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##### stats problems with solution fall 2014

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Question;Question 1A production process sampled 24 times with a sample size of 6 yields an overall mean of 25.2 and anaverage range of 0.8. Determine the control limits for the xbar and R charts.Question 2A Quality Analyst wants to construct a control chart for determining whether ten machines, all producing the same product are in control with regard to a particular quality attribute. Accordingly, she inspected 500 units of output from each machine in random samples, with the following results:a. Construct the appropriate control chart(s) for the data.b. If she sets upper and lower control limits of 0.026 and 0.014, which machines, if any, appear tobe out of control?c. Test for control using WECO rules.Question 3A restaurant manager wants to improve the service and customer satisfactions, and so conducts afour-week study tracking the number of complaints per day. The results are in the Excel spreadsheet. Construct the appropriate control chart(s) for the data. Do any points appear to be out of control?Question 4A company manufactures hardware supplies, including nuts and bolts. The Customer Relations Department reports that in the past two months, the number of returns and complaints has seemed to increase. Customers cite that many of the companys bolts are not fitting into the appropriate nuts.The Board wants to assess the consistency of their bolt making process. The Production Manager measured three samples of bolts produced during each shift every day over the course of two weeks and collected the data found in the accompanying Excel file.a. Construct the appropriate control chart(s) to assess the bolt making process.b. Test for control using WECO rules.c. Provide an interpretive assessment of the current state of the process. If corrective action is warranted, provide some suggestions for investigation.d. Industry specifications for this size bolt call for a target of 0.375 0.03125 in. Compute the value of Cp, Cpk, and Cpl.e. Sketch the process relative to the specifications.f. Provide an interpretive assessment of the process relative to the specifications. Providesuggestions if corrective action is needed.Question 5Piston rings for an automotive engine are produced by a forging process. We monitor the inside diameter of the rings manufactured by this process using an x and an s control chart. Samples of size four are taken at regular intervals, and the sample means and standard deviations are computed and plotted on the charts in time order. The overall mean of the sample means is x = 73.97 mm, and the sample standard deviation of all measurements is s = 0.03 mm. Specifications call for the inside diameter of the rings to be 74.00 0.10 mm.a. Compute the value of Cp, Cpk, and Cpl.b. Sketch the process relative to the specifications.c. Provide an interpretive assessment of the process relative to the specifications, including implications for the process, customers, or the business. Provide suggestions if any corrective action is needed.Question 6Parts manufactured by an injection molding process are subjected to a compressive strength test. We monitor the compressive strength of the parts manufactured by this process using a mean control chart and a range control chart. Samples of size nine are taken at regular intervals, and their mean compressive strength (in psi = pounds per square inch) and standard deviation are plotted on the charts in time order. The overall mean of the sample means is x = 81.2 psi, and the sample standard deviation of all measurements is s = 3.0 psi. Specifications call for the compressive strength of parts to be 80 2.5 psi.a. Compute the value of Cp, Cpk, and Cpl.b. Sketch the process relative to the specifications.c. Provide an interpretive assessment of the process relative to the specifications, includingimplications for the process, customers, or the business. Provide suggestions if any corrective action is needed.

Paper#61294 | Written in 18-Jul-2015

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