ngi c cng sn xut nhn vn khc ngi chu trch nhim mua hng d hai ngi u phi c cng mc tiu.

- K nng khng cng ngnh : mt k s dng k thut nghin cu mt qui trnh khc vi ngi qun l b phn phn phi.

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- Nhiu ngi khng bao gi mo him vt qua phm vi trch nhim ca mnh nghin cu ton th mt qui trnh nn vic nm bt tinh thn qui trnh ca h ch gii hn trong phng s ca mnh.

khc phc cc vn trn, cch gii quyt tt nht l:

- Cn c s hp tc ca mi ngi c lin h n tng bc ca qui trnh nhm m bo s chnh xc ca biu sau khi hon tt.

- Vic xy dng mt lu qui trnh cng l vic xy dng mt qui trnh, thc hin tng bc mt theo cc bc sau:

9 Bc 1 - Xc nh ranh gii : Thn trng trong vic xc nh ranh gii ca qui trnh xy dng biu , nu khng s mt thi gi nghin cu cc qui trnh khng lin quan g vi mc tiu. Cng khng nn gii hn thi qu v s khng qui nh cc hot ng quan trng trong mt qu trnh.

9 Bc 2 - Xc nh mc chi tit : Cc chi tit cn c trnh by va . Mt biu c tnh tng qut th ng bao gm qu nhiu chi tit, ngc li mt biu khng c chi tit th khng li ch g cho vic phn tch tm cc phn ph phm, thiu hiu nng.

9 Bc 3 - i tng cng on mt : Cc bc u tin s c tc ng quan trng ln thnh qu ca qui trnh, nn khi mo t u mi, ni pht sinh ra cc hnh ng tip theo

9 Bc 4 - Xy dng lu d tho : xy dng sn biu m bo c tt c cc cng on ca qu trnh.

9 Bc 5 - Kim sot chnh xc v y : Mi ngi c lin quan phi c mi gp kin nhm m bo rng:

- Mi bc u c trnh by

- Lu qui trnh ang xy dng c trnh by mt cch trung thc nh ang xy ra, khng l tng ha hay lm theo thi c.

9 Bc 6 - Xy dng Lu hon tt : Nu c s thay i hay gp , lu qui trnh c sa i theo yu cu ng gp.

9 Bc 7 - Kim tra li : Lm li bc 5 v nu cn iu chnh ln cui m bo s chnh xc v y .

Cc cu hi phi c t ra cng nhiu cng tt theo sn sau y:

9 Dch v, nguyn vt liu hay vn do u m c, t ai? 9 S tham gia ca cc vn , dch v, nguyn vt liu vo qu trnh nh th no? 9 Ai phi ra quyt nh? Vic g phi lm k tip? 9 Nu tnh hung l C th s vic din bin nh th no? 9 Nu tnh hung l Khng th s vic s din bin nh th no?

16

Thng mt s cc biu tng c dng trong vic thit lp biu . Khng nht thit bt buc phi dng, nhng cc du hiu trn gip nhn nh mt s nhng hot ng trong mi cng on ca qu trnh.

Hnh ch nht tng trng cho mt bc trong qu trnh. Tn ca bc hay cng on c vit bn trong hnh.

Hnh thoi tng trng mt im quyt nh phi c thc hin trc khi tin hnh mt hnh ng tip theo.

Hnh tng ny c dng khi to ra mt vn bn (phiu t hng).

Hnh trn c dng cho bit qu trnh s tip tc im khc

Mi tn ch cc hng i hay hng thc hin trong qu trnh

V. BIU NHN QU

1. Khi nim

Biu nguyn nhn v kt qu ch mi lin h gia cc c tnh mc tiu v cc yu t, nhng yu t dng nh c nh hng n cc c tnh, biu din bng hnh v ging xng c..

Biu nhn qu cn c gi l biu xng cc, biu Ishikawa.

2. Xy dng biu nhn qu

Biu nhn qu c gi l "biu xng c", bi v hnh dng ca n ging hnh xng c. Xng trung tm l xng sng, sau n xng ln, xng va v xng nh ...(Hng mc ln, hng mc va, hng mc nh...) c v ni nguyn nhn v kt qu. Do phi sp xp cc yu t lin quan mt cch c h thng v biu nhn qu.

2.1 Hnh dng ca mt biu nhn qu

17

Hnh 1: M hnh xy dng biu nhn qu

2.2 Phng php pht hin cc yu t ca biu nhn qu

Qu trnh pht hin cc yu t v xy dng biu theo phng php huy ng tr no bao gm cc bc:

Bc 1: a ra cc c tnh tho lun. Cc c tnh phi ph hp vi vn cn gii quyt vi mc ch r rng.

Bc 2: Tho lun v cc yu t, nhng yu t no c nh hng n cc c tnh, v thu thp cc yu t ny. Thng thng, khong 30 - 40 pht pht huy tr no tp th c th a ra cc yu t m t trong giy hoc th. Pht huy tr no phi theo 4 nguyn tc sau:

Khng ph phn ch trch kin ca ngi khc

Vit ra cng nhiu kin cng tt

Hoan nghnh cc kin ca ngi t do v khng cng s thch

B tr, xp xp v sa cha cc kin khc.

Bc 3: Phn loi cc yu t t 4 n 8 hng mc v v xng ln. Yu t xem xt cc hng mc ny bao gm:

My mc/Thit b

Nguyn vt liu

Con ngi/Ngi vn hnh

Phng php

Mi trng

o lng

H thng thng tin

XNG SNG Cc c tnh (Kt qu)

Xng ln

Xng nh

Xng va

18

Bc 4: Xc nh cc xng nh v va. Tm cc yu t t xng ln n xng va, t xng va n xng nh nh hnh 4.2

Bc 5: nh gi tm quan trng ca mi yu t v nh du vo cc yu t c nh hng ln ti c tnh cht lng c xem xt.

3. S dng biu nhn qu

t c cng vic tt, kt qu tt, cn thit l phi la chn nhng yu t no nh hng n cc c tnh v thc hin cc bin php i vi cc nguyn nhn thc lm h thp gi tr trung bnh hoc s bin ng ln. Biu nguyn nhn v kt qu rt c hiu qu trong nhng trng hp di y:

bit c cc nguyn nhn xy ra khuyt tt. Biu nhn qu l cng c hu hiu xp xp mi quan h gia nguyn nhn v kt qu, pht hin ra cc nguyn nhn thc phn tch v phn loi xem vn tn ti u. ng thi n c hiu qu trong vic din gii cc yu t thit k thc nghim.

chun b cc bin php ci tin. N c hiu qu trong vic phn loi hiu qu ca cc bin php lm gim nh hng ca cc nhn t c xc nh.

Cc im cn ch khi s dng biu nhn qu:

(1) V cc kin thu thp c t nhiu ngi

(2) Phi biu din cc c tnh mt cch c th

(3) Thu thp tt c cc yu t

(4) Thu thp cc d liu

(5) Xem xt nghin cu theo thi gian

(6) Pht hin cc yu t xu.

4. V d biu nhn qu

19

Hnh 2: Biu nhn qu v khuyt tt hnh dng ca khun c.

