IGNOU MST 14 2026 - A factory purchases bolts in lots of 800. Acceptance is decided

Question

A factory purchases bolts in lots of 800. Acceptance is decided using a single-sampling plan with sample size n = 20 and acceptance number c = 3. Assume that 2% defective items are considered acceptable quality and 7% defective items are considered unacceptable quality.

Find:

(i) The probability of accepting a lot when the incoming quality level is 5% defective.

(ii) The Average Outgoing Quality (AOQ), assuming rejected lots are completely screened and defectives are replaced.

(iii) The Average Total Inspection (ATI).

24 Mar 2026

Answer :

Word Count : 528

We are asked to solve a classical acceptance sampling problem with given parameters. Let's solve step by step manually. --- Given data: * Lot size: (N = 800) * Sample size: (n = 20) * Acceptance number: (c = 3) * Incoming quality levels: (p = 0.02) (acceptable), (p = 0.07) (unacceptable), but specifically we are asked for (p = 0.05) * Lot is rejected → 100% inspection and defective replaced We are to find: 1. (P_a) (probability of acceptance) at (p = 0.05) 2. Average Outgoing Quality (AOQ) 3. Average Total Inspection (ATI) --- ### Step (i): Probability of accepting the lot For a single-sampling plan, the probability of accepting a lot is: [ P_a = \sum_{i=0}^{c} \binom{n}{i} p^i (1-p)^{n-i}

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