Problem 1. (50 p.) ABC Ltd. has recently been receiving complaints from retailers that their batteries are not lasting as long as other name brands. A quality manager decided, therefore, to take 26 samples (in randomly selected time intervals) of the batteries (each sample consisting of ve batteries) to establish the standards for relevant control chart limits. The results are shown in the table below (the numbers represent how many hours a battery lasted): Sample no. Battery 1 Battery 2 Battery 3 Battery 4 Battery 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 With these limits established, the manager now takes 6 more samples, which are shown in the following table: 2? 28 29 30 3] Q1. (30 p.) Determine the upper and lower control limits for all relevant charts. Show all your calculations. Q2. (20 p.) Is the manufacturing process in control in Time Periods 27-32? Problem 2. (50 p.) One of the Airline XYZ Ltd.'s top competitive priorities is on-time arrivals. Quality VP decided to personally monitor the company's performance in this area. Each week for the past 30 weeks, she checked a random sample of 100 flight arrivals for on-time performance. The table below contains the number of flights that did not meet the Airline XYZ's definition "on time". Sample (week) Late Flights Sample (week) Late Flights 3 16 7 2 0 17 3 3 4 18 11 4 5 19 4 12 20 9 6 6 21 0 7 22 8 3 23 13 9 0 24 6 10 15 25 11 2 26 6 12 27 0 13 8 28 3 14 Uil 29 2 15 0 30 Q1. (20 p.) Determine the upper and lower control limits for a relevant control chart. Q2. (10 p.) Is the process in control? Justify your answer. Q3. (20 p.) Assume that the airline industry's upper and lower control limits for flights that are not on time are 0.1000 and 0.0000, respectively. Assume also that the industry's standard deviation of the percentage of late flights is 0.01. What can the VP report about the quality of her company performance in regards to on-time arrivals