UNIT 4 CONTROL CHARTS FOR DEFECTS

Transcription

1 UNIT 4 CONTROL CHARTS FOR DEFECTS Structure 4.1 Itroducto Objectves 4.2 Cotrol Charts for of Defects (c-chart) 4.3 Cotrol Charts for of Defects per Ut (u-chart) 4.4 Comparso betwee Cotrol Charts for Varables ad Attrbutes 4.5 Summary 4.6 Solutos/Aswers 4.1 INTRODUCTION I Ut 2, you have studed the X, R ad S cotrol charts used for motorg ad cotrollg measurable qualty characterstcs such as dameter, legth, wdth, weght, etc. I Ut 3, you have studed the p ad p cotrol charts appled for motorg ad cotrollg qualty characterstcs whch are ot measurable ad the tems or uts are classfed as defectve or o-defectve. These types of charts are broadly useful statstcal qualty cotrol. Sometmes, a tem may cota may defects, but t may ot be classfed as defectve. For example, suppose a compay maufactures, motorcycles. Suppose there are oe or two mor scratches o the body of the motorcycle, whch do ot affect ts fuctog. So the motorcycle caot be classfed as defectve. However, ths s a defect. But f there are too may scratches, the motorcycle should be classfed as defectve because the scratches would be otceable ad affect ts sale. So there are so may stuatos dustres whch we requre to cotrol the umber of defects rather tha the umber of defectve tems. The c-chart ad u-chart are used to cotrol the umber of defects. I Secs. 4.2 ad 4.3, we dscuss the c-chart whch s used to cotrol the umber of defects ad ts applcatos. We descrbe the u-chart Sec 4.4. It s used to motor ad cotrol the umber of defects per ut whe the sample sze vares. I Sec 4.5, we compare the cotrol charts for varables ad attrbutes. Objectves After studyg ths ut, you should be able to: dstgush betwee defectve ad defect; descrbe the eed of cotrol charts for defects; select the approprate cotrol chart for defects; costruct ad terpret the cotrol chart for umber of defects (c-chart); ad costruct ad terpret the cotrol chart for umber of defects per ut (u-chart). 115

2 4.2 CONTROL CHARTS FOR NUMBER OF DEFECTS (c-chart) You have leart about the p-chart ad p-chart Ut 3. These cotrol charts are used to cotrol the fracto (proporto) defectve ad the umber of defectves, respectvely, o the bass of crtero: whether the tem s defectve or o-defectve. But may stuatos, t s advatageous ecoomcally to ow the umber of defects a tem stead of classfyg t as defectve or o-defectve. For example, a glass bottle may have oe small ar bubble ad the aother glass bottle may have may small ar bubbles. Eve though both bottle sets are defectve, the secod oe s far more serous as t has may defects. So t s also mportat to cotrol the umber of defects wth the tem. The c-chart s used for motorg ad cotrollg the umber of defects a tem/ut. Tradtoally, the umber of defects was deoted by c. Therefore, the cotrol chart for umber of defects s ow as the c-chart. It s used whe the tem/ut s largely assembled, e.g., TV, computer, moble, laptop, arcraft, etc. I such cases, there are may opportutes for a defect to occur ad the probablty of the occurrece of a defect s very small. For example, the case of commercal arplae there s a large umber of rvets, but a small chace of ay rvet havg defects. The sample/subgroup sze for the c-chart s a sgle tem/ut/artcle or costat sze ad we cout the umber of defects wth the tem/ut/artcle. The uderlyg logc ad procedure of costructg the c-chart are smlar to the p-chart. The prmary dfferece betwee the c-chart ad the p-chart s that, stead of collectg data relatg to the umber of defectve tems, we collect data about the umber of defects wth the tem ad plot the umber of defects agast the sample umber. For obtag the cetre le ad cotrol lmts of the c-chart, we requre the samplg dstrbuto of the umber of defects. I ths case, whe there are may opportutes for a defect to occur ad the probablty of the occurrece of a defect s very small, the Posso dstrbuto s appled (recall Ut 10 of MST-003 ettled Posso Dstrbuto). So the umber of defects follows the Posso dstrbuto. If s the average umber of defects the process, the mea ad varace of the Posso dstrbuto are gve as follows: E(c) ad Var(c) (1) We ow the stadard error of a radom varable X s SE(X) V ar(x) SE(c) Var(c) (2) I Ut 10 of MST-003, you have also leart that the Posso dstrbuto s ot symmetrcal. Therefore, the upper ad lower 3 lmts do ot correspod to equal probabltes of a pot o the cotrol chart. But f the sample sze s suffcetly large, the by the cetre lmt theorem, the samplg dstrbuto of the umber of defects s approxmately ormally dstrbuted wth mea λ ad varace λ. Therefore, the cetre le ad cotrol lmts for the c-chart ca be obtaed as follows: 116