VI. BIU PHN B (Histogram Biu ct)

1. S bin ng v phn b

Nu chng ta c th thu thp d liu t mt qu trnh m trong qu trnh tt c cc yu t (con ngi, my mc, nguyn vt liu v phng php) u khng thay i (bt bin), th tt c cc d liu chng ta thu c s c cng gi tr. Tuy nhin, trong thc t, khng th duy tr tt c cc yu t ny trng thi bt bin trong mi lc. Ni ng ra, thm tr c mt vi yu t, chng ta gi thit, c trng thi bt bin nhng khng phi bt bin mt cc hon ton. N chc chn s xy ra s bin ng i vi cc gi tr ca d liu thu c. Gi tr ca d liu khng s khng ging nhau trong mi lc, tuy nhin iu ny khng c ngha rng chng c xc nh theo phng php ba bi. Mc d cc gi tr thay i trong mi lc, chng vn c qun l theo nguyn tc nht nh, v tnh hung ny a n vic cc d liu c phn b theo s phn b nht nh.

2. Tng th v mu

Tng th

Mt nhm thc th c cc c tnh cn iu tra hoc nghin cu.

Khuyt tt hnh dng

Khun mu iu kin c thit lp

L thng kh

S y ga

S bo mn Thit k lnh

ng knh ng

Cng

Dng chy

Thit k dng chy Hnh dng S cn

bng

My lm khun Nguyn vt liu

Cn bng dng chy

Xy lanh

Mi tim L nung S gm mn

Nha r

Pt tng

p lc

Xoay

H hi Chng xoay

Lp di Nc bn ra

Lm kh

Nhit Thi gian

Khi lng kh Bin ng l

nht Ga

tan chy

Khi lng phn t

Du

Hng bm

Mn cc b phn p lc du

Thuc vin

Bt thuc

th

Nhit xy lanh

Nhit thp

iu chnh

Tim

Thi gian p lc

o lng

p lc ngc li

20

Mt nhm cc thc th l i tng ca cc hnh ng c thc hin da trn cc mu. (JIS Z 8101- Vin tiu chun Nht)

V d: Trong sn xut chi tit t mang nhn hiu X120, tt c cc chi tit mang nhn hiu X 120 c to ra l mt tng th

Mu

Mt phn ca tng th c la chn nghin cu cc c tnh ca n (JIS Z 8101)

V d: Khi kim tra cht lng chi tit X120 ni trn, mi ngy c 10 chi tit c ly ra phn tch, o lng cc c tnh v ho, ly l mu ca tng th cc sn phm to ra

Tng th l i tng ca cc hnh ng cn thc hin, da trn cc thng tin da trn cc d liu. Lun lun nh rng nhng g thu c t cc d liu ny ch gii hn i vi tng th ny.

i vi kim sot cht lng, chng ta c gng nhn bit thc t thng qua thu thp d liu v c cc hnh ng cn thit da trn thc t . Trong vic kim tra mu, chng ta ly mu t mt l sn phm, tin hnh cc php o i vi mu , v sau quyt nh xem chng ta c chp nhn ton b l sn phm hay khng. y mi quan tm ca chng ta khng phi l vic ly mu m l cht lng ca ton b l sn phm.

3. Yu cu trong vic ly mu

(1) Cn la chn phng php ly mu ph hp vi mc ch ly mu. Phng php ly mu bao gm ly mu ngu nhin n gin, ly mu 2 giai on v ly mu theo phn vng. S dng phng php ly mu hu ch i vi mc ch.

(2) o to cho nhng ngi thu thp d liu v vic s dng cc thit b o lng, phng php iu chnh chnh xc o, phng php o v phng php lm trn s liu v phng php ghi chp. Xc nhn iu kin hiu chun v chnh xc o.

Bn qui tc ly mu ngu nhin

Qui tc 1: Sn phm khng c ly mu bi nhng cng nhn trc tip sn xut ra chnh sn phm (phng nga s la chn c ch ).

Qui tc 2: Ly mu phi do ngi c thm quyn tin hnh (ly mu khng c kim tra trc).

Qui tc 3: Ngi thc hin ly mu t tng th phi hiu r v ngha v mc ch ca vic ly mu.

Qui tc 4: Ly mu ngu nhin da trn bng s ngu nhin, theo thi gian.

21

Tng th Mu D liu

Hnh ng i vi qu trnh (Kim sot qu trnh, Phn tch qu trnh)

Hnh ng i vi l (Kim tra, c tnh cht lng sn phm)

4. Biu phn b

Biu phn b l mt dng ca th ct trong cc yu t bin ng hay cc d liu c th c chia thnh cc lp hoc thnh cc phn v c din t nh cc ct vi khong cch lp c biu th qua ng y v tn sut biu th qua chiu cao.

4.1. Cc thng s thng k

a) Cc thng s ca phn b tng th

Trung bnh ca tng th: = E (X) lch chun ca tng th: Trn thc t thng khng th xc nh cc gi tr v v trn v khng th o lng ton b tng th. Trong qu trnh sn xut, thng ly mu, o lng v xc nh cc c tnh cht lng ca mu, xc nh cc thng s thng k ca mu v coi cc gi tr i din (bng) cc thng s thng k ca tng th

Qu trnh L Mu

o

Hnh ng

Mu D liu

L

Ly mu

o

Hnh ng

Ly mu

D liu

22

b) Cc thng s ca phn b mu

Gi tr trung bnh : x Tng n gi tr o chia cho n c gi l gi tr trung bnh (gi tr trung bnh s hc) v c k hiu bng ch

x =

Trong x1, x2, ... xn l cc gi tr o c v n l s cc gi tr o c. Gi tr x c coi l i din (bng) ca tng th rng (R) Khong chnh lch gia gi tr ln nht (Xmax) v gi tr nh nht (Xmin) ca cc d liu c gi l rng v k hiu l R

R = Xmax - Xmin

rng khng bao gi c gi tr m

R 0 lch chun (s): lch chun (s) ca mu c coi l i din (bng) lch

chun ca tng th s c tnh theo cng thc:

Trong V l phng sai

Phng sai V: V c tnh theo cng thc

1= n

SV

Trong S l tng cc bnh phng v gi tr (n 1) gi l bc t do. n l s cc gi tr x o c

Tng cc bnh phng (S) Tng cc bnh phng ca cc hiu cc gi tr ring v gi tr trung bnh c gi l tng cc bnh phng v c k hiu l S

S = (x1 - x )2 + (x2 - x )2 + ... + (xn - x )2

= (xi - x )2 Cng thc nh ngha

nxi 2)( Cng thc tnh ton

n

xi

nxnxx

n

i==+++ 1...21

= xi2 -

s = V

23

Trong nxi 2)( c gi l gi tr hiu chnh (CT)

V tng cc bnh phng v phng sai c quan h vi bnh phng cc gi tr o c nn ta khng th so snh cc gi tr da trn tng n v o. lch chun khng c s tr ngi ny nn c th s dng cc n v o.

