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# 7 8-kendali atribut

## by Arie Febrianto Mulyadi on May 08, 2013

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• This slide provides a framework for differentiating between “Process Control” and “Acceptance Sampling,” and “Variables” and “Attributes.” One might also raise the distinction between producer (process control) and customer (acceptance sampling). The next several slides deal with these distinctions.
• This slide simply introduces the various types of control charts.
• Ask the students to imagine a product, and consider what problem might cause each of the graph configurations illustrated.
• An example of a control chart. .

## 7 8-kendali atributPresentation Transcript

• Peta KendaliPeta KendaliPlot of Sample Data Over Time0204060801 5 9 13 17 21TimeSampleValueSampleValueUCLAverageLCL
• StatisticalQuality ControlProcessControlAcceptanceSamplingVariablesChartsAttributesChartsTypes ofStatistical Quality Control
• ControlChartsRChartVariablesChartsAttributesChartsXChartPChartCChartContinuous NumericalDataCategorical or DiscreteNumerical DataControl Chart Types
• S6-5 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458Transparency Masters to accompany Heizer/Render – Principles ofOperations Management, 5e, and Operations Management, 7eXMeanCentral Limit Theoremσσxxn=µ=XStandard deviationX = µTheoretical Basisof Control Charts
• Control ChartsClassification..• Variables - concentrates on mean forsome measurable characteristic(pengukuran)– diameter– length• Attribute - data is based on counts orthe number of times we observe aparticular event (perhitungan)– proportion defective/non-defective– go/no go
• TYPE CONTROL CHARTP,l,b,vData diukurPeta X-R•Jumlah cacat lubang dr ukuran t3,tetapData dihitungPeta c•Jumlah cacat lubang dr ukuranberbeda dan berubahData dihitungPeta u•Jumlah kerusakan•Jenis kerusakanData dihitungPeta p-npExampleSubyekTipe
• Tahapan AnalisisPeta Kendali• Memilih karakteristik yg akan direncanakan(prioritas tinggi pd proses yg sgtmempengaruhi kualitas produk akhir)• Memilih tipe peta kendali• Menentukan garis pusat (Center Line) danbatas kendali atas dan bawah (UCL dan LCL)• Penempatan data dan interpretasi hasil
• p/np/cp/np/c Chart StructureChart StructureUCLUCLLCLLCLProcess MeanProcess MeanWhen in ControlWhen in ControlCenter LineCenter LineTimeTimep/np/c Upper Control LimitUpper Control LimitLower Control LimitLower Control Limit
• Warning Conditions…..Out of ControlWestern Electric :1. 1 titik diluar batas kendali ( 3σ)2. 2 dr 3 titik berurutan diluarbatas kendali (2σ)3. 4 dr 5 titik berurutan jauh dariGT (1σ)4. 8 titik berurutan (pola giliran) disatu sisi GT5. 1/beberapa titik dekat satubatas kendali6. Pola data TAK RANDOM
• Pola Peta Kendali
• Peta KendaliPeta KendaliATRIBUTATRIBUT
• KonsepKonsep• Atribut : karakteristik kualitas ygAtribut : karakteristik kualitas ygsesuai spesifikasi atau tidaksesuai spesifikasi atau tidak• Atribut dipakai jk ada pengukuran ygAtribut dipakai jk ada pengukuran ygtidak mungkin dilakukan ( tidaktidak mungkin dilakukan ( tidakdibuat) spt : goresan,apel yg busuk,dibuat) spt : goresan,apel yg busuk,kesalahan warna, ada bagian ygkesalahan warna, ada bagian yghilanghilang
