Statistic Process Control Week 3 Ananda Sabil Hussein, SE, MCom

Latar Belakang Pertengahan tahun 80 an pangsa pasar pager Motorola di rebut oleh produk-produk Jepang seperti halnya NEC, TOSHIBA dan Hitachi. Motorola melakukan perubahan radikal dengan memperbaiki mutu, pengembangan produk dan penurunan biaya yang berbasis statistik

Statistical Process Control Teknik statistik yang secara luas digunakan untuk memastikan bahwa proses yang sedang berjalan telah memenuhi standar.

Start Produce Good Provide Service Stop Process Yes No Assign. Causes? Take Sample Inspect Sample Find Out Why Create Control Chart

Variasi Alami dan Khusus Variasi alami adalah sumber-sumber variasi dalam proses yang secara statistik berada dalam batas kendali Variasi Khusus/dapat dihilangkan yaitu variasi yang muncul disebabkan karena peralatan yang tidak sesuai, karyawan yang lelah atau kurang terlatih serta bahan baku baru.

Diagram Pengendalian

17 = UCL 16 = Mean 15 = LCL Sample number | | | | | | | | | | | | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 17 = UCL 15 = LCL 16 = Mean

Konsep Rata-rata dan Jarak

Menentukan Batas Diagram Rata-rata Batas Kendali Atas (UCL) = Batas Kendali Bawah (LCL) = = rata-rata dari sampel = = Standar deviasi = 2 (95.5%) 3(99.7%) = Standar deviasi rata-rata sampel

Cara Lain Batas Kendali Atas = Batas Kendali Bawah Dimana : = rentangan rata-rata sampel = Nilai batas kendali = rata-rata dari sampel rata-rata

Batas Bagan Rentangan

Bagan Rata-rata (a) These sampling distributions result in the charts below (Sampling mean is shifting upward but range is consistent) R-chart (R-chart does not detect change in mean) UCL LCL x-chart (x-chart detects shift in central tendency)

Bagan Jarak (b) These sampling distributions result in the charts below (Sampling mean is constant but dispersion is increasing) x-chart (x-chart does not detect the increase in dispersion) UCL LCL R-chart (R-chart detects increase in dispersion) UCL LCL Figure S6.5

Bagan Kendali Atribut Mengukur persentase penolakan dalam sebuah sampel, bagan-p Menghitung jumlah penolakan, bagan-c

Control Charts for Attributes For variables that are categorical Good/bad, yes/no, acceptable/unacceptable Measurement is typically counting defectives Charts may measure Percent defective (p-chart) Number of defects (c-chart)

Control Limits for p-Charts Population will be a binomial distribution, but applying the Central Limit Theorem allows us to assume a normal distribution for the sample statistics UCLp = p + zsp ^ p(1 - p) n sp = ^ Instructors may wish to point out the calculation of the standard deviation reflects the binomial distribution of the population LCLp = p - zsp ^ where p = mean fraction defective in the sample z = number of standard deviations sp = standard deviation of the sampling distribution n = sample size ^

Contoh Soal Jam Rata2 1 17.1 5 16.5 9 16.3 2 18.8 6 16.4 10 3 14.5 7 15.2 11 14.2 4 14.8 8 12 17.3

Ditanyakan : Batas kendali proses 9 boks yang mencakup 99.7% Jawab : = 16 + 3 UCLx = LCLx = = 16 - 3

Setting Control Limits Process average x = 16.01 ounces Average range R = .25 Sample size n = 5

Setting Control Limits UCLx = x + A2R = 16.01 + (.577)(.25) = 16.01 + .144 = 16.154 ounces Process average x = 16.01 ounces Average range R = .25 Sample size n = 5 From Table S6.1

Setting Control Limits Process average x = 16.01 ounces Average range R = .25 Sample size n = 5 UCL = 16.154 Mean = 16.01 LCL = 15.866 UCLx = x + A2R = 16.01 + (.577)(.25) = 16.01 + .144 = 16.154 ounces LCLx = x - A2R = 16.01 - .144 = 15.866 ounces

Contoh Soal Sample Number Fraction Sample Number Fraction Number of Errors Defective Number of Errors Defective 1 6 .06 11 6 .06 2 5 .05 12 1 .01 3 0 .00 13 8 .08 4 1 .01 14 7 .07 5 4 .04 15 5 .05 6 2 .02 16 4 .04 7 5 .05 17 11 .11 8 3 .03 18 3 .03 9 3 .03 19 0 .00 10 2 .02 20 4 .04 Total = 80 p = = .04 80 (100)(20) (.04)(1 - .04) 100 sp = = .02 ^

p-Chart for Data Entry UCLp = p + zsp = .04 + 3(.02) = .10 ^ LCLp = p - zsp = .04 - 3(.02) = 0 ^ .11 – .10 – .09 – .08 – .07 – .06 – .05 – .04 – .03 – .02 – .01 – .00 – Sample number Fraction defective | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 UCLp = 0.10 LCLp = 0.00 p = 0.04

Possible assignable causes present p-Chart for Data Entry .11 – .10 – .09 – .08 – .07 – .06 – .05 – .04 – .03 – .02 – .01 – .00 – Sample number Fraction defective | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 UCLp = p + zsp = .04 + 3(.02) = .10 ^ LCLp = p - zsp = .04 - 3(.02) = 0 UCLp = 0.10 LCLp = 0.00 p = 0.04 Possible assignable causes present There is always a focus on finding and eliminating problems. But control charts find any process changed, good or bad. The clever company will be looking at Operator 3 and 19 as they reported no errors during this period. The company should find out why (find the assignable cause) and see if there are skills or processes that can be applied to the other operators.

Control Limits for c-Charts Population will be a Poisson distribution, but applying the Central Limit Theorem allows us to assume a normal distribution for the sample statistics UCLc = c + 3 c LCLc = c - 3 c Instructors may wish to point out the calculation of the standard deviation reflects the Poisson distribution of the population where the standard deviation equals the square root of the mean where c = mean number defective in the sample

c-Chart for Cab Company c = 54 complaints/9 days = 6 complaints/day UCLc = c + 3 c = 6 + 3 6 = 13.35 | 1 2 3 4 5 6 7 8 9 Day Number defective 14 – 12 – 10 – 8 – 6 – 4 – 2 – 0 – UCLc = 13.35 LCLc = 0 c = 6 LCLc = c - 3 c = 3 - 3 6 = 0