Assignment 5 Questions-2

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Industrial Engineering

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Apr 3, 2024

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Assignment 5 Due: Tuesday, March 19, 2024, at 11:59 pm Please submit your answer as one Jupyter and one PDF file on Quercus Please post your questions on Piazza 1. Explain some causes that would make the control chart pattern follow a gradually increasing trend. What are some reasons for a process to go out of control due to a sudden shift in the level? 2. The time to be seated at a popular restaurant is of importance. Samples of five randomly selected customers are chosen and their average and range (in minutes) are calculated. After 30 such samples, the summary data values are: ∑ 𝑋 𝑖 30 𝑖=1 = 306 ∑ 𝑅 𝑖 30 𝑖=1 = 24 2.1 Find the 𝑋 and R-chart control limit. 2.2 Find the 1σ and 2σ 𝑋 -chart limits 2.3 The manager has found that customers usually leave if they are informed of an estimated waiting time of over 10.5 minutes. What fraction of customers will this restaurant lose? Assume a normal distribution of waiting times. 3. Light bulbs are tested for their luminance, with the intensity of brightness desired to be within a certain range. Random samples of five bulbs are chosen from the output, and the luminance is measured. The sample mean X and the standard deviation s are found. After 30 samples, the following summary information is obtained: ∑ 𝑋 𝑖 30 𝑖=1 = 2550 ∑ 𝑠 𝑖 30 𝑖=1 = 195 The specifications are 90 ± 15 lumens. 3.1 Find the control limits for the 𝑋 - and s-charts. 3.2 Assuming that the process is in control, estimate the process mean and process standard deviation 3.3 Comment on the ability of the process to meet specifications. What proportion of the output is nonconforming? 3.4 If the process mean is moved to 90 lumens, what proportion of output will be nonconforming? What suggestions would you make to improve the performance of the process? 4. Which type of control chart (p, np, c chart) is most appropriate to monitor the following situations? 4.1 Percentage of Defective Parts in Manufacturing 4.2 Number of Customer Complaints per Week 4.3 Percentage of On-Time Deliveries for a Logistics Company 4.4 Number of Defective Items in a Sample Inspection
5. A manufacturing company produces bolts, and the quality control team wants to monitor the defect rate of the bolt production process. The company decides to implement a p-chart to track the number of defective bolts in samples of 200 bolts each day over a period of 20 days. The acceptable defect rate is 3%. The number of defective bolts found in each daily sample over 20 days is as follows: defective_bolts = [5, 7, 3, 4, 6, 8, 9, 4, 5, 6, 3, 6, 7, 5, 4, 8, 6, 3, 5, 7]
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