Studies on a machine that molds plastic water pipe indicate that when it is injecting 25.76 mm diameter pipe, the process standard deviation is 0.75 mm. The pipe has a specification of 25.76 mm plus or minus 1.95 mm. What is the process capability index (Cp)? Оа. 0.4333 O b. 2.6 Ос. 1.733
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- Linda Boardman, I nc., an equipment manufacturerin Boston, has submitted a sample cutoff valve to improve yourmanufacturing process. Your process engineering department basconducted experiments and found that the valve has a mean (J.L)of 8.00 and a standard deviation (cr) of .04. Your desired performanceis f..L = 8.0 ±3cr, where cr = .045. What is the Cpk of theBoardman valve?Quality control in a factory pulls 40 parts with paint, packaging, or electronic defects from anassembly line. Of these, 28 had a paint defect, 17 had a packaging defect, 13 had an electronicdefect, 6 had both paint and packaging defects, 7 had both packaging and electronics defects, and 10had both paint and electronic defects. Did any part have all three types of defect? If so, how many?Type I error (alpha risk). After several investigations of points outside control limits revealed nothing, a manager began to wonder about the probability of a Type I error for the control limits used(z = 1.90).a. Determine the alpha risk (i.e., P [Type I error]) for this value of z.b. What z would provide an alpha risk of about 2 percent?
- John Bruno owns a factory producing electric cords. John observes that recently the number of cords with defect has increased. He monitors the 3 processing machines for 30 days for 100 cords per observation per machine. The results of John Bruno’s observations are presented in the table below.What can he do to make sure that the number of cords with defect to go down? Date Number of Rejects by Cause Number of observations Machine Bad Wind Twisted cord Broken Leads Abraded cord Broken cord Wrong wire Failed Electrical Test 1 100 1 0 1 3 1 0 0 1 100 2 2 1 0 0 2 5 0 100 3 0 0 0 5 0 0 3 2 100 1 1 0 4 0 0 0 0 100 2 3 1 0 0 1 3 0 100 3 0 0 1 6 0 0 0 3 100 1 1 0 0 2 0 0 0 100 2 0 0 0 0 0 3 0 100 3 0 0 1 4 0 0 3 4 100 1 0 0 3 0 0 0 0 100 2 0…Ettlie Engineering has a new catalyst injection system for your countertop production line. Your process engineering departmenthas conducted experiments and determined that the mean is 8.01 grams with a standard deviation of .03. Your specificationsare: m = 8.0 and s = .04, which means an upper specification limit of 8.12 [ = 8.0 + 3(.04)] and a lower specification limit of7.88 [= 8.0 - 3(.04)].What is the Cpk performance of the injection system?West Battery Corp. has recently been receiving complaints from retailers that its 9-volt batteries are not lasting as long as other name brands. James West, head of the TQM program at West's Austin plant, believes there is no problem because his batteries have had an average life of 60hours, about 10% longer than competitors' models. To raise the lifetime above this level would require a new level of technology not available to West. Nevertheless, he is concerned enough to set up hourly assembly line checks. Previously, after ensuring that the process was running properly, West took samples of 5 9-volt batteries for 25 test to establish the standards for control chart limits. Those 25 tests are shown in the following table: Sample Data Sample Data Hour Sample Taken 1 2 3 4…
- Burger Doodle is a fast-food restaurant that processes anaverage of 680 food orders each day. The average cost of each order is $6.15. Four percent of the orders are incor-rect, and only 10% of the defective orders can be corrected with additional food items at an average cost of $1.75. Theremaining defective orders have to be thrown out.a. Compute the average product cost.b. In order to reduce the number of wrong orders,Burger Doodle is going to invest in a computerizedordering and cash register system. The cost of thesystem will increase the average order cost by $0.05and will reduce defective orders to 1%. What is theannual net cost effect of this quality-improvementinitiative?c. What other indirect effects on quality might be realizedby the new computerized order system?The output from a process contains a 0.02 defective unit. Defective units that go undetected into final assemblies cost $25 each to replace. An inspection process, which would detect and remove all defectives, can be established to test these units. However, the inspector, who can test 20 units per hour, is paid $8 per hour, including fringe benefits. Should an inspection station be established to test all units?a. What is the cost to inspect each unit?b. What is the benefit (or loss) from the inspection process?Frank Pianki, the manager of an organic yogurtprocessing plant, desires a quality specification with a mean ofI 6 o unces, an upper specification limi t of I 6.5, and a lowerspecification limit of 15.5. The process has a mean of I 6 ouncesand a standard deviation of I ounce. Determine the Cpk of theprocess.
- 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 0.5Control 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.Studies on a machine that molds plastic water pipe indicate that when it is injecting1-inch diameter pipe, the process standard deviation is 0.05 inches. The one-inchpipe has a specification of 1-inch plus or minus 0.10 inch. What is the processcapability index (Cp) if the long-run process mean is 1 inch?