Concept explainers
i)
Interpretation: by using
Concept introduction: Mean(x-bar) charts:
X bar charts is a type of statistical process control chart which measures a central a shift in the central tendency of the process. In other words, X- bar charts monitor the mean or average of a product characteristics. The central line of the X-bar chart is the average of the samples and limits are defined as
Upper control limit
Lower control limit
(
Abbreviations:
R chart:
R-chart or range-chart is also a type of statistical process control chart, but it monitors the range of dispersion or variability of process. The central line of the r- chart is the average range and limits are:
(
The data corresponding to sampling of the given firm is given below
Mean of the diameter
Average range
Control limits are
ii)
Interpretation: by set up
Concept introduction:In probability sampling method,the systematic sampling is a form of it. In which from a larger population sample member are chosen with a fixed, periodic interval but this starts with random sampling.
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- A company making tires for bikes is concerned about the exact width of its cyclocrosstires. The company has a lower specification limit of 22.8 mm and an upper specification limit of 23.2 mm. The standard deviation is 0.15 mm and the mean is 23 mm.What is the process capability index for the process?arrow_forwardA Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results : Machine #1 measurements [14, 13, 24, 22]; Machine #2 measurements [ 14, 19, 23, 14]; Machine #3 measurements [ 14, 16, 13, 16]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits? a. 24.65and 9.013 b. 22.43and 11.24 c. 18.9and 14.76 d. 39.83and -6.167arrow_forwardAn 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 standard deviation of .01 liter. Output is monitored using means of samples of 25 observations. Determine upper and lower control limits that will include roughly 97% of the sample means when the process is in control. Using Appendix B, Table A to find the value of Z corresponding to the mean control limits.arrow_forward
- An operator wants to determine the standard deviation for a machine she operates. To do this, she wants to create a p-chart. Over a month's time, she collects 30 samples of 75 observations each and records the number of errors. The average proportion defective is found to be 0.024. Which of the following is the standard deviation () of the machine? a. More than 0.5 but less than or equal to 1.0 b. More than 1.0 c. Less than or equal to 0.1 d. More than 0.1 but less than or equal to 0.5arrow_forwardA metal fabricator produces connecting rods with an outer diameter that has a 1 ± .01–inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.002 inches with a standard deviation of .003 inch.a. Calculate the process capability index for this example.b. What does this figure tell you about the process?arrow_forwardA process considered to be in control measures an ingredient in ounces. A quality inspector took 10 samples, each with 5 observations as follows: Using this information, obtain three-sigma (i.e., z=3) control limits for a mean control chart and control limits for a range chart, respectively. It is known from previous experience that the standard deviation of the process is 1.36. Discuss whether the process is in control or not.arrow_forward
- You are an analyst for a company that produces parts for medical devices, and these parts must meet specifications required by your customer. You implement a process improvement to decrease the variation in diameter for one of the parts, and want to determine if the process improvement had any effect. What type of control chart would be most appropriate to determine if the process improvement did in fact reduce variation in the output of the process? Group of answer choices a X-bar b R c P d C e Cpkarrow_forwardThe overall average on a process you are attempting to monitor is 60.0 units. The process population standard deviation is 1.72. Sample size is given to be 4. Part 2 a) Determine the 3-sigma x-chart control limits. Upper Control Limit (UCLx)=enter your response here units (round your response to two decimal places). Part 3 Lower Control Limit (LCLx)=enter your response here units (round your response to two decimal places). Part 4 b) Now determine the 2-sigma x-chart control limits. Upper Control Limit (UCLx)=enter your response here units (round your response to two decimal places). Part 5 Lower Control Limit (LCLx)=enter your response here units (round your response to two decimal places). Part 6 How do the control limits change? A. The control limits are tighter for the 3-sigma x-chart than for the 2-sigma x-chart. B. The control limits for the 2-sigma x-chart and for the 3-sigma x-chart are the same. C. The control limits…arrow_forwardA process considered to be in control measures an ingredient in ounces. A quality inspector took 10 samples, each with 5 observations as follows: SEE ATTACHED PHOTO Using this information, obtain three-sigma (i.e., z=3) control limits for a mean control chart and control limits for a range chart, respectively. It is known from previous experience that the standard deviation ofthe process is 1.36.arrow_forward
- The specification limits for a product are 9.9 cm and 12.35 cm. A process that produces the product has a mean of 11.18 cm and a standard deviation of 0.52 cm. What is the process capability, Cpk? a. 0.8205 b. 1.571 c. 0.7853 d. 0.75arrow_forwardAn 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?arrow_forwardAn insurance company samples claim forms for errors created by its employees as well as the amount of time it takes to process a claim. a. When the process is in control, the proportion of claims with an error is .033. A p chart has LCL = 0 and UCL = .068. Plot the following seven sample results: .035, .062, .055, .049, .058, .066, and .055. Comment on whether there might be concern about the quality of the process.arrow_forward
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