• Tipe Peta KendaliTipe Peta KendaliATRIBUTATRIBUT1.1. Berdasar Distribusi BINOMIALBerdasar Distribusi BINOMIAL– Kelompok pengendali unit ketidaksesuaianKelompok pengendali unit ketidaksesuaian– Dinyatakan dalam proporsi (%)Dinyatakan dalam proporsi (%)– Menunjukkan proporsi ketidaksesuaianMenunjukkan proporsi ketidaksesuaiandalam sampel / sub kelompokdalam sampel / sub kelompokp dan npp dan np ChartChart
• 2. Berdasar Distribusi POISSON2. Berdasar Distribusi POISSON– bagian ketidaksesuaian dalam unit inspeksibagian ketidaksesuaian dalam unit inspeksi– Berkaitan dg kombinasi ketidaksesuaianBerkaitan dg kombinasi ketidaksesuaianberdasar BOBOT yg dipengaruhi banyakberdasar BOBOT yg dipengaruhi banyaksedikitnya ketidaksesuaiansedikitnya ketidaksesuaianc- Chart dan u-chartc- Chart dan u-chart
• Process Control ChartsPlot of Sample Data Over Time0204060801 5 9 13 17 21TimeSampleValueSampleValueUCLAverageLCL
• Sampel SAMA…Sampel SAMA…pp chartchart• Proporsi diketahui• Garis Tengah = p¯σ pp pn=−( )1UCL pLCL pp pp p= += −33σσ
• Sampel SAMA…Sampel SAMA…pp chartchart• Proporsi TIDAK diketahuim nomer sampel (vertikal) n ukuran sampel (horisontal) D bagian tidak sesuaip¯ = ∑Di/(mn)Garis Tengah = p¯σ pp pn=−( )1UCL pLCL pp pp p= += −33σσ
• Sampel BEDA …Sampel BEDA …a.a. Metode INDIVIDUMetode INDIVIDU  Batas Kendali tergantungBatas Kendali tergantungukuran sample tertentu shg BKA/BKB tidakukuran sample tertentu shg BKA/BKB tidakberupa garis LURUSberupa garis LURUSb.b. Metode RATA_RATAMetode RATA_RATA  Ukuran sampel RATAUkuran sampel RATA-RATA dg perbedaan tidak terlalu besar-RATA dg perbedaan tidak terlalu besar( n¯ = ∑n/observasi)( n¯ = ∑n/observasi)c.c. Peta Kendali TERSTANDAR dg GT=0 dan BKPeta Kendali TERSTANDAR dg GT=0 dan BK± 3± 3
• npnp ChartChartUCL = np np p+ −3 1( )LCL = np np p− −3 1( )Note: If computed LCL is negative, set LCL = 0Note: If computed LCL is negative, set LCL = 0
• c-chart dan u-chartc-chart dan u-chart• Mengetahui banyaknya kesalahanMengetahui banyaknya kesalahanunit produk sbg sampelunit produk sbg sampel• Sampel konstanSampel konstan  c-chartc-chart• Sampel bervariasiSampel bervariasi  u-chartu-chart• Aplikasi : bercak pd tembok,Aplikasi : bercak pd tembok,gelembung udara pd gelas,gelembung udara pd gelas,kesalahan pemasangan sekrup pdkesalahan pemasangan sekrup pdmobilmobil
• Number of defects per unit:Number of defects per unit:c¯ = ∑ ci / nc¯ = ∑ ci / nUCL cc c= + 3σLCL cc c= − 3σσ c c=C - chartC - chart
• U-chartU-chart• u¯ = ∑ ci/nu¯ = ∑ ci/n• n ¯ = ∑ ni/gn ¯ = ∑ ni/gg = banyaknya observasig = banyaknya observasiModel IndividuModel Individu• BPA-u = u¯ + 3 √ (u¯ /ni)BPA-u = u¯ + 3 √ (u¯ /ni)• BPB-u = u¯ - 3 √ (u¯ /ni)BPB-u = u¯ - 3 √ (u¯ /ni)Model Rata-rataModel Rata-rata• BPA-u = u¯ + 3 √ (u¯ /n¯)BPA-u = u¯ + 3 √ (u¯ /n¯)• BPB-u = u¯ - 3 √ (u¯ /n¯)BPB-u = u¯ - 3 √ (u¯ /n¯)
• Data yg diplotkan pada …• C-chart : nilai c• U – chart : nilai c/ni