4.2. Xy dng biu phn b

Qu trnh xy dng biu phn b bao gm :

Thit lp bng tn sut V biu

4.2.1. Thit lp bng tn sut

Bc-1 Tnh rng (R)

Tm ra gi tr ln nht v gi tr nh nht ca cc gi tr quan st c v tnh R. R=(gi tr ln nht quan st c) - (gi tr nh nht quan st c)

C th d dng tm ra gi tr ln nht hay gi tr nh nht qua cch sau: Chn cc gi tr ln nht v nh nht t mi dng ca bng cc gi tr quan st c, sau ly gi tr ln nht trong cc gi tr ln nht v ly gi tr nh nht trong cc gi tr nh nht. l gi tr ln nht v nh nht ca ton b cc gi tr quan st c.

Bc-2 Xc nh rng lp

rng ca lp c xc nh sao cho rng R, bao gm cc gi tr ln nht v nh nht, c chia thnh cc khong c rng bng nhau. c c rng cc khong bng nhau, chia R cho 1, 2 hoc 5 (hoc 10, 20, 50, 0.2, 0.5...) thu c t 5 - 20 khong c rng bng nhau. C 2 kh nng, s dng khong hp hn nu s lng cc gi tr o ln hn hoc bng 100. Nu gi tr ny nh hn hoc bng 99 th s dng khong rng hn.

S lp: S lp l bao nhiu th thch hp? Mt s ch dn rt d nh. S lp thng xp x bng cn bc 2 ca s d liu, v c cc iu chnh quyt nh rng thch hp. K c th ly theo bng di y:

S d liu (n) S nhm (k)

50 -100

100 - 250

250 -

6 10

7 12

10 20

Hoc tnh theo cng thc

K= n

24

Trc tin, tt nht hy quyt nh rng lp l 1, 2, 5, v sau iu chnh s lp cho gn bng vi K = n

rng lp Rt hp l khi rng lp c th c quyt nh bng cc con s n gin nh 1, 2 hay 5 (chng ta s dng h thp phn) v s lp phi c iu chnh.

h = (gi tr ln nht - gi tr nh nht)/ K

Gi tr i din ca lp Gi tr i din ca lp l im gia ca mi lp, thm ch c khi im gia ny khng trn s. Gi tr phn s khng gy tr ngi ln nhng nu l s trn th d hiu hn.

Bc-3

Chun b bng tn sut, trong gm cc lp, im gia, nh du tn sut, tn sut, vv...

Bc 4

Xc nh bin v rng ca cc lp sao cho chng bao gm cc gi tr ln nht v nh nht, vit vo bng tn sut

u tin, chn bin di ca lp u tin v cng thm rng ca mt lp xc nh c ng bin gia lp th nht v lp th 2. Khi thc hin vic ny, m bo rng lp th nht c cha gi tr nh nht. Tip tc nh trn ta c lp cui cng, m bo rng lp cui cha gi tr ln nht.

Bc-5

Tnh im gia ca cc lp theo phng trnh sau, tnh im gia ca lp v vit di bng tn sut.

im gia ca lp th nht = (Tng ca bin trn v bin di ca lp th nht)

im gia ca lp th hai = (Tng ca bin trn v bin di ca lp th hai)

V c tip theo nh vy Bc-6 Xc nh tn sut

c cc gi tr nhn c v ghi tn sut vo mi lp s dng cc k hiu.

Tn sut: 1 2 3 4 5 6

K hiu: I II III IIII IIIII IIIII I

4.2.2. V biu phn b

Bc-1

Trn t giy vung, nh du trc nm ngang theo mt t l. T l khng nn da vo rng ca lp m tt hn da trn n v o ca s liu.

V d 10 gam tng ng vi 10 mm

25

iu ny to iu kin thun li khi so snh cc biu phn b cng biu din cc yu t v c trng ging nhau cng nh cc yu cu k thut. Trn trc nm ngang ly mt khong bng rng ca lp v mi pha ca lp th nhtv cc lp cui cng.

Bc-2

nh du trc tung bn tay tri theo t l tn sut, v nu cn thit v trc tung bn tay phi theo t l tn sut tng i. Chiu cao ca lp c tn sut ln nht nn gp 0,5 n 2 ln khong cch gia gi tr ln nht trn trc honh.

Bc-3

nh du t l trc ngang vi cc gi tr bin ca lp.

Bc-4

S dng rng lp nh mt ng c bn, v hnh ch nht vi cao tng ng vi tn sut trong lp.

Bc-5

V mt ng thng trn biu phn b biu th gi tr trung bnh, v ng thi cng v mt ng thng ch ra gii hn k thut, nu c.

Bc-6

Ti ch trng ca biu , ghi ch thng tin v cc d liu ca biu (giai on thu thp d liu...), s d liu n, gi tr trung bnh, lch chun.

4.3. V d v v biu phn b

Trong mt phn xng sn xut trc xe p, sau mi ca sn xut, 10 mu sn phm s c ly ra o kch thc nhm nh gi cht lng qu trnh sn xut. D liu o c sau 3 ngy (9 ca sn xut c trnh by trong bng 6.1). V biu phn b cho cc d liu ny. Tiu chun kim tra kch thc trc l (2.52 0.02) Bc 1 : Tnh rng

Bng 0-1: Bng tnh rng (S liu v kch thc sn phm)

S mu

Cc kt qu ca php o Max Min

1-10 2.510 2.517 2.522 2.522 2.510 2.511 2.519 2.532 2.543 2.525

11-20 2.527 2.536 2.506 2.541 2.512 2.515 2.521 2.536 2.529 2.524

21-30 2.529 2.523 2.523 2.523 2.519 2.528 2.543 2.538 2.518 2.534

S mu

Cc kt qu ca php o Max Min

31-40 2.520 2.514 2.512 2.534 2.526 2.530 2.532 2.526 2.523 2.520

41-50 2.535 2.523 2.526 2.525 2.532 2.522 2.503 2.530 2.522 2.514

51-60 2.533 2.510 2.542 2.524 2.530 2.521 2.522 2.535 2.540 2.528

61-70 2.525 2.515 2.520 2.519 2.526 2.527 2.522 2.542 2.540 2.528

26

71-80 2.531 2.545 2.524 2.522 2.520 2.519 2.519 2.529 2.522 2.513

81-90 2.518 2.527 2.511 2.519 2.531 2.527 2.529 2.528 2.519 2.521

Gi tr ln nht (nh nht)

rng R = 2.545 2.503 =0.042

Bc 2 : Tnh s lp v rng lp:

Vi n=90, s lp K = 9 hoc 10. Ly K=9

h= R/K = 0.042/9 = 0.0047 => Lm trn h = 0.005

Bc 3, 4, 5, 6: Tnh tn sut

Lp 1: Bin di 1 = Xmin - h/2 = 2.503 0.005 /2 = 2.5005

Bin trn 1 = Bin di 1 +h = 2.5005 + 0.005 = 2.5055

im gia 1 = (Bin di 1 + Bin trn 1) /2 = 2.503

Lp 2 : Bin di 2 = Bin trn 1 = 2.5055

Tnh tip nh vy v ta c kt qu trong ct th 2 v 3 bng 4. m s gi tr trong bng 4.3 nm trong khong gi tr (2.5005-2.5055) ca lp 1, ta thy c mt gi tr =2.502 thuc s mu (41-50), in gi tr ny vo ct 4 v 5. Tip tc lm nh vy cho cc lp tip theo t 2 ti 9.

