## 1.5 OPERATING CHARACTERISTIC (OC) CURVES

• Used to estimate the probability of lot rejection, and design sampling plans.

• Drawing the single sampling curve (assuming Poisson distribution)

• Double sampling curves

• Factors that vary OC curves

• Producers/Consumers risk

• The basic trade-off to be considered when designing sampling plans.

- The producer does not want to have lots with higher rejects than the AQL to be rejected. Typically lots have acceptance levels at 95% when at AQL. This gives a producers risk of α = 100% - 95% = 5%. In real terms this means if products are near the AQL, they have a 5% chance of being rejected even though they are acceptable.

- The consumer/customer does not want to accept clearly unacceptable parts. If the quality is beyond a second unacceptable limit, the LQL (Lower Quality Level) they will typically be accepted 10% of the time, giving a consumers risk of β = 10%. This limit is also known as the LTPD (Lot Tolerance Percent Defective) or RQL (Rejectable Quality Level).

• AOQ (Average Outgoing Quality)

• AOQ (Average Outgoing Quality) - a simple relationship between quality shipped and quality accepted.

• ASN (Average Sample Number) - the number of samples the receiver has to do

DESIGNING A SAMPLE PLAN

• On the other hand, given consumers risk (β) and Lower Quality Level (LQL), we can follow a similar approach, still using the table on pg. 314

• Given α and AQL, and β and LQL we can also find a best fit plan through trial and error.

PROBLEMS: pg. 321- #1, 4, 7, 14, 17, 22

### 1.5.1 Practice Problems

1. Show the effect of lot screening if the sample size is n=100 and the reject limit is c=1.

2.

a) Develop a double sampling plan OC curve given that,

N = 1000

n1 = 50

c1 = 2

r1 = 4

n2 = 100

c2 = 3

b) What is the AOQL?

3. a) Develop Operating Characteristic (OC) curves for the three cases below,

a) N = 1000, n = 20, c = 4

b) N = 1000, n = 40, c = 8

c) N = 1000, n = 80, c = 16

b) For each curve indicate the AQL and RQL for a producer risk of 5% and a consumer risk of 10%

(ans. for n=20,c=4, AQL=10%, RQL=40%, for n=40,c=8, AQL=11.8%,RQL=33%, for n=80,c=16, AQL=13.8%,RQL=N.A.)