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Q1:Problem 1. Draw a Context diagram and a Data Flow Diagram for a manufacturing company with a material handling and financial system that works as follows: Widget Corporation makes high-tech fly swatters. The units include a mm-Wave RADAR system that makes a final tweak in the arc of the swing to ensure a successful "end-game". The supply chain follows a classical SIPOC approach: Raw materials arrive from the vendor and are inspected. The materials enter production, products are fabricated, tested, moved to a short- term warehouse, then shipped to distributors. Vendors are paid after incoming inspection verifies the raw materials and Distributors are invoiced after finance is notified that the products are shipped. Distributors have 30-days to pay for their products after invoicing.See Answer
Q2:Problem 2. Construct an FMEA of a simple, theoretical process, or a process that you have worked with. Please describe the process and its shortcomings, then construct the FMEA model based on your description. Include at least 2 but no more than 5 Failure Modes. Please suggest the issues that need to be resolved first using RPN. Briefly discuss costs and impacts associated with remedying the issues. Don't bother filling out the Resulting Status Columns, unless you have an actual example...See Answer
Q3: Assignment 6, 100 pts: Due on 04/27/2021 1. (10 pts) Referring to risk adjusted control chart, in order to detect a change in the system, which variables should one monitor, x, y, or z, and why? 2. (25 pts) Consider the example used in the class for linear regression (weight of the card- board). Using only the first 5 data points, fit a linear regression between weight (y) and humidity (x) and determine the values of Bo, B₁. Also, write down the matrices Y and X (see slide #10). Also, determine the values of ŷ and comapre with the corresponding values of y. 3. (25 pts) Two observable quality characteristic x₁ and ₂ of a production process is recorded for m = 50 samples with a sample size of n = 25. Assume that mean values of the quality characteristics and the covariance matrix were determined as: x 55 30 1 2 3 4 5 6 7 8 and S (a) Determine the UCL for a Hotelling T2 control chart. Consider a = 0.001. (b) The first 15 samples of the data is shown in Table 1. The data are sample means of each quality characteristic. Determine the T² for these 15 samples. Based on the UCL from part (a), do you see any out of control samples? Sample Number X1 X2 58 32 60 33 50 27 54 31 63 38 53 30 42 20 55 31 200 130 Table 1: Data for Exercise 4(b) 1 Sample Number 9 10 130 120 11 12 13 14 15 | X1 X2 46 25 |5049575875 55 29 27 30 33 45 27 4. (15 pts) Consider a T² control chart for monitoring p = 6 quality characteristics. Suppose that the sample size is n = 3 and there are m = 30 preliminary samples available to estimate the sample covariance matrix. Find the control limits assuming that a = 0.005. 5. (25 pts) In a large study, 942 women were surveyed and their daily dietary intake of Calcium, Iron, Protein, Vitamin A, and Vitamin C were recorded. Since we have 5 quality charac- teristic, p = 5. The sample average and sample covariance matrix for the dietary intake are: X = 624.0 mg 11.1 mg 65.8 g 839.6 μg 78.9 mg and S = 157829.4 940.1 6075.8 102411.1 2383.2 6701.6 137.7 940. 5.8 114.1 6075.8 114.1 934.9 7330.1 477.2 102411.1 2383.2 7330.1 2668452.4 22063.3 6701.6 137.7 477.2 22063.3 5416.3 The recommended intake of these nutrients are: Ho = 1000 mg 15 mg 60 g 800 με 75 mg Conduct hypothesis test (with a = 0.01) to verify if the average dietary intake meets the recommendations. Although it is not needed, you may check the data related to this problem on canvas Assignment 6 folder (Women's survey data). 2See Answer
Q4:Data management: 1. Select the machine/country/shift combination that showed the greatest difficulty. By For example, if your worst case scenario was machine 1 in Spain, your selection should be viewed as follows: following way: Table #1 2. Then it is necessary to order the data in a way that represents the sequence in which they were taken. Shifts 1, 2 and 3 of each day must be consecutive. To achieve this it is necessary to add a column that identifies each of the days as presented in the table that follows. Table #2: 3. Sort the data by day and shift. Table #3See Answer
Q5:1. The graphical relationship of the data obtained versus the concentration of an analyte is known as the a. Calibration curve b. Linearity c. Reference range d. Reportable rangeSee Answer
Q6:d. Reportable range 2. An algorithmic comparison of a patient's previous laboratory value to the current laboratory value is known as a: a. Critical value b. Delta check c. Linearity check d. Reference rangeSee Answer
