Concept explainers
(a)
To determine: The upper and lower control limits that include roughly 97% of the sample means when an automatic machine filled a one-liter bottle of cola with a mean of 1 liter, a standard deviation of 0.1 liters, and samples of 25 observations are used to monitor the output.
Introduction: To monitor the process dispersion, range control charts are used and the mean control limit charts are based on a
(b)
To determine: Whether the process is in control at the sample means: 1.005, 1.001, .998, 1.002, .995, .999 when an automatic machine filled a one-liter bottle of cola with a mean of 1 liter, a standard deviation of 0.1 liters and samples of 25 observations are used to monitor the output.
Introduction: To monitor the process dispersion, range control charts are used and the mean control limit charts are based on a normal distribution.
(c)
To determine: Whether the process is in control at sample means of 1.003, .999, .997, 1.002, .998, and 1.004. when an automatic machine filled a one-liter bottle of cola with a mean of 1 liter, a standard deviation of 0.1 liters and samples of 25 observations are used to monitor the output.
Introduction: To monitor the process dispersion, range control charts are used and the mean control limit charts are based on a normal distribution.
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- A large beverage company would like to use a statistical process control to monitor how much liquid beverage it puts into each bottle. The company operated its bottle filling line under careful supervision, confident that the line was under complete control, for seven hours. Each hour, a sample of 20 bottles was taken off the line and the amount of liquid in each bottle was carefully measured. This is the resulting data: Sample Sample Sample Mean (ml) Range (ml) No. #1 350.4 0.5 349.6 0.5 #3 349.6 0.7 # 4 349.5 0.4 #5 349.8 0.5 #6 350.4 0.9 #7 349.8 0.3 Which of the following is closest to the upper control limit on the beverage company's range chart? O A. 0.86 ml O B. 351.15 ml O C. 350.68 ml O D. 1.92 ml O E. 0.5 ml 2. %23 %23arrow_forwardAt Gleditsia Triacanthos Company, a certain manufactured part is deemed acceptable if its length is between 12.45 to 12.55 inches. The process is normally distributed with an average of 12.49 inches and a standard deviation of 0.014 inches. a) is the process capable of meeting specifications? b) Does the process meet specifications?arrow_forwardAuto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 5 pistons produced each day, the mean and the range of this diameter have been as follows: Day Mean (mm) Range R (mm) 158 4.3 151.2 4.4 155.7 4.2 153.5 4.8 156.6 4.5 What is the UCL using 3-sigma?(round your response to two decimal places). 1. 2. 4.arrow_forward
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