IE 1072 HW 2

1. Detail the three plans and explain the steps taken to formulate each one: You are a member of the Quality Assurance team at a leading American automobile manufacturing company. Your responsibilities include creating sampling strategies for key features that might result in major malfunctions in a new engine model. The engine components will be sourced from suppliers in lots of 10,000 parts. a. The first team member proposes a single sampling plan as follows: The batch's quality level deemed acceptable is 1% with a 90% probability of acceptance. The batch quality level that is almost certain to be rejected if presented is 8% with a 10% probability of acceptance. The plan-Ensure quality levels for consumer/producer: 1. Draw a line connecting α on the right with the corresponding AQL on the left on a binomial nomograph a. AQL = 0.01, α = 0.1 2. Draw a similar line connecting β on the right with the corresponding LTPD on the left on the binomial nomograph a. LTPD = 0.08, β = 0.1 3. At the intersection between the two lines, the required sample size (n) and the maximum number of defectives permitted (c) can be found within the sample for acceptance. a. The second team member recommends a different single plan: To achieve an Average Outgoing Quality Limit (AOQL) of 3%, given that the supplier's process average is 0.5%. The plan-Ensure average outgoing quality level: 1. Use the Dodge-Romig inspection table for single sampling plans for AOQL = 3% 2. Look at the row for a lot size between 7,001 and 10,000 3. Look at the column for a process average between 0.07% and 0.6% because the supplier’s process average is 0.5% 4. n = 46, c = 2, LTPD = 11.6% a. The third team member offers a single plan: To guarantee that the quality is no worse than a Rejectable Quality Level (RQL) of 1%, considering the supplier's process average is 0.5%. The plan-Ensure average outgoing quality level: 1. Use the Dodge-Romig inspection table for single sampling plans for LTPD = 1% 2. Look at the row for a lot size between 7,001 and 10,000 3. Look at the column for a process average between 0.41% and 0.5% because the supplier’s process average is 0.5% 4. n = 1500, c = 10, LTPD = 0.47% 2. You are a Quality Control Manager for a top-tier global electronics firm, and you're in charge of devising sampling methods for crucial features that might lead to severe failures in a new smart device. The device components will come from three different suppliers, each providing varying batch sizes. For each specified batch size, formulate a single sampling method using MIL-STD- 105E (Level II). The plan should outline the sample code letter, the sample size, and both the acceptance (Ac) and rejection (Re) figures

a. Supplier A: N = 3,000, AQL = 0.65 Sample code letter: K Sample size: 125 Ac/Re: 2/3 b. Supplier B: N = 1,100, AQL = 1.0 Sample code letter: J Sample size: 80 Ac/Re: 2/3 c. Supplier C: N = 3,500, AQL = 1.5 Sample code letter: L Sample size: 200 Ac/Re: 7/8 As you progress in your review of supplier deliverables, you discern that adjustments to the sampling methods are in order. Considering the performance data of the suppliers, how would you adjust the sampling approach? d. Supplier A: worsened quality performance e. Supplier B: 12 consecutive lots accepted f. Supplier C: 40% of lots rejected 3. You are a Quality Assurance Manager at ElectraTech, a leading electronics manufacturer. Your company has recently entered into a contract with a new supplier who provides integrated circuits for your latest smart device. The supplier sends shipments in lots of 10,000 circuits. Based on preliminary assessments, you decide to randomly sample 100 circuits from each lot to check for defects. The shipment is approved if there are 2 or fewer defective circuits in the sample. However, from your past experience and initial tests, you estimate that about 1% of the circuits in any given lot might be defective. Given this scenario: a. Determine the Average Outgoing Quality (AOQ) for the lots after your inspection. P a = P { d ≤ 2 } = ∑ d = 0 2 100 ! d ! ( 100 − d ) ! ( 0.01 ) d ( 0.99 ) 100 − d ¿ 100 ! 0 ! 100 ! ( 0.01 ) 0 ( 0.99 ) 100 + 100 ! 1 ! 99 ! ( 0.01 ) 1 ( 0.99 ) 99 + 100 ! 2 ! 100 ! ( 0.01 ) 2 ( 0.99 ) 98 = 0.92 AOQ = P a p ( N − n ) N = P a p = 0.92 ∗ 0.01 ( 10000 − 100 ) 10000 = 0.0091 b. Calculate the Average Total Inspection (ATI) you expect to perform on each lot ATI = n + ( 1 − P a ) ( N − n ) = 100 + ( 1 − 0.92 ) ( 10000 − 100 ) = 892 4. You are the Quality Assurance Manager at ToyCrafters, a company renowned for its high-quality toy cars. To ensure the safety and reliability of the toy cars, the wheels sourced from a supplier must pass rigorous testing. A wheel is considered defective if it comes off the car during standard play scenarios. To maintain the brand's reputation, the quality assurance process involves a two- stage sampling of the wheels. In the initial stage, a sample of 20 wheels is tested. If any wheel in