Question

Suppose that a supplier ships components in lots of size 5000. A single-sampling plan with n = 50 and

c = 2 is being used for receiving inspection. Rejected lots are screened, and all defective items are

reworked and returned to the lot.

(a) Draw the OC curve for this plan.

(b) Find the level of lot quality that will be rejected 90% of the time.

(c) Management has objected to the use of the above sampling procedure and wants to use a plan with

an acceptance number c = 0, arguing that this is more consistent with their zero-defects program.

What do you think of this?

(d) Design a single-sampling plan with c = 0 that will give a 0.90 probability of rejection of lots having the quality level found in part (b). Note that the two plans are now matched at the LTPD point. Draw the OC curve for this plan and compare it to the one for n = 50, c = 2 in part (a).

(e) Suppose that incoming lots are 0.5% nonconforming. What is the probability of rejecting

these lots under both plans? Calculate the ATI at this point for both plans. Which plan do you prefer?

Why?

Answer 1

ANSWER:

Calculation in Excel

(b)

Probability of Rejection =90%, So, Probability of acceptance = 10%

Using a goal seek function in excel, we find that % defective for that lot is 10.29%

(c)

The c=0 curve is shown in green. This signifies that at the same level of supplier or producer risk, the AQL and LTPD diminishes. This means that the company is considering the percent defective for good quality as more stringent and the rejection criteria with a lesser percentage than previous. However, if the process of the supplier does not improve, making stringent restrictions on inspection will reduce the numbers accepted and the service level of the company.

(d)

Now, we keep % defective =10.29%, make Pa=10% by varying 'n'. This gives us n=21.

The OC curve is again steeper than the previous case.