14 Variable Sampling Plan - Student

8/8/2019 14 Variable Sampling Plan - Student

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Sampling Techniques

by

Variables

Assoc. Prof. Ir. Dr. Cheong Kuan Yew

School of Materials & Mineral Resources Engineering

Engineering Campus

Universiti Sains Malaysia


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Topic Outcome: At the end of this topic, students will be able to:

Discuss the advantages and disadvantages of

variable sampling.

Describe the Shainin Lot Plot Plan.


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Outline:

An Introduction.

Types of Sampling Plan.

- Shainin Lot Plot Plan.

- ANSI/ASQ Z1.9

Variability Unknown

Standard Deviation Method

Range Method

Variability known


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An Introduction When a quality characteristic is measurable on a

continuous scale, and is know to have a distribution of aspecific type (e.g. normal distribution); it is possible to use

a sampling based on sample measurements such as:

Mean and

Standard Deviation.

Variables Sampling Plans.


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Population

Sample

LSL USL

LSL USL

Compare

Compare to required Quality LevelACCEPT REJECT


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Percent nonconforming below and above specifications.

LSL USL

pu

+g-gpL


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Advantages of Variable Sampling Plan:

Same protection with smaller sample size.

Feedback of data on Process.

Extent of conformity given weightage.

Errors in measurement more likely detected.

Disadvantages of Variable Sampling Plan: Applicable to only one quality characteristic at a time.

Higher inspection cost Measurement.

Higher clerical cost Calculation.

Possibility of no nonconformity in a rejected lot.

Dependence on assumption of distribution shape.


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Types of Variable Sampling Plan

Variable Sampling Plan

Percent nonconforming Process Parameter

To determine the

proportion of product that

is outside specification

To control the averageand standard deviation of

the distribution of the

product to specified level

E.g.:Shainin lot plot

ANSI/ASQ Z1.9-1993

E.g.:Shainin lot plot

ANSI/ASQ Z1.9-1993

E.g.:Acceptance control chart

Sequential sampling for variable

Hypothesis testing


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Shainin Lot Plot Plan

Developed by Dorian Shainin (Hamilton Standard Division

of United Aircraft Corporation, 1950).

The plan uses a plotted frequency distribution

(histogram) to evaluate a sample for decisions

(accept/reject a lot).

It is a practical plan forin-house inspection & receiving

inspection.

Advantages:

Applicable to both normal and non-normal frequency

distributions.

Simple to use.


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The method for obtaining the lot plots is as follows: A random sample of 10 subgroups (g) of 5 each for a

total of 50 items is obtained from the lot.

The average, X-bar and range, R, are calculated for

each subgroup.

A histogram is constructed (number of cell: 7-16).

Calculate the average of averages, X-double bar, and

average of ranges, R-bar. Calculate the upper and lower lot limits (ULL & LLL)

Lot Plotting Method


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Q&A


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7.97

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2

2

!!!

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d

RXLLL

d

R

XULL

37.110

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7.9710

8.976

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!

!!

!

g

RR

g

XX

Chart for Ranges:

Factor for Central Line d2

3Wcontrol

limits


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Fig 10-14: Lot plot histogram


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Decision is based on a comparison of the lot plot with 11

different types of lot plots.

Lot Plot Evaluation

Type Distribution Comments

1

normal

-within spec.limits

- accepted without calculate lot limits.

2-lot limits within spec. limits.

-accept.3 -lot limits outside spec. limits.

-percentage of product beyond spec is obtained.

-Review board determines the final disposition of the stock.4

5nonnormal

skrewed

6 Lot was screened & sorted

7 Bimodal condition

8nonnormal Lot was screened & sorted

9

10 Bimodal condition

11 Stray values


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Once learned, the lot plot procedure is relatively simple and

has resulted in improved quality and lower inspectioncost.

Unacceptable lots are returned to the producer, and this

action will cause a subsequent improvement in quality.

Inspectors can accept lots; however, disposition of

unsatisfactory lots is left to a material-review board.

Many users of the lot plot method have modified the Shainin

method for their own situation.

The majorcriticism of the plan is that the shape of the plot

does not always give an accurate indication of the truedistribution. Shainin states that the plot is close enough to

have no practical effect on the final decision, or if there are

any errors, they are in a safe direction.

Summary


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End

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14 Variable Sampling Plan - Student