• 4 1 5 3 2 7 4 5 2 32 8 5 3 6 4 2 5 3 6TwTwenty samples, eachenty samples, eachconsisting of 250 checks,consisting of 250 checks,The number of defectiveThe number of defectivechecks found in the 20checks found in the 20samples are listed below.samples are listed below.(proporsi tidak diketahui)(proporsi tidak diketahui)Example………Example………p-np chartp-np chart\$\$115006529 25447581 144526552655Simon SaysSimon SaysAugusta, ME 01227Augusta, ME 01227
• LCL = 3 .016 3(.007936) -.007808 0pp σ− = − = =(1 ) .016(1 .016) .015744.007936250 250pp pnσ− −= = = =UCL = 3 .016 3(.007936) .039808pp σ+ = + =Note that theNote that thecomputed LCLcomputed LCLis negative.is negative.EstimatedEstimated pp = 80/((20)(250)) = 80/5000 = .016= 80/((20)(250)) = 80/5000 = .016Control Limits For aControl Limits For a pp ChartChart \$\$115006529 25447581 144526552655Simon SaysSimon SaysAugusta, ME 01227Augusta, ME 01227
• Tdk sesuaiTdk sesuai ProporsiProporsi Tdk sesuaiTdk sesuai ProporsiProporsi44115533227744552233(4/250) = 0,016(4/250) = 0,016(1/250) =0,004(1/250) =0,00422885533664422553366(2/250) = 0,008(2/250) = 0,008(8/250) = 0,032(8/250) = 0,032
• p Chart for Norwest Bank0.0000.0050.0100.0150.0200.0250.0300.0350.0400.0450 5 10 15 20Sample NumberSampleProportionpUCLLCLControl Limits For aControl Limits For a pp ChartChart \$\$115006529 25447581 144526552655Simon SaysSimon SaysAugusta, ME 01227Augusta, ME 01227
• Ukuran sampel sama = 50 (Ukuran sampel sama = 50 ( pp-chart)-chart)nono Banyak produk cacatBanyak produk cacat nono Banyak produk cacatBanyak produk cacat11223344556677889910104422553322113322554411111212131314141515161617171818191920203355552233224410104433
• • nn ==• mm ==• DD ==• p¯p¯ ==• BKABKA ==• BKBBKB ==• Tabel proporsi untuk plot ke grafikTabel proporsi untuk plot ke grafik
• • nn = 50= 50• mm = 20= 20• DD = 72= 72• p¯p¯ = 72 / (20.50) = .072= 72 / (20.50) = .072• σσpp = √ (0,072)(0,928)/50 = .037= √ (0,072)(0,928)/50 = .037• BKABKA = 0,072 + 3(0,037)= 0,072 + 3(0,037) = 0,183= 0,183• BKBBKB = 0,072 - 3(0,037) = -0,039 = 0= 0,072 - 3(0,037) = -0,039 = 0• Tabel proporsi untuk plot ke grafikTabel proporsi untuk plot ke grafik
• Ukuran sampel sama = 50 (Ukuran sampel sama = 50 ( pp-chart)-chart)cacatcacat proporsiproporsi cacatcacat proporsiproporsi44225533221133225544(4/50 ) = 0,08(4/50 ) = 0,08(2/50) = 0,04(2/50) = 0,043355552233224410104433(5/50) = 0,01(5/50) = 0,01(10/50) = 0,20 (out)(10/50) = 0,20 (out) revisirevisi(4/50) = 0,08(4/50) = 0,08(3/50) = 0,06(3/50) = 0,06
• RevisiRevisi• p¯ = (72-10) / (1000-50) = 62/950 = 0,065p¯ = (72-10) / (1000-50) = 62/950 = 0,065• σσp = √ (0,065)(0,935)/50 = 0,035p = √ (0,065)(0,935)/50 = 0,035• BKA = 0,065 + 3 (0,035) = 0.17BKA = 0,065 + 3 (0,035) = 0.17• BKB = 0,065 - 3 (0,035) = -0,04 = 0BKB = 0,065 - 3 (0,035) = -0,04 = 0• Grafiknya juga berubahGrafiknya juga berubah
• Ukuran sampel beda (Ukuran sampel beda (pp chart)chart)nono sampelsampel Produk cacatProduk cacat nono sampelsampel Produk cacatProduk cacat11223344556677889910102002001801802002001201203003002502504004001801802102103803801414101017178820201818252520203030151511111212131314141515161617171818191920201901903803802002002102103903901201201901903803802002001801801515262610101414242415151818191911111212JmlJml sampelsampel 48604860 JmlJml CacatCacat 341341