3 Cetre le (CL) E(c) (3a) Upper cotrol lmt (UCL) E(c) 3SE(c) 3 (3b) Lower cotrol lmt (LCL) E(c) 3SE(c) 3 (3c) Geerally, λ s ot ow. So t s estmated from the sample formato. Suppose we draw samples of costat sze or sze 1 ad c 1,c 2,...,c are the umbers of defects the 1 st, 2 d,, th sample, respectvely. The average umber of defects the process s estmated by the average umber of defects the sample whch s calculated by the formula gve below: Sum of defects 1 c c Total umber of samples spected (4) 1 I ths case, cetre le ad cotrol lmts of the c-chart are obtaed by replacg λ by c equatos (3a to 3c) as follows: Cetre le (CL) ˆ c (5a) Upper cotrol lmt (UCL) ˆ 3 ˆ c 3 c (5b) Lower cotrol lmt (UCL) ˆ 3 ˆ c 3 c (5c) We costruct the c-chart by tag the sample umber o the X-axs ad the umber of defects the sample o the Y-axs. We draw the cotre le as a sold le ad cotrol lmts as dotted les o the chart. We plot the umber of defects the sample agast the sample umber. The cosecutve sample pots are joed by le segmets. Iterpretato of the result If all sample pots le o or betwee the upper ad lower cotrol lmts, the cotrol chart dcates that the process s uder statstcal cotrol. Oly chace causes are preset the process ad o assgable cause s preset. However, f oe or more sample pots le outsde the upper or lower cotrol lmt, the cotrol chart alarms (dcates) that the process s ot uder statstcal cotrol ad some assgable causes are preset the process. To brg the process uder statstcal cotrol, t s ecessary to vestgate the assgable causes ad tae correctve acto to elmate them. Oce the assgable causes are elmated, we delete the out-of-cotrol pots (samples) ad calculate the revsed cetre le ad cotrol lmts for the c-chart by usg the remag samples. These lmts are ow as the revsed cotrol lmts. For the revsed lmts of the c-chart, we frst calculate ew c as follows: c ew c d 1 j1 d where d the umber of dscarded samples, ad c j (6) d c j the sum of the umber of defects wth the dscarded samples. j1 117

4 After fdg the c ew, we recostruct the cetre le ad cotrol lmts for the c-chart by replacg c by cew equatos (5a to 5c) as follows: Cetre le (CL) cew (7a) Upper cotrol lmt (UCL) cew 3 cew (7b) Lower cotrol lmt (UCL) cew 3 cew (7c) Note: If the value of lower cotrol lmt s egatve, we chage the lower cotrol lmt to zero because a egatve umber of defects s ot possble. Let us tae up some examples to llustrate how to costruct the c-chart for practcal stuatos. Example 1: A cotrol chart s to be formed for a process whch laptops are produced. The specto ut s oe laptop ad cotrol chart for the umber of defects s to be used. Prelmary data are recorded ad 45 defects are foud 30 laptops. Obta the cotrol lmts for the chart. Soluto: Sce we eed to cotrol the umber of defects ad the specto ut s oe laptop, we use the c-chart for umber of defects. The average umber of defects the process s ot gve. So, we use equatos (5a to 5c) to calculate the cetre le ad cotrol lmts of the c-chart. It s gve that the total umber of defects laptops = 45, ad the total umber of laptops spected () = c c Hece, usg equatos (5a to 5c), we calculate the cetre le ad cotrol lmts of the c-chart as follows: CL c 1.5 UCL c 3 c LCL c 3 c Example 2: The umber of scratch mars o a partcular pece of furture s recorded. The data for 20 samples are gve below: Scratch Mar Scratch Mar Draw the approprate cotrol chart ad wrte the commets about the state of the process whe: 118

