Find out the quality:

ABC industries manufacture X-band radar scanners utilized to detect speed traps. The printed circuit boards in the scanners are bough from an outside vendor. The vendor generates the boards to an AQL of 2% defectives and is eager to run a 5% risk α of having lots of this level or fewer defectives discarded. The company considers lots of 8% or more defectives (LTPD) unacceptable and wants to ensure that it shall accept such poor quality lots not more than 10% of the time (β). A large shipment has just been delivered. What values of n and c must be choose to find out the quality of this lot?

Solution

It is given in the problem that

AQL = 0.02, α = 0.05, LTPD = 0.08 and β = 0.1. We can use table 14.6 to calculate c and n.

Therefore, the appropriate sampling plan is C = 4 and n = 100. Up to four defects found in the lot, the lot shall be accepted.

Table shows several acceptance numbers C. Corresponding to the specific C values, sample size is constant.

          Table: Data for Deriving a Single Sampling Plan

(Derived from Poisson Cumulative Table with α = 0.05 and β = 0.10)

In the present case LTPD/AQL = 4.

If you look at the Table, ratio ⁿ p_0.10 / ⁿ p_0.95 is 4.06 when C = 4 which is nearby to the ratio of LTPD/AQL.

ⁿ p_0.10  = 7.99

n × 0.08 = 7.99

n ≈ 100