A control chart is used for monitoring a process meanl (X) that is normally distributed with a mean of μ and a standard...
A control chart is used for monitoring a process mean ( 7 ) that is normally distributed with a mean of u and a standard deviation of o, and the sample size is n = 5. A 3-sigma limit (u +30z) 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...
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...
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...
Control charts for x bar and s are maintained on a quality characteristic. The sample size is n=4. After 30 samples, we obtain3030∑ ¯xi=12,870and∑ sj=410i=1i=1A. Find the centerline and three sigma control limits for the s chart.B. Assuming that both charts exhibit control,estimate the aprameters μ and σ.
8.4 14 *9. Suppose that we are using an T-chart with subgroups of size n - 5 in an idealized setting in which the data is Normally distributed with known mean μ and standard deviation σ. We know that σ,-sd(X)-4. Use also the facts that and Assume that the process is under control and that subgroups are indepen- dent. Suppose that 100 subgroup means are plotted onto the chart over the course of a day. (a) What is the probability...
A gear has been designed to have a diameter of 3 inches. The standard deviation of the process is 0.3 inch. A control chart is shown. Each chart has horizontal lines drawn at the mean, μ, μ 2o, and at μ 3G. Determine if the process shown is in control or out of control. Explain Is the process in control or out of control? Select all that apply A. Out of control, because a point lies more than three standard...
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)
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...