5 ) the maagemet sets a goal of 5 scratch mars o a average per pece. ) the maagemet does ot set the average umber of mars per pece. Soluto: Here the umber of defects o a partcular pece of furture s gve. So we use the c-chart. ) The maagemet sets a goal of 5 scratch mars o a average per pece. It meas that the average umber of defects the process s ow. Therefore, we use equatos (3a to 3c) to calculate the cetre le ad cotrol lmts of the c-chart. It s gve that the average umber of defects per sample (λ) = 5, ad the umber of tems the sample () = 1. Therefore, we calculate the cetre le ad cotrol lmts of the c-chart usg equatos (3a to 3c) as follows: CL 5 UCL LCL For costructg the c-chart, we plot the pots by tag the sample umber o the X-axs ad the umber of defects (c) o the Y-axs. We draw the cetre le as a sold le ad cotrol lmts as dotted les o the graph as show Fg of Defects Y UCL = CL = LCL = 0 0 X Fg. 4.1: The c-chart for umber of defectes o a average per pece of the furture, whch s 5. Iterpretato of the result From Fg. 4.1, we observe that the pots correspodg to the sample umbers 3, 7 ad 19 le outsde the upper cotrol lmt. Therefore, the process s ot uder statstcal cotrol wth respect to the average umber of defects per pece, whch s 5. ) Here, the average umber of defects the process s ot gve. So we use equatos (5a to 5c) to calculate the cetre le ad cotrol lmts of the c-chart. 119

6 Here total umber of defects = = c c Therefore, usg equatos (5a to 5c), we calculate the cetre le ad cotrol lmts of the c-chart as follows: CL c 6.55 UCL c 3 c LCL c 3 c We costruct the c-chart by tag the sample umber o the X-axs ad the umber of defects (c) o the Y-axs as show Fg of Defects Fg. 4.2: The c-chart for umber of defectes o a average per pece of the furture, whch s Iterpretato of the result From the c-chart (show Fg. 4.2), we observe that o pot les outsde the cotrol lmts ad there s o specfc patter of the sample pots o the chart. So t dcates that the process s uder cotrol wth respect to the average umber of defects per pece, whch s Example 3: As part of a overall qualty mprovemet programme, a textle maufacturer decdes to motor the umber of defects foud each spected bolt (large budle) of cloth. The data from 20 spectos are recorded the table gve below: Bolt of Cloth of Defects Bolt of Cloth of Defects Y UCL = CL = 6.55 LCL = 0 X

7 ) Whch cotrol chart should be used ths case? Calculate the cotrol lmts for ths chart. ) Soluto: Do these data from a cotrolled process? If ot, calculate the revsed cotrol lmts. ) Here the maufacturer motors the umber of defects foud each spected bolt of cloth ad oly oe bolt s spected each sample. So we ca use the c-chart. The average umber of defects the bolt of cloth s ot gve ths case. So we use equatos (5a to 5c) to calculate the cetre le ad cotrol lmts of the c-chart. It s gve that = 20 ad = 1. The total umber of defects bolts = = c c Hece, usg equatos (5a to 5c), we calculate the cetre le ad cotrol lmts of the c-chart as follows: CL c UCL c 3 c LCL c 3 c We costruct the c-chart by tag the sample umber o the X-axs ad the umber of defects (c) o the Y-axs as show Fg Y 25 of Defects UCL = CL = LCL = 0 X Fg. 4.3: The c-chart for umber of defects the bolt of cloth. Iterpretato of the result From Fg. 4.3, we observe that the pots correspodg to the sample umbers (bolt) 2 ad 11 le outsde the upper cotrol lmt. Therefore, the process s ot uder statstcal cotrol wth respect to the umber of defects. To brg the process uder statstcal cotrol, t s ecessary to vestgate the assgable causes ad tae correctve acto to elmate them. ) For calculatg the revsed cotrol lmts for the c-chart, we frst delete the out-of-cotrol pots (2 ad 11) ad the calculate the ew c by usg remag samples. 121

