الاحصاء الهندسي

ISE 325 Engineering Statistics Sample Final Exam

  1. The management of the Savola Group has its reservations on the performance of the workers in the Al-Asra sugar production line. Over the last year only, the production volume had been constantly under the production target. The management has hired an industrial engineer to identify the causes of the low production performance and to suggest ways to elevate the production volume. The industrial engineer met with a representative group of workers, and after careful analysis, he has found that the production volume, measured in kg of sugar produced in a day, may be affected by the average workload and the average number of repeated tasks. He used the following measures:

    measures

    He spent 15 days in the production line and collected the following data:

    Day Kg produced in a day
    y    		 Workload factor
    x1    		 Repeating-tasks factor
    x2
    1 1138 65 20
    2 579 72 88
    3 1121 71 21
    4 516 74 95
    5 608 77 82
    6 906 78 45
    7 1080 85 21
    8 883 98 41
    9 910 68 48
    10 843 77 54
    11 972 94 31
    12 507 96 89
    13 833 75 55
    14 1022 93 24
    15 1107 65 24

    regression model
    He believes that a multiple linear regression model will be adequate to explain the variability in the production volume. Test the significance of regression at α = 0.05, and state your conclusion clearly and completely. Note: maintain 2 decimal places in all the calculations.

  2. The industrial engineer in the Colgate Toothpaste plant in Dammam First Industrial City has observed that about 2% of toothpaste tubes leak, caused by weak seals. Tube sealing is performed by the sealing press, by applying high pressure. He believes if the pressure is supplied by heat, the seal will be stronger. He randomly selected 3 temperature levels, used them with the sealing press, and measured the strength of the seal. He performed three replicates of each trial. The data he collected are (the higher the number, the stronger):
      Observations
    Temperature (oC) 1 2 3
    67 57 46 40
    62 84 81 86
    71 65 57 54

    Test the significance of the effect of heat on the strength of the seal. Maintain 2 decimal places.

  3. In the National Manufacture for Cartoons -Riyadh, the last stages of box manufacturing are the folding and gluing stages. These two stages are considered by the quality department as the most critical. According to the production manager, the number of box defects is influenced by these two stages. However, the production manager suspects the folding stage is the major cause of defects. The stages can be controlled by the feed rates. So, he resolves to statistics to help him confirm his suspicion. For the folding stage, he has determined two setting for the feed rate, 20 and 30 parts per minute. For the gluing stage, two setting have been chosen, 25 and 30 parts per minute. Under each combination of effects of the factors, he counted the number of defects in one thousand in one hour; he repeated each experiment three times. He took the observations totally random, and came up with the following observations:

     

     

    		 Gluing

     

     

    		 25 33
    Folding 20 15 11 12 28 27 29
    30 39 28 34 43 41 44

    What can you say about the contribution of the folding stage on the number of defects? Maintain 1 decimal place in all calculations.

  4. In a metal fabrication shop, two factors are thought to influence the size of the hole in mm on a specific metal type: rotation speed of the bit and the addition of lubricant. A 22 factorial experiment has been run with rotation speed of 700 and 950 rpm and with and without lubrication. Each run of the experiment is replicated twice:
        Lubrication
        no lubrication with lubrication
    Rotation speed 700 8.34 7.44 7.01 7.09
    950 5.2 4.96 4.45 4.7
    1. Test the significance of the main effects of the rotation speed, lubrication, and their interaction on the size of the hole.
    2. Estimate the main effects of the factors and their interaction and comment on what they indicate.

    Note: maintain 2 decimal places.

  5. Assume for a two variable linear regression model, R2adj=0.93. When a third variable is added, R2adj comes to be 0.82. Would you recommend adding the third variable to the regression model?
  6. In conducting an experiment, the industrial engineer has one important factor and another factor he is not interested in. To remove the effect of the less important factor, he must
    1. Fix its value
    2. Take observations for different values of the factor
  7. The industrial engineer in Saudi Ceramics wants to know how weight and thickness of a certain tile brand affect the load strength. He has collected a random sample of 17 tiles and measured weight, thickness, and load strength. The data is summarized as follows:
    n = 17; SST = 654.12; SSR = 240.22
    Test the significance of regression and make an appropriate conclusion. Use α=0.05. Maintain two decimal places.
  8. In a shoe manufacturing plant, the industrial engineer is interested to test three types of glue on the strength of the shoe. The manufacture of the shoe will require the application of heat to the glue; but this factor is not of interest to him, so he is going to treat the heat factor as a nuisance factor and he will make a block design. For every blue type, he has taken observations for four temperature levels:
      Temperature
    Glue type 70° 80° 90° 100°
    CTT 49.9 52.4 48.9 52.7
    Xglue 51.8 50 51 52.4
    MaxSR 51.4 48.8 50.8 48.5

    Perform analysis of variance and make an appropriate conclusion. Maintain two decimal places.

  9. In the Advanced Electronics Company, the industrial engineer is studying the effects of experience of workers and laptop model on the assembly time. He has examined three levels of experience and three laptop models; for every combination of experience and model, he made two observations in minutes:
      Laptop models
    Experience level LT1 LT2 LT2
    1 year 210 208 205 201 208 207
    5 years 111 113 102 105 108 111
    7 years 10 6 11 15 14 10
    1. Test the significance of interaction between experience level and laptop model under 0.05 significance level.
    2. What can be said about the contribution of laptop model on the assembly time?

Dr Muhammad Al-Salamah