• Metode Rata-rataMetode Rata-rata• Sampel rata-rataSampel rata-ratan¯n¯ = total sampel /observasi= total sampel /observasi= 4860/20 = 243= 4860/20 = 243p¯p¯ = D/(n¯m)= D/(n¯m)= 341 / (243.20) = 0,07 (CL)= 341 / (243.20) = 0,07 (CL)σσpp = √ (0,07(0,93))/243 = 0,0164= √ (0,07(0,93))/243 = 0,0164BPAp = 0,07 + 3 (0,0164) = 0,119BPAp = 0,07 + 3 (0,0164) = 0,119BPBp = 0,07 - 3 (0,0164) = 0,021BPBp = 0,07 - 3 (0,0164) = 0,021
• Metode IndividuMetode Individu• Sampel rata-rataSampel rata-ratan¯ = total sampel /observasin¯ = total sampel /observasi= 4860/20 = 243= 4860/20 = 243pp ¯¯ = D/(n¯m)= D/(n¯m)= 341 / (243.20) = 0,07 (CL)= 341 / (243.20) = 0,07 (CL)  semuasemuatitik samatitik sama• BP (obs-1)BP (obs-1)σσpp = √ (0,07(0,93))/200 = 0,018= √ (0,07(0,93))/200 = 0,018BPA = 0,07 + 3 (0,018) = 0,124BPA = 0,07 + 3 (0,018) = 0,124BPB = 0,07 - 3 (0,018) = 0,016BPB = 0,07 - 3 (0,018) = 0,016 BP (obs-2)……………….dstBP (obs-2)……………….dst
• Tabel Proporsi untuk GrafikTabel Proporsi untuk GrafikNo observasiNo observasi sampelsampel cacatcacat proporsiproporsi112233445566778899101011111212131314141515161617171818191920202002001801802002001201203003002502504004001801802102103803801901903803802002002102103903901201201901903803802002001801801414101017178820201818252520203030151515152626101014142424151518181919111112120,0700,0700,0550,0550,0850,0850,0670,067………………………………………………………………0,0950,0950,0500,0500,0550,0550,0670,067
• Example…c-chartExample…c-chartnono ByknyaByknyakesalahankesalahannono Byknya kesalahanByknya kesalahan11223344556677889910105544776688556655161610101111121213131414151516161717181819192020997788111199557766101088
• • c¯ = ∑c/n = 152/20 = 7,6c¯ = ∑c/n = 152/20 = 7,6• σσc =c = √7,6√7,6• BPA c = (7, 6) + 3 (√7,6) = 15,87BPA c = (7, 6) + 3 (√7,6) = 15,87• BPB c = (7, 6) - 3 (√7,6) = -0,67 = 0BPB c = (7, 6) - 3 (√7,6) = -0,67 = 0• Titik yang diplotkan adalah nilai cTitik yang diplotkan adalah nilai c
• Example…u-chartExample…u-chartnono SampelSampel cacatcacat nono sampelsampel cacatcacat11223344556677889910102020303025251515252510102020151515152525551414888812126620201010661010111112121313141415151616171718181919202030302525252525251010202020201010303020209916161212101066885555141488
• Metode Rata-rataMetode Rata-rata• Sampel Rata-rataSampel Rata-ratau¯ = 192/415 = 0,462 (CL)u¯ = 192/415 = 0,462 (CL)n¯ = 415/20 = 20,75n¯ = 415/20 = 20,75BPAu = (0,462) + 3 √ (0,462/20,75) = 0,906BPAu = (0,462) + 3 √ (0,462/20,75) = 0,906BPBu = (0,462) - 3 √ (0,462/20,75) = 0,018BPBu = (0,462) - 3 √ (0,462/20,75) = 0,018
• Metode IndividuMetode Individu• Sampel Rata-rataSampel Rata-ratau¯ = 192/415 = 0,462 (CL)u¯ = 192/415 = 0,462 (CL)n¯ = 415/20 = 20,75n¯ = 415/20 = 20,75• Batas KendaliBatas Kendali• Observasi -1Observasi -1BPA-1 = (0,462) + 3 √ (0,462/20) = 0,916BPA-1 = (0,462) + 3 √ (0,462/20) = 0,916BPB-1 = (0,462) - 3 √ (0,462/20) =BPB-1 = (0,462) - 3 √ (0,462/20) =0,008…….dst0,008…….dst