8 I our case, d 20,d 2, c j1 j d c cj 1 j cew d 20 2 After fdg the p ew, we calculate the revsed cetre le ad cotrol lmts of the chart usg equatos (7a to 7c) as follows: CL cew UCL cew 3 cew LCL cew 3 cew So far you have studed the c-chart ad leart whe t s used ad how t s costructed. We ow dscuss the applcato of the c-chart. Applcatos of the c-chart Although the applcatos of the c-chart are lmted compared to the X, R, p ad p-charts, yet a umber of practcal stuatos exst where we apply the c-chart. Some area where the c-chart s appled are lsted below: 1. c s the umber of defects observed a televso, computer, laptop, moble, etc. 2. c s the umber of defects observed a woolle carpet, cloth, paper, etc. 3. c s the umber of ar bubbles a glass, bottle, paper weght, etc. 4. c s the umber of defects observed arcraft eges. 5. c s the umber of breadows at wea spots sulato a gve legth of sulated wre. 6. c s the umber of mperfectos observed a bolt (large budle) of cloth. 7. c s the umber of surface defects observed a galvased sheet, furture, automoble, etc. 8. The c-chart s also used a) chemcal laboratores, b) accdet statstcs both hghway accdets ad dustral accdets. You may le to chec your uderstadg of the c-chart by aswerg the followg exercses. E1) Choose the correct opto from the followg: ) The cotrol chart for umber of defects s called the ) a) X -chart b) p-chart c) p-chart d) c-chart The cotrol lmts for the c-chart are a) 3 b) 3 122

9 c) d) 3 ) The cotrol chart for umber of defects per ut s called the a) u-chart b) p-chart c) p-chart d) c-chart E2) Wrte the cotrol lmts of the c-chart whe the average umber of defects of the process s ot ow. E3) Twety fve samples of pacets of match boxes cotag 10 match boxes each, were selected at regular tervals. The match boxes each sample were spected ad the umber of defects wth regard to the umber of broe stcs, paste o the stcs, labelg, etc. were oted the followg table: of Defects of Defects Commet o the state of the process. E4) A qualty cotrol techca has recorded the umber of defects per 100 square meter o whte papers. The results of 25 spectos are show the followg table: of Defects of Defects of Defects Costruct a cotrol chart for the umber of defects. Revse the cotrol lmts, assumg specal causes for the out-of-cotrol. 4.3 CONTROL CHARTS FOR NUMBER OF DEFECTS PER UNIT (u-chart) I Sec. 4.2, you have leart that the c-chart s used for motorg ad cotrollg the umber of defects. But t s appled oly whe the sample (subgroup) sze s oe or costat,.e., we have spected the same umber of uts or tems each sample. To overcome ths drawbac, we use the u-chart. 123

10 Whe the sample sze vares due to some reaso, such as machery, raw materal, worers, etc., the u-chart s costructed to motor the umber of defects per ut. The u-chart ca also be used whe the sample sze s costat. The procedure for drawg the u-chart for varable sample sze s smlar to the c-chart wth costat sze. The prmary dfferece betwee the c-chart ad u-chart s that stead of plottg the umber of defects per sample, we plot the umber of defects per tem/ut ad motor them. Sce the cotrol lmts are fucto of the sample sze (), these wll vary wth the sample sze. So we should calculate the cotrol lmts separately for each sample. I such cases, the cotrol lmts are ow as varable cotrol lmts. Geerally, two approaches are used for costructg varable cotrol lmts for the u-chart. Frst Approach I ths approach, we calculate the cotrol lmts for each sample. Suppose c,c,...,c represet the umber of defects 1 st, 2 d,, th samples of sze 1 2 1, 2,...,, respectvely, we frst calculate the umber of defects per tem for each sample as follows: c c c u, u,...,u (8) The average umber of defects per tem s gve by 1 u u or 1 u 1 1 c (9) The cetre le remas costat for each sample because t s ot a fucto of sample sze ad s gve by CL u (10a) The cotrol lmts chage due to varable sample sze. The cotrol lmts for the th sample are gve by u (10b) UCL u 3 u (10c) LCL u 3 Secod Approach I ths approach, we calculate the cotrol lmts by usg the average sample sze. Ths approach s used oly whe there s o large varato the sample szes ad t s expected that the future sample szes wll ot dffer sgfcatly from the average sample sze. Usg ths approach, we get costat cotrol 124

11 lmts just as we get the case of costat sample sze. We calculate the average sample sze as follows: (11) 1 CL u (12a) u UCL u 3 (12b) u LCL u 3 (12c) Therefore, the cetre le ad cotrol lmts of the u-chart are as follows: The costructo ad terpretato of the u-chart are smlar to that of the c-chart. We ow cosder a example to llustrate the use of the u-chart. Example 4: Twety samples of carpets are spected for varyg sample sze ad the umber of defects each sample s oted the followg table: of Carpet Ispected of Defects of Carpet Ispected of Defects Costruct a sutable cotrol chart for the umber of defects per carpet. Soluto: Sce the umber of defects s gve for varyg sample sze, we use the u-chart. We solve ths example usg both approaches. Frst Approach We use equatos (10a to 10c) to calculate the cetre le ad cotrol lmts of the th sample. To calculate the cotrol lmts ad draw the u-chart, we frst calculate the umber of defects per carpet usg equato (8) ad the u. 125

