SAMPLING PLAN. Dasar - Dasar Penarikan Contoh (Sampling)

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Dasar - Dasar Penarikan

Contoh (Sampling)

▸ Baca selengkapnya: contoh catatan tubuh

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Apa Itu Sampling?

• Pendugaan karakteristik suatu populasi

berdasarkan contoh (

sample

) yang diambil

dari populasi tersebut

• pengukuran hanya dilakukan pada sebagian

elemen dari populasi: tidak semua elemen

dalam populasi diukur

• Digunakan untuk memperoleh nilai dugaan

dari populasi yang sedang dipelajari

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Apa itu sampling…(2)

• Perumpamaan:

“seorang koki yang

mencicipi satu sendok

sup untuk mengatakan

bahwa satu panci sup

yang dimasaknya

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Bandingkan…!

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Populasi & contoh…(2)

• Ukuran populasi:

– banyaknya unit populasi di dalam populasinya dinotasikan: N

• Ukuran contoh:

– banyaknya unit populasi yang terambil sbg contoh dinotasikan: n

• Intensitas sampling (IS):

– Proporsi ukuran contoh terhadap ukuran populasi:

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Populasi & contoh…(3)

• Parameter:

nilai yang mencerminkan karakteristik populasi • Statistik: nilai mencerminkan karakteristik contoh Misalnya: – Rata-rata/nilai tengah (mean) – Ragam (variance)

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Studi Kasus

• Misalkan dalam kelas Anda ini: Apabila akan dipilih 10 orang wakil:

– Apakah populasinya? – Berapakah ukuran

populasinya?

– Apakah wujud unit populasinya?

– Apakah sampling frame-nya? – Berapakah ukuran

contoh-nya?

– Berapakah intensitas sampling-nya?

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Mengapa Sampling?

Keuntungan sampling:

– Menghemat sumberdaya: biaya, waktu, tenaga – Kecepatan mendapatkan informasi (up to date) – Ruang lingkup (cakupan) lebih luas

– Data/informasi yang diperoleh lebih teliti dan mendalam

– Pekerjaan lapangan lebih mudah dibanding cara sensus

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Mengapa Sampling ?

Sampling lebih disukai dibanding

inspeksi

100%

bilamana

– inspeksi bersifat destruktif.

– inspeksi butuh biaya yang mahal

– inspeksi 100% tidak layak untuk

dijalankan

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Kesalahan dalam Sampling

Jenis kesalahan:

A. Kesalahan non-sampling:

• Kesalahan yang bukan berasal dari pengambilan

contoh, muncul karena:

– kesalahan pengukuran (measurement error) – kesalahan alat (instrumental error)

– Kesalahan karena faktor pengukur (human error) – Kesalahan karena faktor lingkungan

(environmental error)

• Besarnya kesalahan jenis ini sulit dihitung secara

pasti

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Kesalahan dalam sampling…(2)

B.Kesalahan sampling (

sampling error,

SE

):

– Kesalahan yang disebabkan oleh

pengambilan contoh (

sampling

) yang

dilakukan secara tidak tepat

– Besarnya kesalahan dapat dihitung dengan

formula berikut:

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Ukuran contoh yang paling optimal adalah satu titik dimana banyaknya unit populasi yang terambil sebagai contoh akan menghasilkan total error yang paling minimal

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Teliti, Akurat, Bias

• Dalam sampling:

Contoh (

sample

) digunakan untuk

memperoleh nilai dugaan (

estimate

) yang

akurat/tepat bagi parameter populasi

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Teliti, Akurat, Bias

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Teliti, akurat, bias

Ketelitian (precision):

– Derajat kesesuaian (degree of agreement) dari suatu rangkaian pengukuran

– Dalam sampling : Penyimpangan nilai-nilai pengukuran (dari contoh) thdp nilai rata-ratanya sendiri {Ditunjukan oleh nilai simpangan baku (s)}

