Use the Binomial monograph given in the formula sheet to determine a single samp

Question

Use the Binomial monograph given in the formula sheet to determine a single sampling plan for p_1 =0.01, alpha =0.05, p_2 =0.8, beta =0.05. Note, in the monograph, the left side is for the parameters p_1 and p_2 while the right side is for alpha and beta. For a single sampling plan with N=5000, n=100 and c=1, the corresponding type-B OC curve is shown below. Based on this OC curve, estimate the Average Outgoing Quality Limit (AOQL) for this plan. Briefly explain the inspection procedure for sampling plans indexed on AOQL.

Explanation / Answer

6.1 Using the binomial graph, we get n = 80 and c = 2 for alpha = 0.05, p1 = 0.01, p2 = 0.8 and beta = 0.05.

Connect the lines (Line 1 - p1 = 0.01 and 1-alpha = 0.95 , Line 2 - p2 = 0.8 and beta = 0.05) to get n=80 and c= 2

6.2 For p = 0.01, Pa = 0.8 in the OC curve,

AOQ = Pa * p * (N-n)/N

= 0.8 * 0.01 * (5000-100)/5000 = 0.00784

Calculated for other probabilities, p = 0.02 and Pa = 0.4; p = 0.03, Pa = 0.2; p=0.04, Pa = 0.1, the maximum value of AOQ is 0.00784 for p = 0.01 and Pa = 0.8.

So the AOQL = 0.00784

6.3 The analyst can calculate AOQ to estimate the performance of the plan over a range of pos- sible proportion defectives in order to judge whether the plan will provide an acceptable degree of protection. The maximum value of the average outgoing quality over all possible values of the proportion defective is called the average outgoing quality limit (AOQL). If the AOQL seems too high, the parameters of the plan must be modified until an acceptable AOQL is achieved.

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.