A control chart is used for monitoring a process mean ( 7 ) that is normally...
A control chart is used for monitoring a process meanl (X) that is normally distributed with a mean of μ and a standard deviation of σχ , and the sample size is n-5. А 3-sigma limit (μ ±30% ) is used as control limits. Two decision rules are given here. Rule 1: If one or more of the next seven samples yield values of the sample average that fall outside the control limits, conclude that the process is out of...
Two decision rules are given here. Assume they apply to a normally distributed quality characteristic, the control chart has three-sigma control limits, and the sample size is n=5. Rule 1: If one or more of the next seven samples yield values of the sample average that fall outside the control limits, conclude that the process is out of control. Rule 2: If all of the next seven sample averages fall on the same side of the center line, conclude that...
A manufacturing process is in-control and centered. A critical quality characteristic is normally distributed with a mean of 20 and a standard deviation of 2. The DPMO of the process is 318. (1) What is the upper specification limit for the characteristic? (2) The daily production rate is 1000 parts. How many parts per day would you expect to have a dimension less than 21 but greater the 19.5? (3) A 3-sigma Xbar chart based on a sample of size...
A 3-sigma control chart is established and the following two rules are used together to detect process outof-control situations. Rule 1: A point is plotted outside of the control limits. Rule 2: A run of eight consecutive points on one side of the center line but still inside the control limits. Compute the following: (a) Type I error of Rule 1 (b) Type I error of Rule 2 (c) Type 1 error of using both rules together
I will rate 2. A process has a X-bar control chart with UCL-17.4. LCL-12.79 using a 3-sigma limit. The subgroup sample size is 3. (a) Estimate the standard deviation of the process, sigma hat. (6 pts) (b) Suppose that the process mean shifts to 13. Find the probability that this shift will be detected on the next sample. (8 pts) (c) Calculate the average run length (ARL) before detecting the shift. (6 pts)
2. A process has a X-bar control chart with UCL=17.4, LCL=12.79 using a 3- sigma limit. The subgroup sample size is 3. (a) Estimate the standard deviation of the process, sigma hat. (6 pts) (b) Suppose that the process mean shifts to 13. Find the probability that this shift will be detected on the next sample. (8 pts) (c) Calculate the average run length (ARL) before detecting the shift. (6 pts)
Product filling weights are normally distributed with a mean of 365 grams and a standard deviation of 19 grams. a. Compute the chart upper control limit and lower control limit for this process if samples of size 10, 20 and 30 are used (to 2 decimals). Use Table 19.3. For samples of size 10 UCL =| LCL For a sample size of 20 UCL = LCL For a sample size of 30 UCL = LCL = b. What happens to...
Use the applet "Mean Control Chart: Out of Control" to answer the following questions. (a) Set the slider below the graph to 16.05 and push 'Restart'. Observe the simulation of the process. Push 'Restart' several more times. What do you notice about the behavior of the process before and after Period 7? The sample means are outside the control limits at first but fall within the limits after Period 7. The sample means are within the control limits at first,...
Samples of n5 units are taken from a process every hour. The and R values for a particular quality char acteristic are determined. After 25 samples have been collected, we calculate 20 and R 4.56 (a) What are the three-sigma control limits for x and R? (b) Both charts exhibit control. Estimate the process standard deviation (c) Assume that the process output is normally dis- tributed. If the specifications are 19 t 5, what are your conclusions regarding the process...
Temperature is used to measure the output of a production process. When the process is in control, the mean of the process is μ = 126.5 and the standard deviation is σ = 0.4. (a)Compute the upper and lower control limits if samples of size 6 are to be used. (Round your answers to two decimal places.) UCL= LCL= Construct the x bar chart for this process. (b) Consider a sample providing the following data. 126.8 126.2 127.1 126.7 126.4...