Q7: You are a third year technical apprentice and you have been asked by your supervisor to contribute to the quality standards for particular products because your company feel that they need to develop their quality processes. The company feel that using statistics will enable them to enhance the quality of their product and so they are considering statistics to examine processes and wish you to evaluate what is available and then to apply the best methods to a particular product. The company produce a small component that has a hole in it that is critical and checked with a plug gauge. The company produce these in batches of 50 and initially carries out 100% inspection. The company are concerned that the process is not in control and have asked you to investigate. Table One gives the defects for 50 batches which you need to use to produce attribute control charts, np and p charts. Table Two gives the next 100 batches. You are expected to: 1. construct the control charts np and p using table one, 2. document your research into ways in which the data can be used to inform the company about the process; 3. determine the extent that the process is under control using that data in table two The tables on following pages give the actual sizes of the diameter "A" and length "B" of a stud that the company produces on one of their CNC machines. Design statistical variable control charts involving the mean and range, X and R charts for diameter A. The measurements were taken in batches of 5 and recorded on the table as 1-5 first batch, 6-10 second batch etc. Use the first 50 entries [10 batches] to do this. 1. construct the control charts X and R using this data, 2. document your research into ways in which the data can be used to inform the company about the process; 3. determine the extent that the process is under control using the rest of the data in the table for diameter A, remember these are in batches of 5. Using the data in the table for the length B of the stud produce: 1. a statistical process capability chart for length B for the first 100 studs. 2. an evaluation regarding the machine's capability based on a calculation of Cp and Cpk for the length of the stud, and how the process can be improved. 3. produce a modified control chart and plot the rest of the data from the table for the length B of the stud Produce a report that includes: An evaluation of the use of the statistical methods possible and how they have influenced the design and successful use of process control charts. A Process Capability Study based on your outcomes from the data used from the table for the length B of the stud. The size for dimension A is 12.5mm ±0.3. The sizes given in the table are in millimetres. The size for dimension B is 20.2mm ±0.2. The sizes given in the table are in millimetres. Table One Batch Batch Number Output 100 100 100 1 2 3 4 5 6 7 8 9 23 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Batch Defects 17 19 11 3 2 17 15 13 14 5 2NFRAREamonn Hagang 12 19 14 18 17 14 20 20 15 19 16 14 11 9 3 6 5 20 20 17 5 18 8 4 6 18 17 7 11 9 19 19 20 7 5 9 7 20 Table Two Batch Number 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Batch Output 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Batch Defects 19 20 12 15 12 18 17 15 18 15 19 11 4 12 11 3 17 5 13 15 17 7 10 14 17 5 15 11 4 11 4 14 16 11 14 2 16 6 12 16 9 10 16 9 3 13 15 13 15 8 Batch Number 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 Batch Output 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 106 107 109 111 104 110 103 108 112 111 106 107 109 111 104 110 103 108 112 111 106 107 119 111 104 110 113 108 112 111 Batch Defects 2 10 21 13 3 3 6 2 10 5 14 12 14 16 7 14 6 2 9 19 8 14 12 17 13 13 9 18 18 5 7 17 12 16 12 13 9 12 18 5 8 14 12 17 18 17 9 18 17 6 TABLE 3 Dimension A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 0 u 2 3 44 45 46 47 48 49 50 40 41 42 43 12.488 12.685 12.636 12.448 12.470 12.381 12.383 12.403 12.611 12.520 12.666 12.404 12.627 12.580 12.414 12.636 12.538 12.553 12.424 12.681 12.365 12.675 12.413 12.624 12.617 12.324 12.537 12.446 12.610 12.622 12.370 12.499 12.342 12.515 12.573 12.444 12.348 12.553 12.359 12.365 12.652 12.359 12.522 12.362 12.643 12.348 12.423 12.432 12.603 12.696 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 12.613 12.678 12.475 12.643 12.539 12.669 12.699 12.410 12.551 12.612 12.390 12.520 12.697 12.324 12.429 12.405 12.587 12.545 12.441 12.402 12.390 12.708 12.355 12.357 12.528 12.534 12.693 12.353 12.714 12.459 12.490 12.496 12.611 12.476 12.510 12.403 12.629 12.518 12.551 12.492 12.366 12.496 12.506 12.364 12.403 12.692 12.343 12.627 12.581 12.412 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 12.717 12.618 12.359 12.453 12.383 12.663 12.345 12.391 12.696 12.501 12.383 12.409 12.606 12.591 12.604 12.668 12.658 12.521 12.466 12.458 12.389 12.408 12.506 12.447 12.555 12.441 12.447 12.484 12.595 12.467 12.612 12.432 12.636 12.570 12.404 12.401 12.516 12.401 12.330 12.647 12.351 12.660 12.625 12.487 12.692 12.711 12.388 12.543 12.343 12.551 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 12.358 12.437 12.699 12.570 12.565 12.628 12.469 12.451 12.582 12.355 12.611 12.542 12.707 12.652 12.498 12.657 12.646 12.559 12.551 12.699 12.495 12.365 12.602 12.613 12.445 12.488 12.702 12.489 12.525 12.355 12.355 12.359 12.557 12.471 12.550 12.585 12.592 12.572 12.349 12.478 12.582 12.731 12.685 12.533 12.520 12.422 12.654 12.693 12.663 12.709 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 12.359 12.711 12.617 12.719 12.444 12.397 12.730 12.692 12.413 12.474 12.537 12.527 12.646 12.467 12.601 12.549 12.395 12.671 12.474 12.556 12.385 12.515 12.391 12.468 12.542 12.496 12.536 12.389 12.491 12.372 12.584 12.623 12.426 12.559 12.677 12.475 12.628 12.579 12.457 12.383 12.663 12.462 12.493 12.536 12.607 12.569 12.609 12.675 12.450 12.719See Answer
