acceptance sampling (sqc)

ACCEPTANCE SAMPLING (SQC)

By Prof N D Sadaphal

Assistant Professor

Sanjivani College of Engineering, Kopargaon (Maharashtra State) 423601

Mechanical Engineering

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ACCEPTANCE SAMPLING

P R O F N D S A D A P H A L M E C H A N I C A L E N G G . D E P A R T M E N T

Statistical Quality Control &

Acceptance Sampling

Acceptance sampling is a method used to accept or reject Lot of product based on a random sample of the product.

The purpose of acceptance sampling is to sentence lots (accept or reject) rather than to estimate the quality of a lot.

Acceptance sampling plans does not improve the quality. The nature of sampling is such that acceptance sampling will accept some lots and reject others even though they are of the same quality.

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When this tool be used in your organization?

•When developing new products. •When dealing with new suppliers. •When a supplier’s product has had excellent quality in the past. •Large numbers of items must be processed in a short amount of time. •When product testing is, Expensive & time consuming Purposes

• Determine quality level. • Ensure quality is within predetermined level.

Advantages Advantages Disadvantages Disadvantages

Less expensive

Rejection on entire lot motivates quality improvement for suppliers

less handling damage of the product

Less man power is involved in inspection activities.

It often greatly reduces the amount of inspection error

Producer risk - can reject “good” lots (Type I Error)

Consumers Risk- can accept “bad” lots.(Type II Error)

Sample provides less information than 100-percent inspection.

Advantages and Disadvantages of Sampling

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Inspection

Inspection:

a. No inspection – all products are accepted.

b. 100% inspection

accept goods & reject bads,

uneconomical for large size of lot,

time consuming, more man power.

c. Acceptance sampling

reduces the inspection.

verify quality level of lot.

OC Curve (Operating characteristic curve)

Ideal OC Curve

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Parameters of OC Curve

Consumer risk- bad lot is accepted. Producer risk- good lot rejected. This risk should kept as low as possible. AQL- It is the max. %defective or max. no. of defect/hundred for purpose of sampling inspection. Producer risk should be less or equal to AQL. RQL- Level of defectiveness so rejected by sampling plan. AQL & RQL level decided by negotiation between customer & producer. IQL- quality level between AQL & RQL. Probability of acceptance is 50%. AOQL(Avg. outgoing quality limit)- quality of lot after acceptance. It is lowest quality level of lot that will generally accepted.

RQL also called as LTPD- lot tolerance % defective

AOQ (Avg. outgoing quality)- quality that leaves the inspection. Pd = true percent defective of the lot

Pa = probability of accepting the lot

N = number of items in the lot

n = number of items in the sample

Acceptance Number (c)- it is a permissible number of defective units in a selected sample size.

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Characteristics of OC Curve

Changing Lot size- larger lot size will have better characteristic as, it reduce the risk of error. Lot size increases, sample size also increases.

•Changing sample size- larger the number items in the sample, more is the possibility of finding defects.

Changing acceptance number- acceptance number increases, probability of acceptance also increases.

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Sampling Plan Methods

Sampling Plans specify the lot size, sample size, number of samples and acceptance/rejection criteria.

Sampling plans involve:

Single sampling Plan

Double sampling Plan

Multiple sampling Plan

Random sample

Lot

Single sampling Plan

Single Sampling Plan

N = lot size

n = sample size

C=acceptance number

Each item in the sample is examined and classified as good/defective.

If c or less non-conforming units are found in the sample, the lot is accepted, else it is rejected.

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Double Sampling Plan

A Double Sampling Plan allows to take a second sample if the results of the original sample are inconclusive.

Specifies the lot size, size of the initial sample, the accept/reject/inconclusive criteria for the initial sample (N, n1, c1 , r1)

Specifies the size of the second sample and the acceptance rejection criteria based on the total number of defective observed in both the first and second sample (n2,c2,r2)


First Random sample

Lot

C1 r1

First sample inconclusive, take second sample

Reject Lot Accept Lot

Compare number of defective found in the first random sample to C1 and r1 and make appropriate decision.

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C2

Reject Lot Accept Lot

Compare the total number of defective in both lots to C2 and make the appropriate decision

Lot First Random sample

Second Random sample

• A double sampling plan is associated with four numbers:

• The interpretation of the numbers is shown by an example:

1. Inspect a sample of size 20

2. If the sample contains 3 or less defectives, accept the lot

3. If the sample contains more than 5 defectives, reject the lot.

2121 ccnn and ,,

531020 2121 ccnn ,,, Let

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If the sample contains more than 3 and less than or equal to 5 defectives (i.e., 4 or 5 defectives), then inspect a second sample of size 10

5. If the cumulative number of defectives in the combined sample of 30 is not more than 5, then accept the lot.

6. Reject the lot if there are more than 5 defectives in the combined lot of 30

Multiple sampling Plan

A Multiple Sampling Plan is similar to the double sampling plan in that successive trials are made, each of which has acceptance, rejection and inconclusive options.

