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- At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.The following data was recorded while observing the increase in the number of butterflies in two different ponds, Pond A and Pond B. Number of Butterflies Present Over 5 Years Year Pond A Pond B 0 50 65 85 1 2 3 4 5 100 O 110 121 133 146 161 110 143 186 What is the rate of growth, r, for each pond and which pond has the fastest average rate of growth over the five years? TA = 1.1, TB = 1.3, mg = 3.72 butterflies/yr TA=0.9, TB=0.8, mg = 3.72 butterflies/yr TA=0.9, TB=0.8, mg=27.2 butterflies/yr TA = 1.1, TB = 1.3, mg=27.2 butterflies/yr2. A beverage company would like to use a mean chart to monitor how much liquid beverage it puts into each 500-ml bottle. They know from experience that whenever this process is under control, bottle weight is normally distributed with a mean of 500 ml and a standard deviation of 2 ml. The company plans to measure samples of 30 bottles from the production lineevery hour and record the mean weight of liquid beverage in the bottles. If the company uses z = 3 as its standard for establishing the mean chart, where will the upper and lower control limits be on the chart? (Noteshaper: Scenario #28)
- 1. Statistical process control, hypothesis testing, and control charts Consumers value prompt service when they order takeout or delivered pizza, and pizza restaurants compete for customers by making time promises. Papa John's, for instance, offers a 10-minute takeout guarantee. Domino's advertises a 30-minute delivery time. Suppose that the quality control manager at a nationwide pizza chain defines this production variable: An order is processed on time or late. Every night, a random sample of pizza orders is selected, and data are collected on the production variable for each order in the sample. To detect a change in the number of orders that are late, the quality control manager uses Based on the control chart, the quality control manager decides that the variation in output is due to assignable causes. Consequently, the manager concludes that the production process is ; it is Statistical procedures for process control use a hypothesis-testing framework. The null and alternative…The following is the temperature control system of a heat exchanger. a)Identify the type of system. b) Calculate the steady state error when it is subjected to an input. r(t) = 2 c) Calculate the steady state error when subjected to an input. r(t) = 3t R(s) 15 C(s) 5³ - 5²² + 5sGiven this frequency distribution, what demand values would be associated with the following random numbers? (Do not round intermediate calculations.) Demand Frequency 23 1 16 2 18 43 Random Number Simulated Demand 0.1 0.6 0.4
- The manager of the main laboratory facility at MetroHealth Center is interested in being able to predict the overhead costs each month for the lab. The manager that varies with the of lab performed but that some costs same each month of the lab tests performed. The lab manager collected the following data for the first seven months of the year. (Click the icon to view the data.) Read the requirements. Requirement 1. Prepare a scatter plot of the lab's volume (number of lab tests performed) and total laboratory overhead costs. Plot the points on the graph. (Enlarge the graph and use the point tool button displayed below to draw the graph.) Relationship of Total Laboratory Overhead Costs to Number of Lab Q Tests Performed Total Laboratory Overhead Co $36.000 $34.000- $32.000 $30,000 $28.000 $26.000 $24.000 $24,000 $22.000- $20,000- $18,000 $16.000 $14,000 $12,000 1,0001.7502 5003,2504,0004,750 Number of Lab Tests Performed Click to enlarge graph Data table Month January..... February....…The number of yearly breakdowns for the power generator observed over the past 20 years at Orlando Utilities is presented in the following data: Number of breakdowns Number of years in which breakdowns occurred For Orlando Utilities, the expected number of breakdowns (round your response to two decimal places). 0 2 = 1 3 2 5 3 5 4 3 5 1 6 1 DUSE: A=20X210 B=10X210 C=12X210
- A scatter diagram is useful to determine if a relationship exists between two variables.TrueORFalseBill Kime's bowling ball factory makes bowling balls of adult size and weight only. The standard deviation in the weight of a bowling ball produced at the factory is known to be 0.39 pounds. Each day for 24 days, the average weight, in pounds, of 9 of the bowling balls produced that day has been assessed as follows Day 1 2 3 4 5 6 Average (lb) 9.9 9.9 10.1 10.1 99 99 Day 7 8 9 10 11 12 Average (lb) Day Average (b) 13 14 15 16 17 18 10.1 10.0 10.0 10.1 10.1 10.0 9.9 10.1 10.1 10.0 10.1 10.1 Day 19 20 21 22 23 24 Average (lb) 99 10.0 10.1 9.9 10.0 10.0 a) Establish a control chart for monitoring the average weights of the bowling balls in which the upper and lower control limits are each two standard deviations from the mean What are the values of the control limits? Upper Control Limit (UCL)=b (Round your response to two decimal places)The time to deliver packaged containers by a logistics company is found fromsamples of size 4. The mean and standard deviation of delivery times is estimated tobe 140 hours and 6 hours, respectively.(a) Find the 2 sigma and 3 sigma control limits for the average delivery time.(b) Explain a type I and type II error specifically in this context.(c) If the mean delivery time shifts to 145 hours, what is the probability of notdetecting this by the second sample after the shift?(d) What is the ARL? Explain