Q8: 4) A product developer is interested in reducing the drying time of a primer paint. Two formulations of the paint are tested; formulation 1 is the standard chemistry, and formulation 2 has a new drying ingredient that should reduce the drying time. From experience, it is known that the standard deviation of drying time is eight minutes,and this inherent variability should be unaffected by the addition of the new ingredient. Ten specimens are painted with formulation 1 and another ten specimens are painted with formulation 2; the 20 specimens are painted in random order. The two-sample average drying times are X1=121 min and x2=112 min, respectively.What conclusions can the product developer draw about the effectiveness of the new ingredient, using a=0.05? Use the analysis of variance to test the hypothesis that different concentrations do not affect the mean tensile strength of the paper.See Answer
Q9: 1) A Manufacturing process produces thousands of semi-conductors chips per day. On the average, 1% of these chips do not conform to the specifications. Every hour, an inspector selects a random sample of 25 chips and classifies each chip in the sample as conforming or non – conforming. If we let x be the random variable representing the number of non-conforming chips in the sample, then what is the probability distribution of x?why?See Answer
Q10: 2) The diameter of a metal shaft used in a disk-drive unit is normally distributed with mean 0.2508 in. and standard deviation 0.0005 in. the specifications on the shaft has been established as 0.2500±0.0015 in. what fraction of the shafts produced conform to specifications?See Answer
Q11: 5) The data shown in Table 6E.3 a re the deviations from nominal diameter for holes drilled in a carbon-fiber composite material used in aerospace manufacturing. The values reported are deviations from nominal in ten-thousandths of an inch. (a) Set up x-bar and R charts on the process. Is the process in statistical control? (b) Estimate the process standard deviation using the range method. (c) If specifications are at nominal +-100, what can you say about the capability of this process? (d)Calculate the PCR CpSee Answer
Q12: 6) The fill volume of soft-drink beverage bottles is an important quality characteristic. The volume is measured(approximately) by placing a gauge over the crown and comparing the height of the liquid in the neck of the bottle against a coded scale. On this scale, a reading of zero corresponds to the correct fill height. Fifteen samples of size n = 10 have been analyzed, and the fill heights are shown in Table 6E.5. a)What control charts are more suitable to monitor the mean and variability of the process? b) Construct the control charts and set the valid control limits c) Is the process in control?See Answer
Q13: 3) The time to failure for an electronic component used in a flat panel display unit is satisfactorily modeled by a Weibull distribution with B=1/2 and 0 =5000.Find the mean time to failure and the fraction of components that are expected to survive beyond 20,000 hours.See Answer
Q14: Consider a tolerance chain given in Figure Q1 with dimensions shown in Table Q1. 1. Allocate tolerances using Worst Case – Average Tolerance Grade Method 2. Allocate tolerances using RSS methodSee Answer
Q15: A company intending to produce components for a fit with guaranteed clearance / interference as given in Table Q2 (Jmin, Jmax Or Smin, Smax respectively). It has been experiencing problems when machining both holes and shafts caused by lack of process capability, see Manufacturing Methods in Table Q2. Maintaining fit characteristics transform the tolerances to suit company's capability implementing selective assembly method. 1. Determine tolerances of the mating parts based on the manufacturing methods 5. Calculate maximum and minimum interference / clearance for each group 4. Draft the tolerances, indicating the groups 3. Calculate upper and lower limit deviations for the hole and the shaft 2. Calculate the number of groupsSee Answer
Q16: You are employed as a quality engineer and you have been asked to help in designing a limit gauge for quality control of machined shafts. Your company quality policy requires prevention of acceptance of any defective parts. a) Using the appropriate approach allocate the tolerances for 'GO' and ʼNOT-GO' ends of a snapgauge for controlling diameter of a shaft ØAB . Support your answer with all relevant tolerance diagrams.Table 02 b) Using the diagram from part (a) showing the allocation of Limit Gauge tolerances, give an example of a situation where a shaft with a particular actual dimension is made in the tolerance, but when inspected by this Limit Gauge (worn, but still within the gauge tolerance),might be misjudged as bad. Plot it on the tolerance diagram.See Answer

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