Bng tn sut

Lp im gia K hiu tn sut Tn sut

1 2.5005-2.5055 2.503 I 1

2 2.5055-2.5105 2.508 IIII 4

3 2.5105-2.5155 2.513 IIIII IIII 9

Lp im gia K hiu tn sut Tn sut

4 2.5155-2.5205 2.518 IIIII IIIII IIII 14

5 2.5205-2.5255 2.523 IIIII IIIII IIIII IIIII II 22

6 2.5255-2.5305 2.528 IIIII IIIII IIIII IIII 19

7 2.5305-2.5355 2.533 IIIII IIIII 10

8 2.5355-2.5405 2.538 IIIII 5

9 2.5405-2.5455 2.543 IIIII I 6

Tng 90

27

V biu phn b v tnh cc thng s theo cng thc cho:

28

4.4. S dng biu phn b

Nguyn tc ca kim sot cht lng l nm bt c cc nguyn nhn gy ra s bin ng v cht lng v qun l cc yu t . Vi mc ch ny, cn thit phi bit c s bin ng (phn b) ca cc d liu c th mt ng n. Thng qua cc b tr nhiu d liu trn mt biu phn b, chng ta c th hiu tng th mt cch khch quan

Mc ch ca vic thit lp biu phn b l:

1) Bit c hnh dng phn b lm cho biu c th d hiu hn.

2) Bit c nng lc qu trnh so snh vi cc tiu chun (qui nh k thut).

3) Phn tch qu trnh v qun l n.

4) Bit c trung tm v bin ng ca s phn b.

5) Bit mt dng phn b thng k.

V t cc thng tin trn ngi s dng c th :

1) Pht hin ra cc vn v thit lp cc chng trnh ci tin.

2) Xem xt hnh ng no l hiu qu.

3) Khng nh kt qu ca hnh ng.

Qu trnh s dng biu phn b bao gm hai giai on:

- V biu phn b v phn tch dng ca biu . Nu hnh dng biu cho thy khng c hin tng d liu b pha trn, tin hnh phn tch bin ng ca qu trnh

- Tnh h s nng lc ca qu trnh, t phn tch nng lc ca qu trnh

4.5. Phn tch hnh dng biu phn b

Kim tra cc im sau y

(1) Hnh dng ca biu phn b c bin dng hay khng? N c b dng o hoc dng cp hai nh hay khng ?

- Phn tch hnh dng, nu thy c kh nng c s pha trn d liu, tin hnh phn vng d liu v cc biu phn b s c thit lp li da trn cc d liu phn vng .

- Sau khi vic phn vng thc hin tt, tin hnh phn tch su hn

(2) V tr ca trung tm phn b.

(3) bin ng so vi ch tiu tng ng.

(4) Cc d liu c ph hp vi ch tiu tng ng hay khng?

29

4.6. Xc nh v phn tch nng lc qu trnh

Chng ta c th xc nhn rng nng lc sn xut ca qu trnh hin hnh tho mn yu cu k thut bng cch so snh biu phn b vi gi tr ch tiu.

Nng lc qu trnh c nh gi thng qua h s nng lc qu trnh, cn c gi l nng lc cht lng qu trnh, h s nng lc qu trnh cho bit nng lc qu trnh v cht lng. Nng lc qu trnh ch ra mc bin ng cht lng c th t c, thng thng c biu th qua 3 (3s) hoc 6 (6s). Cc h s thng c s dng gm Cp (hoc Cpk).

Ch s nng lc qu trnh

Trng hp gii hn hai pha: Tiu chun cho sn phm c hai gii hn trn v gii hn di:

Cp = s

SlSu6 Trong : Su l gii hn tiu chun trn

Sl l gii hn tiu chun di

Ch :

Trong trng hp lch tm ( x rt chnh lch vi (Su+Sl)/2), h s nng lc qu trnh c tnh theo Cpk

Cpk = min (Cpu, Cpl)

Trong Cpu v Cpl c tnh theo cng thc sau

Cpu = s

xSu3

Cpl = sSlx

3

Trng hp gii hn 1 pha: Tiu chun sn phm ch c gii hn trn Su hoc gii hn di Sl

H s nng lc c tnh theo cc cng thc sau

Cp = s

xSu3 (Trong trng hp gii hn trn)

Hoc Cp = sSlx

3 (Trong trng hp gii hn di)

T gi tr tnh c ca h s nng lc qu trnh c th nh gi c nng lc ca qu trnh nh sau :

30

Bng 6.3 Xc nh nng lc qu trnh

STT Cp (hoc Cpk) nh gi nng lc qu trnh

1 Cp 1.67 Nng lc qu trnh l y v d tha

2 1.67 > Cp 1,33 Nng lc qu trnh l y 3 1,33 > Cp 1,00 Nng lc qu trnh l st vo gii hn 4 1,00 > Cp 0,67 Nng lc qu trnh l khng y 5 0,67 > Cp Nng lc qu trnh l qu km

ng thi t gi tr ca h s nng lc qu trnh, c th d on c t l khuyt tt trung bnh ca qu trnh:

Bng 6.4 Mi quan h gia h s nng lc qu trnh Cp v t l khuyt tt trung bnh ca qu trnh p

Cp (H s nng lc qu trnh) p (t l khuyt tt trung bnh

ca qu trnh)

0,67 4,55%

1 0,27%

1,33 0,0063%

1,67 0,000057%

2 0,0000002%

i khi, s bin ng ni ti (do cc nguyn nhn khch quan) v s bin ng do cc nguyn nhn ch quan c kt hp vi nhau v mang li s bin ng ln (h s nng lc thp). phn tch cc yu t cu thnh nn s bin ng ny, dng biu kim sot theo di v phn tch s bin ng th rt hiu qu.

31

VII. BIU PHN TN (Scatter diagram)

1. Biu phn tn

Biu phn tn ch ra mi quan h gia 2 bin trong phn tch bng s. gii quyt cc vn v xc nh iu kin ti u bng cch phn tch nh lng mi quan h nhn qu gia cc bin s.

2. H s tng quan

H s tng quan r biu hin mc quan h gia hai c tnh v c gi tr thuc khong t -1 n +1.

3. Phng trnh hi qui

Phng trnh hi quy th hin mi quan h gia hai c tnh y v x, trong y l bin mc tiu v x l bin gii thch.

Phng trnh hi qui c cc dng khc nhau ph thuc vo cc bin c s dng v s cc bin. y chng ta nghin cu trng hp trong y c biu din bng phng trnh bc nht ca x nh sau:

y = a + bx

Trong a l hng s v b l h s hi qui.

Biu ca phng trnh hi quy

y

.

.

. . . .

. . . .

y . . .

. . .

. . . . .

