show you work pleaae

Problem 1. [10 points] What is the reliability of the system shown? Problem 2. [30 points] Let's assume we have a batch of 20 light bulbs, and each bulb is designed to work for 50 hours. We observe their lifetimes and note the following: - By the end of 10 hours, 5 light bulbs have failed. - By the end of 15 hours, an additional 3 bulbs have failed. Based on this information, answer the following: (a) What is the percentage of failures? (b) What is the number of failures per unit hour? (c) What is the MTBF (Mean Time Between Failures)? Problem 3. [10 points] Suppose that a metal rod is supposed to be cut 74.0mm. in length. The upper spec limit is set at 78.5mm, and the lower spec limit set at 69.5mm. A metal rod that is out of spec must be scrapped at a cost of $42.00. The company uses the Taguchi quality loss function to estimate quality costs. Suppose that a sample of 2 units was taken, and the rod measurements were 68.70 and 71 , respectively. What is the total Taguchi quality cost of that sample of 2 units? Please round all costs to the nearest penny. Problem 1. [10 points] What is the reliability of the system shown? Problem 2. [30 points] Let's assume we have a batch of 20 light bulbs, and each bulb is designed to work for 50 hours. We observe their lifetimes and note the following: - By the end of 10 hours, 5 light bulbs have failed. - By the end of 15 hours, an additional 3 bulbs have failed. Based on this information, answer the following: (a) What is the percentage of failures? (b) What is the number of failures per unit hour? (c) What is the MTBF (Mean Time Between Failures)? Problem 3. [10 points] Suppose that a metal rod is supposed to be cut 74.0mm. in length. The upper spec limit is set at 78.5mm, and the lower spec limit set at 69.5mm. A metal rod that is out of spec must be scrapped at a cost of $42.00. The company uses the Taguchi quality loss function to estimate quality costs. Suppose that a sample of 2 units was taken, and the rod measurements were 68.70 and 71 , respectively. What is the total Taguchi quality cost of that sample of 2 units? Please round all costs to the nearest penny