Statistic Process Control

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Statistic Process Control

Week 3

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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

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Statistical Process Control

 Teknik statistik yang secara luas digunakan untuk memastikan bahwa proses yang

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Start _{Provide Service}Produce Good

Stop Process

Yes No

Assign. Causes? Take Sample

Inspect Sample

Find Out Why Create

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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

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17 = UCL

15 = LCL

16 = Mean

Sample number Sample number

|

| || || || || || || || || || || || 1

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Konsep Rata-rata dan Jarak

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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

n

x

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Cara Lain

R A X  ₂

 

 A R

X ₂

Batas Kendali Atas =

Batas Kendali Bawah

Dimana :

x

A

R

2

= rentangan rata-rata sampel

= Nilai batas kendali

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Batas Bagan Rentangan

R

D

LCL

R

D

UCL

R R

3 4

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Bagan Rata-rata

(Sampling mean is (Sampling mean is shifting upward but shifting upward but range is consistent) range is consistent)

R-chart

R-chart (R-chart does not detect change in (R-chart does not _{detect change in} mean)

mean)

UCL

x-chart

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R-chart

R-chart (R-chart detects increase in (R-chart detects _{increase in} dispersion)

(Sampling mean (Sampling mean is constant but is constant but dispersion is dispersion is increasing) increasing)

x-chart

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Bagan Kendali Atribut

 Mengukur persentase penolakan dalam sebuah sampel, bagan-p

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 _{For variables that are categorical}_{For variables that are categorical}  _{Good/bad, yes/no,}_{Good/bad, yes/no,}

acceptable/unacceptable

 _{Measurement is typically counting defectives}_{Measurement is typically counting defectives}  _{Charts may measure}_{Charts may measure}

 _{Percent defective (p-chart)}_{Percent defective (p-chart)}  _{Number of defects (c-chart)}_{Number of defects (c-chart)}

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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

where pp == mean fraction defective in the samplemean fraction defective in the sample z

z == number of standard deviationsnumber of standard deviations



_p_p == standard deviation of the sampling distributionstandard deviation of the sampling distribution

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Contoh Soal

Jam Rata2 Jam Rata2 Jam Rata2

1 17.1 5 16.5 9 16.3

2 18.8 6 16.4 10 16.5

3 14.5 7 15.2 11 14.2

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Setting Control Limits

Process average x

Process average x = 16.01= 16.01 ounces ounces Average range R

Average range R = .25= .25

Sample size n

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Setting Control Limits

UCL

UCL_x_x = x + A= x + A₂₂RR

= 16.01 + (.577)(.25)

= 16.01 + .144

= 16.154

= 16.154 ouncesounces

Average range R = .25= .25

Sample size n

Sample size n = 5= 5

From

From Table S6.1

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Setting Control Limits

LCL

LCL_x_x = x - A= x - A₂₂RR

= 16.01 - .144

= 15.866

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Contoh Soal

Sample

Sample NumberNumber FractionFraction SampleSample NumberNumber FractionFraction Number

Number of Errorsof Errors DefectiveDefective NumberNumber of Errorsof Errors DefectiveDefective

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p-Chart for Data Entry

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p-Chart for Data Entry

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Control Limits for c-Charts

Population will be a Poisson distribution, Population will be a Poisson distribution,

but applying the Central Limit Theorem but applying the Central Limit Theorem allows us to assume a normal distribution allows us to assume a normal distribution

for the sample statistics for the sample statistics

where

where cc == mean number defective in the samplemean number defective in the sample

UCL

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