. .

x x

Cng thc tnh

Hng s a

y = a + bx

S gia ca y

S gia ca x

H s hi qui b ( dc: t s s gia ca y/ s gia ca x)

32

Tnh tng cc bnh phng ca cc c tnh x

=

==

== n

i

n

ii

i

n

ii n

xxxxxxS

1

2

12

1

2)()(

Tnh tng cc bnh phng cacc c tnh y

=

==

== n

i

n

ii

i

n

ii n

yyyyyyS

1

2

12

1

2)()(

Tnh lch ca tng sn phm ca cc c tnh x v y

=

===

== n

i

n

ii

n

ii

ii

n

iii n

yxyxyyxxxyS

1

11

1))(()(

Tnh h s tng quan (r)

r = )()(

)(

* yyxxxy

SSS

Phng trnh hi qui

xbya

xxSxySb

bxay

==

+=

)()(

H s hi quy thng c lm trn n phn nghn Gi tr b trong phng trnh hi quy biu th dc ca ng hi quy hay

cng chnh l mc quan h

tnh h s hi quy, phi m bo gn ng cc gi tr bin i ca x v y

Nguyn tc ny cng c s dng xc nh phng trnh hi quy. Nn cn thn bc ny v nu gn nhm cc gi tr ca x cho y hay ngc li s to ra phng trnh hi quy khc

4. Xy dng biu phn tn

Bc 1:

33

Thu thp cp d liu (x, y). x v y l hai c tnh c gi nh l c quan h vi nhau. Nn c t nht 30 cp d liu

Bc 2:

Xc nh gi tr ln nht v nh nht ca x v y, t xc nh t l n v trn trc tung v trc honh sao cho chiu di c s liu trn hai trc gn bng nhau.

Bc 3 :

V cc im tng ng vi tng cp d liu trn biu

Bc 4:

in cc d liu lin quan nh:

Tn biu Khong thi gian thu thp d liu S cp d liu Tn cc trc Tn ngi xy dng biu

Bc 5:

Tnh h s tng quan. Nu r >0.85 hoc r < -0.85, tnh tip cc h s ca phng trnh hi qui theo cng thc trong phn 7..2 v v ng thng tng ng vi phng trnh hi qui. Phng trnh hi qui ny c th s dng cho cc mc ch : d bo qu trnh, lp k hoch....

5. S dng biu phn tn

Xc nh mc tng quan da trn biu phn tn. Biu phn tn c s dng xc nh c tn ti mi quan h gia hai c tnh

bng cch nh du cc cp s liu trn h to X-Y hoc nh du 1 c tnh trn trc Y cn c trng khc trn trc X.

Khi xc nh c tn ti mi quan h gia 2 c tnh th chng ta ni rng chng c quan h vi nhau. Khi mt c tnh tng th c tnh khc cng tng chng ta ni rng chng c mi quan h thun. Nu mt c tnh gim m c tnh khc tng th chng ta ni rng chng c mi quan h nghch. Khi hai c tnh c mi quan h thun th cc im ca d liu nm trong vng elip nghing v bn tri. Khi hai c tnh khng c mi quan h th chng ta ni rng chng khng c mi quan h v cc im d liu phn tn trong mt vng trn

Mi quan h c th hin qua gi tr ca h s hi qui R. Gi tr ny gn vi -1 (0.85) th c mi quan h thun rt ln (quan h thun cht). Gi tr ny gn 0 th mi quan h gia 2 c tnh rt km.

34

Khng c quan h

Quan h nghch ln Quan h thun ln

H s quan h nghch H s quan h thun

-1 0 +1

Trn c s phn tch biu phn tn, h s r v phng trnh hi qui, c th d bo c c tnh cht lng v c tnh qu trnh, cng nh xc nh cc yu t cn c kim sot cht ch m bo cht lng sn phm

2. V d

xc nh quan h gia p sut lm vic v bn lc ca sn phm to ra, ngi ta lm th nghim vi cc gi tr khc nhau ca p sut. Qu trnh xy dng biu nh sau :

Bc 1:

Thu thp cp d liu (x, y). D liu c ly trong 30 ngy ca thng 5/2001. Mi ngy ly mt mu. Bng d liu thu c nh sau :

Bng d liu quan h gia p sut (X) v sc bn lc (Y)

Th t ln ly mu

X Y Th t ln ly mu

X Y

1 5 6.3 16 22 28.5

2 6 7.3 17 8 9.3

3 24 30.5 18 9 10.3

4 25 31.5 19 10 11.3

5 26 32.5 20 17 23.5

6 1 2.3 21 18 24.5

7 2 3.3 22 19 25.5

8 3 4.3 23 20 26.5

9 4 5.3 24 11 12.3

10 27 33.5 25 12 13.3

11 28 34.5 26 13 14.3

12 29 35.5 27 14 15.3

13 30 36.5 28 15 16.3

35

14 31 37.5 29 12 13.4

15 21 27.5 30 14 15.7

Bc 2:

Xc nh gi tr ln nht v nh nht ca x v y : Xmax = 31; Xmin=1 ; Ymax= 37.5; ymin=2.3

T xc nh t l n v trn trc tung t 0-40 v trc honh t 0 ti 35

36

Bc 3 :

V cc im tng ng vi tng cp d liu trn biu

Bc 4:

in cc d liu lin quan nh:

Tn biu Khong thi gian thu thp d liu S cp d liu Tn cc trc Tn ngi xy dng biu

Bc 5:

Tnh h s tng quan, cc h s ca phng trnh hi qui theo cng thc trong phn 7..2 v v ng thng tng ng vi phng trnh hi qui.

Sxx= 2369.47

Syy= 3761.45

Sxy= 2965.64

r = 0.994 > 0.85 -> Xc nh cc h s ca phng trnh hi qui

X = 15.9 ; y = 19.61

b= 1..253

a= -0..249

y = - 0.249 + 1.253 x

VIII. BIU KIM SOT

1. Khi nim biu kim sot

Biu kim sot l th ng gp khc biu din gi tr trung bnh ca cc c tnh, t l khuyt tt hoc s khuyt tt. Chng c s dng kim tra s bt thng ca qu trnh da trn s thay i ca cc c tnh (c tnh kim sot). Biu kim sot bao gm 2 loi ng kim sot: ng trung tm v cc ng gii hn kim sot, c s dng xc nh xem qu trnh c bnh thng hay khng. Trn cc ng ny v cc im th hin cht lng hoc iu kin qu trnh. Nu cc im ny nm trong cc ng gii hn v khng th hin xu hng th qu trnh n nh. Nu cc im ny nm ngoi gii hn kim sot hoc th hin xu hng th tn ti mt nguyn nhn gc. Trong trng hp sau, tm v loi tr nguyn nhn (JIS Z 8101).

p sut

chulc

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

40 n = 30 r = 0.993 y = -0.249 + 1.252x

Sc bn lc

p sut

37

2. ngha

C hai loi bin ng ca qu trnh. Loi th nht l bin ng ngu nhin lun tn ti trong qu trnh. Loi th hai l loi bin ng do cc nguyn nhn c th loi b c. Tnh ton lch chun do bin ng ngu nhin v lp cc ng gii hn kim sot c rng bng 3 ln lch chun tnh t ng trung tm (gi tr trung bnh ca phn b) (qui lut 3 ). Nu qu trnh n nh, cc d liu ca cc c tnh kim sot s bin ng nm trong vng ca 2 ng gii hn kim sot.