12 of Carpet Ispected () of Defects (c) u c / CL UCL LCL Total From the above table ad equato (9), we have c u Therefore, usg equatos (10a to 10c), we calculate the cetre le ad cotrol lmts whch are show the table as follows: CL u u UCL 1 u , ad so o u LCL 1 u , ad so o We costruct the u-chart by tag the sample umber o the X-axs ad the umber of defects per carpet (u) o the Y-axs. We draw the cetre le as a sold 126

13 le ad cotrol lmts as dotted les o the graph ad plot the pots as show Fg of Defects per tem Y Iterpretato of the result Fg. 4.4: The u-chart for umber of defects per carpet. From the u-chart show Fg. 4.4, we observe that the pot correspodg to sample 13 les outsde the upper cotrol lmt. Therefore, the process s ot uder statstcal cotrol wth respect to the umber of defects per carpet. Secod Approach Accordg to ths approach, the cotrol lmts are calculated usg the average sample sze ad we get costat cotrol lmts. We frst calculate the average sample sze usg equato (11) as follows: Usg equatos (12a to 12c), we calculate the cetre le ad cotrol lmts as follows: CL u u UCL u UCL CL = LCL X u LCL u We draw the u-chart the same way as the frst approach (see Fg. 4.5). 127

14 Numbre of Defects per tem Y Iterpretato of the result Fg. 4.5: The u-chart for umber of defects per carpet. From the u-chart show Fg. 4.5, we observe that the pot correspodg to sample 13 les outsde the upper cotrol lmt. Therefore, the process s ot uder statstcal cotrol wth respect to the umber of defects per carpet. You ca chec your uderstadg of the u-chart by aswerg the followg exercses. E6) A qualty cotrol techca otes the umber of defects per 100 square meter o whte paper, but the amout of paper spected for each sample vares. The results of 25 spectos are show the followg table: Amout of the Paper Ispected ( square meter) of Defects Amout of the Paper Ispected ( square meter) UCL = CL = LCL = 0 X of Defects Costruct a cotrol chart for the umber of defects per 100 square meter. 4.4 COMPARISON BETWEEN CONTROL CHARTS FOR VARIABLES AND ATTRIBUTES 128

15 Now that you have studed the cotrol charts for varables ad attrbutes, you ow whch type of cotrol chart to use a gve stuato. I the table below, we preset a comparso of the cotrol charts for varables ad attrbutes. S. No. Cotrol Charts for Varables 1 These charts are used for measurable characterstcs. 2 The types of charts are the X-chart,R-chart ad S-chart. Cotrol Charts for Attrbutes These charts are used for o-measurable characterstcs ad the stuatos where the cotrol charts for varables are ot appled due to tme ad cost factors. The types of charts are the p-chart, p-chart, c-chart ad u-chart. 3 A separate cotrol chart s eeded for each qualty characterstc. 4 Small samples serve the purpose very well. 5 The cost of specto of uts s large. 6 These charts provde the better qualty cotrol. 7 These charts are ot easly uderstood. A sgle chart s eough for a umber of qualty characterstcs. Large samples are requred for correct coclusos. The cost of specto of uts s small sce o measuremets are made. These charts are ot very effectve qualty cotrol. These charts are easly uderstood. Wth ths we ed the ut ad summarse our dscusso. 4.5 SUMMARY 1. The c-chart s used whe we wat to cotrol the umber of defects ad sample sze s oe ut or costat. 2. The u-chart s used whe we wat to cotrol the umber of defects per ut ad sample sze vares. 3. The cetre le ad cotrol lmts of the c-chart are gve as Cetre le (CL) c Upper cotrol lmt (UCL) c 3 c Lower cotrol lmt (UCL) c 3 c where Sum of defects 1 c c. Total umber of samples spected 1 4. The cetre le ad cotrol lmts of the u-chart are gve as Cetre le (CL) u 129

