Quality Assurance

1. ACCEPTANCE SAMPLING (AS)
• INSPECTION AFTER PRODUCTION.
• Acceptance Sampling IS AN AUDITING
TOOL.
• CONCEPTS ARE MOST IMPORTANT -
FORMULAS FOR APPLICATIONS.

2. Basic Forms of Statistical
Sampling for Quality Control
Sampling to accept or reject the
immediate lot of product at hand
(Acceptance Sampling).
Sampling to determine if the process
is within acceptable limits
(Statistical Process Control)

3. Acceptance Sampling
• Purposes
– Determine quality level
– Ensure quality is within predetermined level
• Advantages
– Economy
– Less handling damage
– Fewer inspectors
– Upgrading of the inspection job
– Applicability to destructive testing
– Entire lot rejection (motivation for improvement)

4. Statistical Sampling--Data
• Attribute (Go no-go information – right or
wrong)
– Defectives--refers to the acceptability of product
across a range of characteristics.
– Defects--refers to the number of defects per unit--
may be higher than the number of defectives.
Variable (Continuous – by measuring to get
a value)
– Usually measured by the mean and the standard
deviation.

5. 5
Necessity of Sampling
• In most cases 100% inspection is too costly.
• In some cases 100% inspection may be impossible.
• If only the defective items are returned, repair or
replacement may be cheaper than improving quality.
But, if the entire lot is returned on the basis of sample
quality, then the producer has a much greater
motivation to improve quality.

6. 6
Some Sampling Plans
• Single sampling plans:
– Most popular and easiest to use
– Two numbers n and c
– If there are more than c defectives in a sample of
size n the lot is rejected; otherwise it is accepted
• Double sampling plans:
– A sample of size n1 is selected.
– If the number of defectives is less than or equal to
c1 than the lot is accepted.
– Else, another sample of size n2 is drawn.
– If the cumulative number of defectives in both
samples is more than c2 the lot is rejected;
otherwise it is accepted.

7. 7
Some Sampling Plans
• Sequential sampling
– An extension of the double sampling plan
– Items are sampled one at a time and the
cumulative number of defectives is recorded at
each stage of the process.
– Based on the value of the cumulative number of
defectives there are three possible decisions at
each stage:
• Reject the lot
• Accept the lot
• Continue sampling

8. Acceptance Sampling--Single
Sampling Plan
A simple goal
Determine (1) how many units, n, to
sample from a lot of size N and
(2) the maximum number of defective
items, c, that can be found in the
sample before the lot is rejected.

9. DESIGNING THE PLAN
• Acceptable Quality Level (AQL) = Max.
acceptable percentage of defectives defined by
producer.
• (Producer’s risk) =The probability of
rejecting a good lot.
• Lot Tolerance Percent Defective (LTPD) =
Limiting Quality Level (LQL) = Percentage of
defectives that defines consumer’s rejection
point.
• b (Consumer’s risk) =The probability of
accepting a bad lot.

10. 10
Operating Characteristic Curve
AQL LTPD
b = 0.10
1- =
0.05Probabilityofacceptance,Pa
{
0.60
0.40
0.20
0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
0.80
{
Percent defective
1.00
OC curve for n and c

11. The OC Curve
• Why is OC Curve So Important?
• It Provides Trade-Offs between, N, n, c,
AQL, , LTPD, and .
• The Resulting OC Curve should achieve the
desired characteristics for producer and
consumer.

12. Example: Acceptance Sampling
A manufacturer of computers, PH Electronics purchases
motherboards from a vendor, HAL Inc.. HAL has set an
acceptable quality level of 1% and accepts a 5% risk of
rejecting lots at or below this level. PH Electronics
considers lots with 3% defectives to be unacceptable and
will assume a 10% risk of accepting a defective lot.

13. GENERAL TYPES OF
PLANS
• SINGLE - TAKE A SINGLE SAMPLE,
ACCEPT (A) OR REJECT (R)
• DOUBLE - TAKE A SAMPLE, Aaccept / ,
Reject, OR INSPECT A 2ND LOT, THEN
Accept OR Reject
• MULTIPLE - TAKE 1 TO 7 SAMPLES
TO REACH A CONCLUSION

14. SINGLE PLAN
• SIMPLER
• ON AVERAGE, n IS HIGHER
• INSPECTION COST ARE HIGHER
• MORE INFO FROM A SINGLE PLAN

15. CHARACTERISTICS OF
PLANS
• AVG. OUTGOING QUALITY
• AVG. TOTAL INSPECTION
• AVERAGE SAMPLE NUMBER
• THESE STATISTICS BETTER DEFINE
EACH PLAN AND THUS HELP US
BETTER UNDERSTAND THE PLAN.

16. OTHER PLANS
• CHAIN SAMPLING PLANS
• SEQUENTIAL SAMPLING PLANS
• SKIP-LOT SAMPLING PLANS
• CONTINUOUS PRODUCTION PLANS
• DEMING’S kp RULE
• EACH HAS UNIQUE GOOD AND BAD
CHARACTERISTICS

17. VARIABLE PLANS
• MIL-STD-414 = ANSI/ASQCZ1.9
= ISO 3951
• TWO TYPES OF PLANS
• CONTROL MEAN AND STD. DEV.
• CONTROL OF PROPORTION NOT
MEETING SPECIFICATIONS OF THE
PROCESS

18. ADV. OF VARIABLE PLANS
• SAMPLE SIZES ARE SMALLER THAN
ATTRIBUTE PLANS
• MORE INFO FROM VAR. PLANS
• THIS MORE INFO PROVIDES
INSIGHTS INTO IMPROVED METHODS

19. DISADV. OF VAR. PLANS
• EACH CHARACTERISTIC REQUIRES A
SEPARATE PLAN.
• ADMIN. AND UNIT INSP. COSTS ARE
HIGH.
• MEASURING INSTRUMENTS ARE
MORE EXPENSIVE.
• MUST KNOW THE UNDERLYING
DISTRIBUTION OF PROCESS.

20. Thank you