Khi v cc ng kim sot theo hng dn trn i vi 1000 gi tr o th ch c 3 gi tr nm ngoi cc ng ny do cc iu kin qu trnh hoc iu kin mi trng, iu kin my mc hoc yu cu k thut i vi nguyn vt liu khng thay i.

Khi nim ny c rt ra t l thuyt xc sut i vi phn b chun. Cc qu trnh c coi l n nh khi cc im d liu gia cc ng kim sot khng to thnh mt lot, c xu hng hoc tun t, bi v s bin ng nm trong dung sai hoc khong cho php di mt iu kin c lp ra. y gi l bin ng ngu nhin.

Biu kim sot c s dng xc nhn rng qu trnh n nh v duy tr tnh n nh ca qu trnh

3. Cc nh ngha

3.1. Cc ng kim sot

Cc ng kim sot bao gm ng trung tm (CL), ng gii hn kim sot trn (UCL) v ng gii hn kim sot di (LCL) c v trn biu kim sot kim tra xem qu trnh c c kim sot hay khng.

3.2. Cc c tnh kim sot (cc gi tr)

0

5

10

15

20

25

CL=12.7

UCL=23.39

LCL=2.01

k = 10

38

Cc c tnh kim sot biu th cc kt qu qu trnh, qua chng ta thy c trng thi kim sot ca qu trnh.

Cc c tnh kim sot bao gm cht lng u ra, linh kin gc, kh lng tng s sn phm bn ra, t l ngi tham d, cng vic ngoi gi, s lng khiu ni v cc gi tr nh lng khc biu th kt qu nh lng cui cng (cc c tnh) v trng thi kim sot.

3.3. Cc bin lin tc hay d liu lin tc

Cc bin lin tc hay d liu lin tc bao gm cc con s v di, khi lng, cng , dung lng, sn lng, nguyn cht v nhng d liu ny c th o c theo cch thng thng (JIS Z S101). D liu loi ny c th o theo n v nh n mc no bn mun. Mt s lng tin t cng c coi l mt bin lin tc.

3.4. Cc gi tr ri rc hay d liu m c

Cc gi tr ri rc hay d liu c th m c bao gm cc s liu v s lng sn phm khuyt tt, s lng khuyt tt, t l sn phm khuyt tt, s lng trung bnh ca khuyt tt v cc gi tr khc c th m c (JIS Z 8101).

Mt t l phn trm ch ra t l so vi tng s l mt bin lin tc nu s liu ca n l s bin thin. Gi tr gi l ri rc nu s liu ca n c th m c.

3.5. Nhm nh (mu)

Cc nhm nh (hay nhm mu) l tp hp cc gi tr o c chia cho cc thnh phn khi c s khc bit v cc iu kin nh thi gian, sn phm, nguyn vt liu khi kim tra xem chng c n nh hay khng (JIS 8101).

Vic chia cc gi tr o c thnh cc nhm c gi l chia nhm nh. Mt tp hp cc gi tr o c to ra theo cch ny c gi l mt nhm nh (mt mu).

S cc i lng trong mt nhm nh c gi l c nhm (C mu).

4. Cc loi biu kim sot

4.1. Biu kim sot cho cc d liu dng bin s

4.1.1. Biu kim sot RX Biu kim sot x-R bao gm mt biu kim sot x s dng kim tra s thay i ca gi tr trung bnh v mt biu kim sot R kim tra s thay i v bin ng. Biu kim sot x -R trnh by mt s lng ln cc thng tin v s bin ng ca qu trnh.

39

4.1.2. Biu kim sot SX Biu kim sot SX bao gm mt biu kim sot x s dng kim tra s thay i ca gi tr trung bnh v mt biu kim sot s kim tra s thay i v bin ng. Tng t biu kim sot RX , biu kim sot SX trnh by mt s lng ln cc thng tin v s bin ng ca qu trnh. Hnh dng ca biu ny tng t biu RX , ch khc cng thc tnh

4.1.3. Biu kim sot X -Rs

Biu kim sot ny s dng cc gi tr o ring (X) m khng chia chng thnh cc nhm. Dng biu ny bao gm mt biu kim sot X s dng kim tra s thay i ca gi tr o c cho tng sn phm v mt biu kim sot Rs kim tra s thay i v bin ng. Hnh dng ca biu ny tng t biu RX

4.1.4. La chn loi biu

Vic la chn mt trong ba biu nu trn ph thuc vo c mu (s n v sn phm trong mi ln ly mu) nh sau:

C s chn biu cho d liu dng bin s

Gi tr c mu Loi biu nn s dng

C mu =1 Biu X- Rs

1< C mu < 10 Biu X - R C mu >10 Biu X - s

xy dng biu kim sot cho d liu dng bin s trn, cn thit lp phiu kim tra thu thp d liu v sau s dng cc cng thc tng ng cho tng loi d liu xc nh cc ng kim sot.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

10

20

30

40

50

CL=29.86

UCL=45.7

LCL=14.03

0

20

40

60

CL=27.44

UCL=58.04

xx

x x x xx

x

xx x

x

xx

xx

xx

x x x x xx

x

n = 5 k = 25 Biu

X

Biu R

40

4.1.5. Thu thp d liu cho biu kim sot (d liu dng bin s):

Bng d liu biu RX v SX : Thu thp d liu qua m ln ly mu, k hiu ni cho s n v sn phm trong ln ly mu th i (c mu ca ln ly mu th i). Nu c mu khng thay i: ni=n2...=nm=n. D liu thu thp c trnh by nh dng bng di.

Bng d liu dng bin s cho biu kim sot

Th t ln lymu

Sn phm 1

Sn phm 2

... Sn phm j

.... Sn phm n

1 X11 X12 X1j X1n

2 X21 X22 X2j X 2n

...

i Xi1 Xi2 Xlj X3n

...

m Xm1 X11 Xmj Xmn

Lu :

- Tt nht, c mu t 2 n 6 cho i vi biu kim sot RX

- i vi biu X - s, mi ln ly mu ch c mt d liu, do bng d liu tng t bng trn nhng ch c 2 ct

41

Cng thc tnh

Dng biu Cng thc tnh trung bnh

Cng thc tnh ng gii hn

Biu RX

x ( X trung bnh)

C mu n khng thay i

)*/()(1 1= =

=m

i

n

jij nmxx

.1.1.1.1 C mu n thay i (ni)

= ==

=m

ii

m

i

n

jij nxx

i

1 11/)(

RAxLCL

xCL

RAxUCL

2

2

==

+=

R

( rng) m

RR

i

m

i== 1

Trong :

R : rng trung bnh Ri: rng ca d liu cho ln ly mu th i

RDLCLRCL

RDUCL

3

4

===

Trong :

:X gi tr trung bnh tng th

UCL: ng gii hn trn

CL: ng trung tm

LCL: ng gii hn di

A2,D4,D3: H s (tra bng theo n)

