**Quality Control Management in Home Appliances Manufacturing - Acceptance Sampling Plan****Introduction**KALI, Inc. manufactures home appliances marketed under a variety of trade names. While KALI does not manufacture every component used in its products, it procures several components directly from suppliers. One critical component for in-home air conditioners is the overload protector, which prevents the compressor from overheating by turning it off. Ensuring the quality of these overload protectors is essential as a malfunction can cause significant damage to the compressor. Although ideally, each component would be tested exhaustively, this process is impractical due to time and cost constraints.**Acceptance Sampling Plan**KALI's quality control inspectors use an acceptance sampling plan to monitor the quality of overload protectors. This plan involves selecting and testing a sample from each shipment. If the sample contains very few defective units, the lot is deemed acceptable and of high quality. Conversely, a large number of defective units in the sample would indicate poor quality, leading to the lot being rejected.**Scenario Overview**A quality control manager has set the following risk criteria:- A producer's risk (\( \alpha \)) of 0.10 when \( p_0 \) (the acceptable defect rate) is 0.05.- A consumer's risk (\( \beta \)) of 0.20 when \( p_1 \) (the unacceptable defect rate) is 0.30.An acceptance sampling plan is considered with a sample size of \( n = 20 \) and an acceptance number \( c = 1 \), meaning the lot is accepted if there is at most 1 defective unit in the sample.**Questions to Consider**(a) **Producer’s Risk Calculation:** What is the producer’s risk for the \( n = 20 \), \( c = 1 \) sampling plan? (Round your answer to four decimal places.) **Answer:** \[ \alpha = 0.1184 \](b) **Consumer’s Risk Calculation:** What is the consumer’s risk for the \( n = 20 \), \( c = 1 \) sampling plan? (Round your answer to four decimal places.) **Answer:** \[ \beta = 0.3095 \](c) **Evaluation of Sampling Plan:** Does the \( n = 20 \), \( c = 1 \) sampling plan satisfy the risks

Given data: Producer's risk of 0.10 when Po= 0.05 Consumer's risk of 0.20 when P1 =0.30 Sample size…

Inc. of trade names. However, does not manu every component used in its products. Several ures home appliances that are marketed und components are purchased directly from suppliers. For example, one of the components that KALI purchases for use in home air conditioners is an overload protector, a device that turns off the compressor if it overheats. The compressor can be seriously damaged if the overload protector does not function properly, and therefore KALI is concerned about the quality of the overload protectors. One way to ensure quality would be to test every component received through an approach known as 100% inspection. However, to determine proper functioning of an overload protector, the device must be subjected to time-consuming and expensive tests, and KALI cannot justify testing every overload protector it receives. Instead, KALI uses an acceptance sampling plan to monitor the quality of the overload protectors. The acceptance sampling plan requires that KALI's quality control inspectors select and test a sample of overload protectors from each shipment. If very few defective units are found in the sample, the lot is probably of good quality and should be accepted. However, if a large number of defective units are found in the sample, the lot is probably of poor quality and should be rejected. The quality control manager requested a producer's risk of 0.10 when p was 0.05 and a consumer's risk of 0.20 when p, was 0.30. Consider the acceptance sampling plan based on a sample size of 20 and an acceptance number of 1. Answer the following questions. (a) What is the producer's risk for the n = 20, c = 1 sampling plan? (Round your answer to four decimal places.) 0.1184 x (b) What is the consumer's risk for the n = 20, c = 1 sampling plan? (Round your answer to four decimal places.) (c) Does the n = 20, c = 1 sampling plan satisfy the risks requested by the quality control manager? Discuss. (Select all that apply.) The producer's risk is acceptable since it is less than 0.10. The producer's risk is not acceptable since it is greater than 0.10. The consumer's risk is acceptable since it is less than 0.20. The consumer's risk is not acceptable since it is greater than 0.20.