Maddox Smith Staff asked 4 years ago

Experiment and statistics

Part 1: A certain feature on the NVG is produced using high speed milling. Currently two different manufacturers (Supplier 1 and Supplier 2) supply tools to the manufacturing cell. A number of tests have been conducted with the results for tool life given in Tables 1 and 2. All values are in meters. The supplier is the only variable factor with all other factors fixed. 121 113 114 131 126 131 127 123 140 124 121 111 136 127 147 116 103 126 118 132 123 120 125 118 131 136 116 126 109 107 120 127 132 141 137 113 118 121 136 135 116 128 Table 1: Supplier 1 results 118 120 123 95 118 130 116 119 131 124 110 116 111 131 130 126 125 106 117 98 138 109 126 121 99 121 127 129 126 100 121 115 108 146 125 105 101 113 115 126 136 122 Table 2: Supplier 2 results a) Provide as much basic statistical data and corresponding anal analysis concerning the results as possible. b) Produce separate histogram plots of each set of results. c) Are both data sets normally distributed? Explain how you arrived at your answer. d) Compare with discussion, the values of skewness and kurtosis for the two samples. e) Which supplier’s tools have the longest distance machined? Provide statistical evidence to support your conclusion. Part 2: The NVG is heat treated to improve mechanical properties. The company purchases a furnace to enable them to carry out the heat treatment operation. The furnace temperature is controlled by a dial and digital readout. The temperature of the furnace has been calibrated using an infra-red camera to measure a block of workpiece material in the furnace at various temperature settings up to the furnace maximum dial temperature of 1600ºC. The results are detailed in Table 3. The current heat treatment procedure involves heating the NVG at 926ºC for 20hours. a) What temperature should the dial be set to ensure the required temperature is maintained? You are allowed ±4ºC of error in your answer. Provide evidence of your reasoning and method of calculation. Dial (ºC) 200 400 500 600 700 800 900 1000 1200 1400 1600Camera (ºC) 190 226 302 452 486 510 571 716 991 1452 1750Table 3: Temperature measurement results Part 3: As part of a new product introduction (NPI), an experiment was performed to improve the strength of the material that NVG’s are produced from. The factorial experiment involved a single factor at three levels and two factors each at two levels. In total three replications of each test were completed. The first factor was the heat treatment temperature which was varied at three levels (1200, 1400 & 1600 ºC) with the alloy the NVG’s made from varied at two levels (A & B). These two alloys are commercially sensitive and are produced by different suppliers hence the coding requirement. A final factor, cooling method was investigated at two levels (air and quench). The results from this factorial experiment are given in Table 4. Analyse the results to determine which combination of factors and levels gives the largest percentage improvement in strength. Main Effects Plots, Interaction Plots and ANOVA in tabulated form should be provided as part of this. The percentage contribution ratio for each factor should also be given. Provide the reasoning for your choice in the form of conclusions and recommendations. Part 4: A different material supplier produces an alloy (Alloy C) which they state has far superior properties to that of Alloy A or B used in Part 3. The different supplier also states that the effect of cooling method is the same for Alloy C as Alloy A or B found in Part 3. It has been decided to perform an experiment to determine if this is true or not. a) Using the information in Parts 2 and 3, design an experiment to achieve this. Your experiment should include at least five tests. Due to time and material restrictions only a maximum of thirty tests can be conducted. Provide justification and reasoning behind your choice of design. Note: There is no right or Note: There is no right or wrong answer for Part D. You should follow the guidelines for successful experimental design and explain why you decided on the factors, levels and design. The output measure (% improvement) should be the same as that used in Part 3. As there are a large number of experimental designs available, I would expect everyone to give a slightly different answer.  Test number Temperature (ºC) Alloy Cooling method Improvement (%) 10 1200 B Air 11.4 32 1200 B Quench 11.7 5 1200 A Air 16.5 18 1200 A Quench 16.5 26 1400 B Air 12.0 22 1400 B Quench 12.0 17 1400 A Air 16.2 12 1400 A Quench 16.2 4 1600 B Air 16.8 8 1600 B Quench 16.8 27 1600 A Air 17.4 31 1600 A Quench 17.1 34 1200 B Air 12.0 7 1200 B Quench 12.0 1 1200 A Air 15.0 33 1200 A Quench 15.0 14 1400 B Air 12.9   1