Biu SX

x ( X trung bnh)

sAxLCL

xCL

sAxUCL

3

3

==

+=

42

s

( lch chun) m

ss

i

m

i== 1

Trong :

s : lch chun trung bnhsi: rng ca d liu cho ln ly mu th i

sBLCLsCL

sBUCL

3

4

===

Trong :

A3, B3,B4: Cc h s (tra bng theo n)

Biu x- Rs

x- Rs

(Gi tr o - rng)

12

==m

RR si

m

is

1

*26.2

*26.2

==

=+=

iisi

s

s

xxRRxLCL

xCL

RxUCL

Bng tra h s A2, D3 v D4

43

4.2. Biu kim sot cho d liu nguyn:

4.2.1. Biu kim sot np

Biu kim sot np c s dng kim sot qu trnh theo s sn phm khuyt tt (np) trong mi ln ly mu - trong n l c mu ca mt ln kim tra, v p l t l khuyt tt trong mi ln kim tra. Mi ln ly mu, nh gi cht lng ca tng sn phm xem n s c chp nhn (sn phm tt) hay loi b (sn phm khuyt tt). C mu (s lng sn phm) ca mi ln ly mu phi bng nhau. Biu kim sot pn l trng hp c bit ca biu kim sot p trong c mu khng i.

biu trn, gi tr cc ng kim sot CL, UCL, LCL c tnh theo cng thc. Cc im hin th trn biu l gi tr ca s sn phm khuyt tt np cho mi ln ly mu

4.3. Biu kim sot p

Biu kim sot p c s dng kim sot qu trnh theo t l sn phm khuyt tt (p) trong mi ln ly mu. C mu (n) khng cn thit phi nh nhau i vi cc nhm khc nhau.

0

1

2

3

4

5

6

7

CL=2.35

UCL=6.89 n = 100 k = 20

biu trn, gi tr cc ng kim sot CL, UCL, LCL c tnh theo cng thc. Cc im hin th trn biu l gi tr ca t l sn phm khuyt tt p cho mi ln ly mu.

4.4. Biu kim sot c

Biu kim sot c c s dng kim sot qu trnh theo s khuyt tt, tai nn hoc sai li trong mt khong thi gian nht nh khi kch thc sn phm (chiu di, rng, din tch..) hay c mu l khng i.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

CL=0.0269

UCL

Mean of n = 87 k = 20

62Ti liu o to K thut thng k

biu trn, gi tr cc ng kim sot CL, UCL, LCL c tnh theo cng thc trong phn 9.4..2.7 Cc im hin th trn biu l gi tr s khuyt tt c m c cho mi ln ly mu

4.5. Biu kim sot u

Biu kim sot u c s dng kim sot qu trnh theo s khuyt tt trong mt n v sn phm nht nh khi kch thc sn phm (chiu di, din tch, khi lng..) hay c mu thay i hoc khng i.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

CL=0.026

UCL Mean of n = 100 k = 10

0

5

10

15

20

25

CL=12.7

UCL=23.39

LCL=2.01

k = 10

46

Ti liu o to K thut thng k

biu trn, gi tr cc ng kim sot CL, UCL, LCL c tnh theo cng thc. Cc im hin th trn biu l s khuyt tt trn mt n v (u) xc nh c cho mi ln ly mu

5. La chn biu kim sot d liu dng nguyn

Vic la chn mt trong bn biu nu trn ph thuc vo loi d liu (s sn phm khuyt tt hay s khuyt tt) nh sau:

C s chn biu kim sot d liu dng nguyn

Loi d liu Loi biu nn s dng

S sn phm khuyt tt Biu np

(Ch s dng c khi c mu khng i)

T l sn phm khuyt tt Biu p

S khuyt tt

(V d: S vt xc)

Biu c

(Ch s dng c khi c mu khng i)

S khuyt tt trn mt n v (m, m2, 1 sn phm)

(V d: S vt xc/m2)

Biu u

6. Thu thp d liu cho biu kim sot (d liu dng nguyn)

Bng d liu biu p v biu np: Thu thp d liu qua m ln ly mu, k hiu ni cho s n v sn phm trong ln ly mu th i (c mu ca ln ly mu th i). Nu c mu khng thay i: n1=n2...=nm=n

Lu :

Tt nht, c mu t 100 n 1000 cho biu kim sot p v np.

47

Ti liu o to K thut thng k

Bng d liu dng bin s cho biu kim sot p v np

Th t ln ly mu

C mu

(S n v sn phm/

ln ly mu)

S sn phm khuyt

tt

(np)

T l sn phm khuyt

tt (p)

1 n1 (np)1 (np)1 / n1

2 n2 (np)2 (np)2 / n2

...

i ni (np)i (np)i / ni

...

m nm (np)m (np)m / nm

Dng d liu biu c v biu u: Thu thp d liu qua m ln ly mu, k hiu ni cho s n v sn phm trong ln ly mu th i (c mu ca ln ly mu th i). Nu c mu khng thay i: n1=n2...=nm=n

Bng d liu dng bin s cho biu kim sot c v biu u

Th t ln ly mu

C mu

(S n v sn phm/

ln ly mu)

S khuyt tt xc nh

c

(c)

S khuyt tt trn mt n v sn phm (u)

1 n1 c1 c1 / n1

2 n2 c2 c2 / n2

...

i ni ci ci / ni

...

m nm cm cm / nm

7. Cng thc tnh

xy dng biu kim sot, cn xc nh cc gi tr ca cc ng kim sot v gi tr cc im hin th trn biu . Cng thc xc nh cc ng kim sot nh sau

48

Ti liu o to K thut thng k

Cng thc tnh ng kim sot biu np v biu p

Dng biu Cng thc tnh trung bnh Cng thc tnh ng gii hn

np

(S sn phm khuyt tt)

nm

pn

npnp

m

pnpn

m

ii

m

ii

*

)(

)(

1

1

=

=

==

= )1(*3

)1(*3

pnppnLCL

pnCL

pnppnUCL

==

+=

p

(T l sn phm khuyt tt)

=

== mi

i

m

ii

n

pnp

1

1

)(

)(

npppLCL

pCL

npppUCL

/)1(*3

/)1(*3

==

+=

Cng thc tnh ng kim sot biu c v biu u

c

(S khuyt tt) m

cc

m

ii

== 1

ccLCL

cCL

ccUCL

*3

*3

==

+=

u

(S khuyt tt trn mt n v sn

phm)

=

== mi

i

m

ii

n

cu

1

1 nuuLCL

uCL

nuuUCL

/*3

/*3

==

+=

Ch : Khi tnh theo cc cng thc trn, nu gi tr ca LCL < 0 th ly LCL=0 (V cc gi tr np, p, c, u u lun >=0)

49

Ti liu o to K thut thng k

8. Xy dng biu kim sot

8.1. Cc bc xy dng biu x - R Bc 1:

Thu thp d liu. Tin hnh l mu 20 ti 25 ln , c mu t 5 ti 10 n v. o gi tr cn kim sot x.