16 Upper cotrol lmt (UCL) Lower cotrol lmt (UCL) u u 3 u u 3 where 1 u u or 1 u 1 1 c ad 4.6 SOLUTIONS / ANSWERS E1) ) Opto (d) s the correct opto because we ow that the c-chart ad u-chart are the cotrol charts for umber of defects. ) ) Opto (b) s the correct opto because we ow that the cotrol lmts for the c-chart are 3. Opto (a) s the correct opto because we ow that the u-chart s the cotrol chart for umber of defects per ut whereas the c-chart s the cotrol chart for umber of defects. E2) The cotrol lmts of the c-chart whe the average umber of defects of the process s ot ow are Cetre le (CL) c Upper cotrol lmt (UCL) c 3 c Lower cotrol lmt (UCL) c 3 c where Sum of defects 1 c c. Total umber of samples spected 1 E3) Sce the sample sze s costat, we ca use the c-chart. Also, the average umber of defects the process s ot gve. So we use equatos (5a to 5c) to calculate the cetre le ad cotrol lmts of the c-chart. It s gve that = 25 ad = 10. The total umber of defects all match boxes = = c c Hece, usg equatos (5a to 5c), we calculate the cetre le ad cotrol lmts of the c-chart as follows: CL c UCL c 3 c LCL c 3 c We costruct the c-chart by tag the sample umber o the X-axs ad the umber of defects (c) per sample o the Y-axs as show Fg

17 of Defects Y UCL = CL = LCL = 0 X Fg. 4.6: The c-chart for the umber of defects pacets of match box. Iterpretato of the result From the c-chart show Fg. 4.6, we observe that o pot les outsde the cotrol lmts ad there s o specfc patter of the sample pots o the chart. It dcates that the process s uder statstcal cotrol. E4) Sce the umber of defects o the whte paper per 100 square meter s gve. It meas that the sample sze s costat. So we use the c-chart. Sce the average umber of defects of the process s ot gve, So we use equatos (5a to 5c) to calculate the cetre le ad cotrol lmts of the c-chart. It s gve that = 25 ad = 1. The total umber of defects = = c c Hece, usg equatos (5a to 5c), we calculate the cetre le ad cotrol lmts of the c-chart as follows: CL c UCL c 3 c LCL c 3 c We costruct the c-chart by tag the sample umber o the X-axs ad the umber of defects (c) o the whte paper o the Y-axs as show Fg

18 of Defects Y X Fg. 4.7: The c-chart for the umber of defects o the whte paper. Iterpretato of the result From Fg. 4.7, we observe that the pots correspodg to the sample umbers 6 ad 15 le outsde the upper cotrol lmt. Therefore, the process s ot uder statstcal cotrol wth respect to the umber of defects. To brg the process uder statstcal cotrol t s ecessary to vestgate the assgable causes ad tae correctve acto to elmate them. For calculatg the revsed lmts of the c-chart, we frst delete the out-of-cotrol pots (6 ad 15) ad calculate the ew c usg remag samples. UCL = CL = LCL = 0 I our case, d 25,d 2, c j1 j d c c j 1 j cew d After fdg the p ew, we calculate the revsed cetre le ad cotrol lmts usg equatos (7a to 7c) as follows: CL cew UCL cew 3 cew LCL cew 3 cew E5) Sce the umber of defects s gve, we may use ether c-chart or u-chart. Sce the sample sze vares, we use the u-chart. For calculatg the cetre le ad cotrol lmts of the u-chart, we frst calculate the defects per ut (u) ad the u. 132

19 Amout of the Carpet Ispected of Ut Ispected () of Defects (c) u = c/ CL UCL LCL Total From the above table ad equato (9), we have c u Therefore, usg equato (10a to 10c), we calculate the cetre le ad cotrol lmts whch are show the table as follows: CL u u UCL 1 u , ad so o. 133

20 u LCL 1 u , ad so o. We costruct the u-chart by tag the sample umber o the X-axs ad the umber of defects per 100 square meter paper (u) o the Y-axs as show Fg of Defects per tem Y UCL X CL = LCL Fg. 4.8: The u-chart for the umber of defects per 100 square meter paper. Iterpretato of the result From Fg. 4.8, we observe that o pot les outsde the cotrol lmts of the u-chart ad there s o specfc patter of the sample pots o the chart. So t dcates that the process s uder statstcal cotrol wth respect to the umber of defects per 100 square meter paper. 134