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- An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approximately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitoredusing means of samples of 25 observations.a. Determine upper and lower control limits that will include roughly 97 percent of the samplemeans when the process is in control.b. Given these sample means: 1.005, 1.001, .998, 1.002, .995, and .999, is the process in control?A pharmaceutical company producing vitamin capsules desires a proportion of calcium content between 40 and 55 ppm. A random sample of 20 capsules chosen from the output yields a sample mean calcium content of 44 ppm with a standard deviation of 3 ppm. Find the natural tolerance limits of the process. If the process is in control at the present values of its parameters, what proportion of the output will be nonconforming, assuming a normal distribution of the characteristic? Answer letters a, b, and c. a. Find the Cp index. Comment on the ability of the process to meet specifications. b. What proportion of the specification range is used up by the process? c. If it is easier to change the process mean than to change its variability, to what value should the process mean be set to minimize the proportion of nonconforming product?An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approximately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitoredusing means of samples of 25 observations.a. Determine upper and lower control limits that will include roughly 97 percent of the samplemeans when the process is in control.
- Control charts for X-bar and R, using a subgroup size of 5, are to be applied to control thecritical dimension of a certain manufacturing process. Specifications call for a nominal dimension of1,250.000 + 0.050 mm. The process is believed to have a σ of 0.015 mm Determine appropriate control limits for the X-bar and R charts. a) After 12 subgroups have been drawn and X-bar and R plotted on the charts, a computation of X-double bar give 1,250.015. b1) What is the probability that a value of X-bar will fall within the limits if this is the true value of the mean setting? b2) What is the probability that all 12values fall within the control limits? b) Make the necessary calculations to determine if the process can meet specifications by solvingfor Cp, Cpu, CpL, Cpk . Assume a normal distribution of product output. Illustrate how the processwould look like relative to the result of the computations of the process capability analysis.At Quick Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 390 seconds for the wash process. Suppose the average range for a sample of 10 cars is 11 seconds. Use the accompanying table to establish control limits for sample means and ranges for the car wash process. The UCL Subscript x overbar equals seconds and the LCL Subscript x overbar equals seconds. (Enter your responses rounded to two decimal places.)Develop a p chart with 3 sigma control limits and evaluate whether the process is in statical control
- At Webster Chemical Company, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Even when the process is in control, an average of four lumps per tube of caulk will remain. Testing for the presence of lumps destroys the product, so an analyst takes random samples. The following results are obtained: Tube No. Lumps Tube No. Lumps Tube No. Lumps 1 6 5 6 9 5 2 5 6 4 10 0 3 0 7 1 11 9 4 4 8 6 12 2 Determine the c-chart two-sigma upper and lower control limits for this process. Is the process in statistical control?point on a control chart falls outside one of the controllimits, this suggests that the process variation is non random and should be investigated . a FALSE b TRUE1. A hospital is monitoring the surgeries that result in surgical complications. The number of surgeries each month and those resulting in a complication were recorded. The number of surgeries each month and those resulting in a complication were recorded. The number of surgeries each month can vary. Which of the following control charts is most appropriate to monitor this process? a. c-chart b. xbar and R chart c. p-chart d. np-chart 2. A factory collected data on the number of nonconforming parts and constructed a p-chart. 15 samples of size 150 were collected. They determined that the average fraction of non-conforming parts was pbar=0.037. During production, a sample of 150 parts was taken, of which 11 were non-conforming. At the time this sample was taken: a. the lower control limit was -0.01 b. the sample was outside the control limits c. the sample was within the control limits d. the upper control limit was 0.073 3. What is the upper control limit for a…
- The central limit theorem:a) is the theoretical foundation of the c -chart.b) states that the average of assignable variations is zero.c) allows managers to use the normal distribution as thebasis for building some control charts.d) states that the average range can be used as a proxy forthe standard deviation.e) controls the steepness of an operating characteristiccurve.The Awake Coffee Company produces gourmet instantcoff ee. Th e company wants to be sure that the average fi ll of coff eecontainers is 12.0 ounces. To make sure the process is in control,a worker periodically selects at random a box of six containers ofcoff ee and measures their weight. When the process is in control,the range of the weight of coff ee samples averages 0.6 ounces.(a) Develop an R-chart and an x-chart for this process.(b) Th e measurements of weight from the last five samplestaken of the six containers follow Is the process in control? Explain your answer.1. An ad agency tracks the complaints, by week received, about the billboards in its city: Week No. of Complaints 1 8 2 4 3 11 4 16 5 8 6 9 This exercise contains only parts a, b, and c. a) The type of control chart that is best to monitor this process is c minus chartc−chart . b) Using z = 3, the control chart limits for this process are (assume that the historical complaints rate is unknown): UCLc =?complaints per week (round your response to two decimal places). LCLc =?complaints per week (round your response to two decimal places).