Keakuratan/ketepatan (accuracy):

– Derajat kedekatan suatu nilai pengukuran terhadap nilai sebenarnya

– Dalam sampling : Besarnya penyimpangan nilai-nilai dugaan dari contoh thdp nilai parameter populasinya (Catatan:

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Teliti, akurat, bias

Bias

kesalahan sistematis yg dapat disebabkan oleh : kesalahan dlm prosedur pengukuran, alat, prosedur sampling, perhitungan, pencatatan, …dsb…

Hubungan ketiganya:

(A=akurasi, B=bias, P=presisi)

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Dua Metoda Pengambilan Contoh

1. Pengambilan contoh secara acak (random sampling): Sampel diambil tanpa mengikuti satu pola tertentu,

setiap unit populasi punya peluang yang sama untuk terambil dan menjadi bagian dari contoh

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Dua Metoda Pengambilan Contoh

2. Pengambilan contoh secara sistematik (systematic sampling):

• Unit contoh diambil dengan pola ttt, keteratutan ttt (sistematis)

• Tidak memiliki penduga ragam yang sah:

– Dalam penerapannya, sering dimodifikasi menjadi

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Acceptance Sampling

• Another area of quality control and improvement • Closely connected with inspection and testing of

product

• Inspection can occur at many points in a process

The inspection and classification of a sample of nits selected at random from a larger batch or lot and ultimate decision about disposition of the lot –

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Acceptance Sampling

• Berhubungan dengan keputusan untuk

menerima atau menolak lot produk

• Acceptance sampling dari lot ke lot

adalah suatu proses pengambilan

keputusan

• Suatu keputusan yang didasarkan pada

sample yang diambil dari unit - unit yang

terdapat dalam lot produk

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Acceptance Sampling

A batch (lot) of items has been produced.

– Before shipment, the producer tests the lot

for outgoing quality,

or

– After receiving shipment, the consumer

tests the lot for incoming

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Persyaratan Suatu Lot



Lots should be

homogeneous

:

– produced on the same machines, by same operators, from common raw materials, at

approximately the same time period (come from a single source)

– units should be as similar to each other as possible.



Larger lots are more preferable

than smaller

lots

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Dasar Penentuan Suatu

Acceptance Sampling Plans

1. By

Attributes

– each sampled item is inspected and

classified

as conforming or nonconforming

(defective).

– Or, the number of defects or

nonconformities is counted for each item.

– Large numbers of nonconforming or

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2. By

Variables

– some

quantitative

quality characteristic is

measured

for each sampled item.

– the sample mean of the measurements is

computed.

– if the sample mean lies outside an

acceptable range, the lot is rejected.

Dasar Penentuan Suatu

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Beberapa Skema

Acceptance Sampling Plan

Sampling Plan for Attributes Sampling Plan for Variables

• Single-Sampling Attributes plans • Dodge-Romig Plans

• Double Sampling Plans • MIL-STD-105E

• Sequential Sampling

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Single-Sampling Attributes Plans

• Inspected units should be selected at

random

• each combination of n items has an

equal chance of comprising the sample.

• Inspected units should represent all

items in the lot

• eliminates bias

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Single-Sampling Attributes Plans

• A lot of size N has been submitted for inspection

• A simple random sample is selected from a lot for inspection. – n = sample size.

– c = acceptance number.

• If there are more than c nonconforming items in the sample, then the lot is rejected.

N = 10,000 n = 89 Example N = 10,000 n= 89 c = 2

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Contoh

A manufacturer of silicon chips produces lots

of 1000 chips for shipment. A single-sampling

plan with

n = 65 and c = 2

is used to test for

bad outgoing lots.

– In one sample, 4 defective chips are discovered. Since 4 > 2, the lot is rejected and not shipped. The source of the defective chips should be found and eliminated.