Sample Sample size

Combined samples

size Acceptance number

Rejection number

First n1 n1 c1 r1

Second n2 n1+n2 c2 r2

Third n3 n1+n2+n3

c3 r3

Fourth n4 n1+n2+n3+n4

c4 r4

Fifth n5 n1+n2+n3+n4+n5

c5 c5+1

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Steps for problem solution

Step 1 Sample size,

Step 2 Average Outgoing Quality AOQ,

For double sampling plan:- No. of defectives articles= Lot size × percent defective = N × Pd

No. of non defectives articles= Lot size – no. of defective article=N-(N ×Pd)

Total no. of defective in first sample, say x=(n × Pd)I

the lot is accepted if, (n × Pd)≤C1, C1=acceptance no. of 1st sample.

For Single sampling plan:-

For 2nd sample, if no. of defectives >C1 then take 2nd sample for inspection.

if defect ≤ C2 then 2nd lot is accepted. C2=acceptance no. of 2nd sample.

If defects are greater than C2 lot is rejected.

No. of defective in 2nd sample say y=(n × Pd) II

Probability of acceptance for 2nd sample,

lot can be accepted if

Max. defects=C1 (for 1st ) &

Max. defects=(C2-C1) (for 2nd )

Total probability of acceptance,

Average Outgoing Quality AOQ,

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Table for solving the Problem

0.6 0.7 0.8 0.9 1.0

0 0.549(0.549) 0.819(0.819) 0.499(0.499) 0.406(0.406) 0.368(0.368)

1 0.329(0.878) 0.164(0.983) 0.359(0.808) 0.366(0.772) 0.368(0.736)

2 0.099(0.977) 0.016(0.999) 0.144(0.952) 0.166(0.938) 0.184(0.92)

nP’ c

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Single Sampling Plan Single Sampling Plan Double Sampling Plan Double Sampling Plan

No. of samples one.

Decision of acceptance & rejection depend on sample taken.

Sample size is large.

Amount of record keeping is least

Chance/probability of acceptance of lot is less.

No. of samples two.

Decision of acceptance & rejection depend on first & second sample taken.

First sample size is about half of single sampling.

1st sample & 2nd sample results are noted.

Chance/probability of acceptance of lot is more.

Comparison between Single & Double Sampling Plan

Statistical Quality Control

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SQC

It is the collection, analysis & interpretation of data to solve a particular problem.

Products of uniform acceptable quality are manufactured.

Statistical Quality Control

Statistical concept

Data:- collected for quality control purpose. Classified as,

Variables- These are quality characteristics that are measured. e.g. weight- in KG, diameter in mm.

Attributes- These are those quality characteristics that are classified as either present or absent in the product.

e.g. Order is either complete or incomplete , Go-No Go gauge inspection, presence of crack in welding.

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Frequency Diagram

1. Manufacturing variability-

No parts can be produced with identical measurements. Their will be variation due to manufacturing process or measuring equipment.

Histogram

Freq.

Dia. Of pins in mm

join top point of each histogram rectangle by line, the obtained graph is known as frequency polygon.

If we join these points by smooth curve, obtained graph is called as frequency distribution.

• Frequency Distribution

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Concept of variation

No two items are exactly alike.

Some sort of variations in the two items is bound to be there. In fact it is an integral part of any manufacturing process.

This difference in characteristics known as variation.

This variation may be due to substandard quality of raw material, carelessness on the part of operator, fault in machinery system etc.

Types Of Variations 30

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Variation due to chance causes

Variation occurred due to chance.

This variation is NOT due to defect in machine, Raw material or any other factors.

Variation due to slight vibration in machine, sudden failure of power supply.

Behave in “random manner”.

Negligible but Inevitable

The process is said to be under the state of statistical control.

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Variation due to Assignable causes

Non – random causes

like:

Difference in quality of raw material

Difference in machines

Difference in operators

Difference of time

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Graph of sample data plotted over time Assignable Cause Variation

Random Variation

Process Average

Control Charts

LCL

UCL

Mean

Mean, Median & Mode Mean-

Average of measured reading.

or if frequency of data is given then,

Median- if set of reading is given

2,9,4,8,10

----median is 8 i.e. central value

2,4,7,8,9,10

-----median is avg. of central two values i.e. 7 & 8 i.e.(7.5)

For calculating median arrange the reading in ascending order.

Mode- value which occurs more time.

or value having higher position in graph. (last example mode is 1.8)

2,4,8,9,10

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Range & Standard Deviation

Range-

Difference between highest & lowest reading.

Set of readings 2,9,4,8,10

Range= (10-2)=8

Standard Deviation-

X1, X2,….,Xn are individual reading is mean

Control charts

The control chart is a statistical quality control tool used in the monitoring variation in the characteristics of a product or service

Data collected from a control chart may form the basis for process improvement.

UCL = Process Average + 3 Standard Deviations

LCL = Process Average - 3 Standard Deviations

Process Average

UCL

LCL

X

+ 3

- 3

TIME

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X-chart (Variable data)

It is used to monitor changes in the mean of a process.

To construct a mean chart we first need to construct the center line of the chart

Step 1 calculate mean

Step 2 calculate Grant mean

Step 3 standard deviation of the distributed sample means

Step 4 calculate control limits

Step 5 plot graph

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Control charts for variable

X-chart & R-chart

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A quality control inspector at the Cocoa Fizz soft drink company has taken 5 samples with four observations each of the volume of bottles filled. The data and the computed means are shown in the table. If the standard deviation of the bottling operation is 0.14 ounces, use this information to develop control limits of three standard deviations for the bottling operation.