(a) x̅bar = 816/24 = 34
UCL = x̅bar + A2Rbar = 34 + 0.577*4.7083 = 36.7167
LCL = x̅bar - A2Rbar = 34 - 0.577*4.7083 = 31.2833
(b) Rbar = 113/24 = 4.7083
UCL = D4*Rbar = 2.114*4.7083 = 9.9533
LCL = D3*Rbar = 0.0000
(c) P (z = (36 - 34)/ 0.9056) - P (z = (32 - 34)/ 0.9056) = P (z = 2.21) - P (z = -2.21) = 0.9864 - 0.0136 = 0.9728
The fraction of defectives = 1 - 0.9728 = 0.0272 = 2.72%
I will rate 1. For constructing a X-bar chart, subgroup sample average (x bar) and range(r)...
1. For constructing a X-bar chart, subgroup sample average (x bar) and range (r) are computed for each of 24 preliminary samples using a sample size n=5. We have the following data summary: 24 24 Ex;=816 and Er;= 113 i = 1 i = 1 (a) Find the following for X-bar chart: 06 pts) Upper control limit, Center line, and Lower control limit (b) Find the following for R chart: (6 pts) Upper control limit, Center line, and Lower control...
based on the given data: 1.) What is the centerline of the x-bar chart? 2.) what is the upper control limit of x bar chart? 3.) what is the upper control limit of moving R chart? 4.) Based on the X bar and R charts is the process in control? Question 1 1 pts Subgroup 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Value 7.09 7.05 7.05 7.07 7.03 7.05 7.03 7.08 7.07 7.04...
In developing a Bar X chart, the centerline of the Bar X chart is determined to be 0.4949, the centerline of the R chart is determined to be 0.0130, and the factor A2 used in the formulas to calculate the lower and upper limits of the Bar X chart is determined to be 0.7290. Based on these information, a. The lower control limit of the Bar X chart is 0.4854 b. The upper control limit of the Bar X chart...
can the X̄ (x bar) and R control chart be used for controlling processes where subgroup size is one? (ie n=1)? Identify the sytuation where the X bar and S control chart are more appropriate then the X bar and R chart
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)
Checkout time at a supermarket is monitored using a mean and a range chart. Six samples of n = 20 observations have been obtained and the sample means and ranges computed: Sample Mean Range Sample Mean Range 1 3.06 .42 4 3.13 .46 2 3.15 .49 5 3.06 .46 3 3.11 .41 6 3.09 .45 Factors for three-sigma control limits for x¯x¯ and R charts FACTORS FOR R CHARTS Number of Observations in Subgroup, n Factor for x¯x¯ Chart, A2 Lower...
04)- 244+3-15 marás) Control charts for X and R are mairnt S marks) Contr ol charts for X and R are maintained for quality characteristic. The and R are computed for each sample. After 30 samples, the following a computed: 6690 R-1030 a- What are the tria Ilimits for the R chart ? tb) Assuming that the R chart is in control, what are the trial limits for the X char? Estimate the process mean and standard devintion. (d- Ifthe...
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)
Construct an X chart-R chart for the following data set (Leave no cells blank be certain to enter "O" wherever required. Do not round intermediate calculations. Round your answers to 2 decimal places.) Sub group No 6:00 10:00 14:00 18:00 22:00 Points Central line Lower control limit (LCL) Upper control limit (UCL)
1. Design X-bar and R charts a control chart with "standards given" as an aimed-at mean of Xo = 4.0, Sigma = .0033, and Subgroup size -5. It is not necessary to sketch the control-chart since we have no points to put on it. Just specify, CL, UCL and LCL. That is the design. 2. Then find the probability of in-control nonconformance given, USL = 4.00995 and LSL 3.99005 3. Also, by theory, what is the Probability of an out-of-control...