– In a random sample of 65 chips taken from

another lot, 2 defective chips are discovered. This

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Fungsi Operating Characteristic (OC)

Sebuah fungsi untuk mengukur performa design

suatu sampling plan

– Probabilitas diterimanya suatu lot dihitung

berdasar fungsi OC berikut:

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The OC Curve

Plot of OC Function

Curve plots the probability of accepting the lot (P_a)

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Latihan

1. A single sampling plan has parameters n = 2

and c = 0.

– What is the OC function for such a plan?

– How much the probability of accepting a lot with 5% defective ?

– How much the probability of acceptance of a lot with 20% defective ?

2. What is the OC function for a plan having

n = 2 and c = 1?

3. What is the OC function for a plan with

n = 10 and c = 2?

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Latihan

4. An apple producer has 500 baskets of

apples, containing 20 each. A buyer wants

to inspect 10 of the apples before accepting

the lot (if 2 or less are bruised).

– How many n , N, and c ?

– Suppose 20% of the apples in the lot are bruised, What is the probability of accepting such a lot? – If 50 % of the apples are bruised, then the

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Contoh

Suatu sampling plan dengan:

n1 = 10 n2 = 20 ac1 = 0 ac2= 3 re1 = re2 = 3 N = 1000 D = 50

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Example B:

Consider a double sampling plan with n1 = 100, c1 = 2, r1 = 6, n2 = 200, c2 = 5. Find that the probability of

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Military Standard 105E

Procedure

 Choose the AQL

 Choose the inspection level

 Determine the lot size

 Fine the appropriate sample size code letter (from Table 14-4)

 Determine the appropriate type of sampling plan to use (single)

 Enter the appropriate table to find the type of plan to be used

 Determine the corresponding normal and reduced inspection plans to be used when required

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Acceptable quality level (AQL)

• The poorest quality level for the supplier’s process that a consumer would consider to be acceptable

• A property of the supplier’s manufacturing process, not a property of the sampling plan

• This is the maximum proportion of defectives allowed. The producer requires that the probability of acceptance at this level be fairly high. i.e. Pa(AQL) should be large, typically this should be near 0.99 or 0.95.

• Type I error probability:

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Lot tolerance percent defective (LTPD)

• or consumer’s quality level

• The protection obtained for individual lots of poor quality • This is a numerical definition of an unacceptable lot. The

consumer requires that this kind of lot be rejected with

high probability. In other words Pa(LTPD) should be small, typically this is chosen to be 0.1

• Pa(LTPD) is often referred to as , the probability of Type II error.

• Also called rejectable quality level (RQL) and the

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Latihan

1. Suppose MIL STD 105E is used, lots

of 15000 are to be examined, and

AQL is .4 %.

a. If double sampling is used. How many n and c we need

b. Now, suppose single sampling is used. Calculate n and c we need

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Latihan

c. Suppose that the following sequence of rejected (R) and accepted (A) lots with the number of

defectives D occur: 0 0 1 0 1 0 1 2 0 1 12 0 0 14 0 D A A A A A A A A A A R A A R A A/R 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Lot

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MENDISAIN

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Mendesign Suatu Acceptance

Sampling plan

How can we decide

1. how many items n to sample, and

2. how many nonconforming items c in

that sample are enough to convince us

that the lot is unacceptable

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Optimal Plans

• The ideal OC curve places high probability on

accepting good lots (p close to 0), and low probability on accepting bad lots.

• The producer wants all good lots to be accepted.

(minimize type I error probability = producer’s risk). In other words, if p is small, then the producer wants

Pa(p) to be close to 1

• The consumer wants all bad lots to be rejected.

(minimize type II error probability = consumer’s risk). If p is large, then the consumer wants Pa(p) close to 0.

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Finding a Plan

,

given

_α

,

_β

,

LTPD and AQL

To construct sampling plan such that

for n and c, where p1 = AQL and p2 = LTPD.

To solve these equations, we could use a binomial nomograph OR

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Binomial Nomograph

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