Ta s c cc gi tr Xij trong i=1-m v j=1-n. m l s ln ly mu v n l c mu

Bc 2

Tnh gi tr trung bnh ca X

nxxxX iniii /)...( 21 +++= Tnh gi tr trung bnh ln 2 X theo cng thc trong mc 4.8.4 Bc 3 Tnh gi tr R trong mi nhm mu

Ri = (Gi tr max trong nhm i - gi tr min trong nhm i)

Bc 4:

Tnh gi tr trung bnh ca R R = (R1 + R2+. . . + Rm)/ m

Bc 5

Tnh gi tr cc ng kim sot CL. UCL, LCL v v ln th

Bc 6

V cc im tng ng vi cc gi tr iX in cc thng tin cn thit

8.2. Xy dng cc biu khc

Cc bc xy dng cc biu khc cng tng t trn theo nguyn tc:

Xc nh loi biu , phng n thu thp d liu v tin hnh thu thp d liu vo phiu kim tra

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Ti liu o to K thut thng k

Tnh ton cc gi tr trung bnh tng ng vi tng loi biu Tra cc h s theo gi tr ca c mu (nu cn) Tnh gi tr ca cc ng kim sot: UCL, LCL, CL theo cc cng thc trong

phn 7.4

V th: trc tung, trc honh, cc ng kim sot V cc im tng ng vi mi ln ly mu in cc thng tin cn thit

9. Phn tch biu kim sot

Di y l tiu ch s dng xc nh xem qu trnh c c kim sot hay khng hoc c n nh hay khng. L tng nht l trng thi ca qu trnh c xc nh vi 25 php o tr ln.

(1) Mt qu trnh c coi l c kim sot cht ch nu nh cc im d liu khng nm ngoi cc gii hn kim sot hoc khng to ra mt xu hng. Cc im sau y cng ch ra qu trnh c kim sot:

25 hoc hn cc im d liu nm trong gii hn kim sot Trong s 35 im d liu, ch c 1 im d liu nm ngoi ng gii hn

kim sot m qua im ny cng khng xc nh c c s bt thng.

Trong s 100 im d liu, ch c 1 hoc 2 im d liu nm ngoi gii hn kim sot m qua im ny cng khng xc nh c c s bt thng hay khng.

(2) Mt qu trnh c coi l c s bt thng trong nhng trng hp sau:

Cc im d liu nm trn hoc ngoi cc ng gii hn kim sot Mc d tt c cc im d liu nm trong cc ng gii hn kim sot, n

ch ra mt trong nhng xu hng sau:

7 im d liu lin nhau nm trn cng mt pha ca ng trung tm (ng trung bnh)

Thm ch nu cc im lin nhau nm v mt pha ca ng trung tm t hn 7 im d liu, qu trnh vn khng bnh thng nu gp 1 trong nhng trng hp sau:

10 trong s 11 im d liu nm v mt pha.

t nht 12 trong s 14 im d liu nm v 1 pha.

t nht 14 trong s 17 im d liu nm v 1 pha.

t nht 16 trong s 20 im d liu nm v 1 pha.

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Ti liu o to K thut thng k

Qu trnh c th c xem l bt thng khi cc im d liu xut hin thng xuyn gn vi cc ng gii hn kim sot.

V c hai pha ca ng trung tm, chia phm vi gia ng trung tm v ng gii hn kim sot 1 ng cch 2/3 tnh t ng trung tm ti ng gii hn kim sot. Nu cc im d liu nm khong gia ng ny v ng gii hn kim sot, th qu trnh c coi l bt thng nu gp cc trng hp sau:

Hai trong s 3 im d liu nm trong phm vi 3 trong s 7 im d liu nm trong phm vi . trong s 10 im d liu nm trong phm vi . Trong cc trng hp trn, qu trnh c coi l bt thng v qu trnh bnh thng ch cho php khong 5% cc im d liu nm ngoi phm vi 2 t ng trung tm.

Qu trnh c th c xem l bt thng khi t nht c 7 im d liu hnh thnh nn xu hng i ln hoc i xung.

Nu cc im d liu th hin tnh chu k, qu trnh bt thng. Phn ln cc d liu t nhin bt u tp trung xung quanh ng trung tm - trong phm vi 1 hoc 1,5 t ng trung tm - th qu trnh c coi l bt thng. Hin tng ny xut hin khi d liu khng ng nht c nhm vo mt nhm hoc c s t bin ca qu trnh

Qu trnh c th c xem l bt thng khi c xu hng ln xung lp i lp li

10. V d

Trong qu trnh kim tra sn phm c x l b mt, ngi ta kim tra theo tng l, mi l c 200 sn phm. Bng di ch ra s sn phm khuyt tt b mt trong tng l sau kim tra. Xc nh xem qu trnh c n nh khng.

S th t l

S sn phm khuyt tt

STT S sn phm khuyt tt

1. 4 11. 3

2. 5 12. 5

3. 0 13. 5

4. 1 14. 6

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Ti liu o to K thut thng k

5. 2 15. 1

6. 1 16. 0

7. 2 17. 0

8. 2 18. 1

9. 3 19. 2

10. 5 20. 4

Tng s 52

n = 200

Trc ht, kim sot qu trnh cn xc nh loi biu kim sot s dng. Do d liu dng nguyn v l s sn phm khuyt tt, ta thy ch c 2 loi biu c th s dng c l p hoc np. C mu n khng thay i nn c hai loi biu ny u c th s dng c. Trong tnh hung ny, biu np s c s dng kim sot v phn tch qu trnh.

Xy dng biu :

Bc 1: Tnh gi tr np trung bnh

6.22052

204....54)(1 ==++++==

=

m

pnpn

m

ii

Bc 2: Tnh gi tr p trung bnh

013.0200

6.2 ===n

npp

Bc 3: Tnh gi tr cc ng kim sot.

Thay cc gi tr tnh c trn vo cng thc trong phn 9.4.2.7, ta c:

UCL = 7.4

CL = 2.6

LCL = -2.2 =>= 0

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Ti liu o to K thut thng k

Bc 4: V trc tung vi gi tr t 0 8 (gi tr nguyn gn nht vi gi tr ln nht trong s cc gi tr UCL, (np)i). V trc hnh vi 20 im chia (tng ng vi 20 ln ly mu)

Bc 5: V cc ng kim sot CL, UCL v LCL song song vi trc honh v ct trc tung ti cc gi tr tng ng tnh c ti bc th 3

Bc 6: V cc im vi to (i, npi) ln biu , trong i l s th t ca ln ly mu th i (i t 1 n 20)

Bc 7: Ghi cc thng tin cn thit: s ln ly mu, c mu...

Phn tch biu :

T biu trn ta thy t d liu th 3 c xu hng i ln vi 7 d liu lin nhau chng t qu trnh ang c bin ng v ang khng c kim sot. Trong thc t nu gp trng hp ny cn phn tch k hn tm ra nguyn nhn ca xu hng ny v tin hnh hnh ng khc phc loi b nguyn nhn .

0

1

2

3

4

5

6

7

8

CL=2.6

UCL=7.41 n = 200 k = 20