Casestudie Breakdown prediction Contell PILOT - Transumo

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Inferential statistical methods do not describe available datasets but try to gain additional information from the existing data. These methods are applied to problems, where datasets cannot be obtained entirely ([Scharnbacher04], p. 43). After obtaining parts of the totality, inferential statistical methods are used to generalize gained results ([Bourier03], p. 3). Due to the fact that modern computer systems and mainframes are able to compute large amounts of data within very short time, statistical analysis offers additional calculation possibilities (e.g. data mining). Furthermore, the ability to collect data in an automated way increases the data base. As a result, the probability is higher that the gained generalized results are correct ([Eckey02], p. 3). 5.3 Basic Descriptive Statistical Measures Section 1.2 defined the two main goals of this diploma thesis. The first one was to gain additional knowledge of the cooling device’s condition from recorded datasets to offer additional decision support in case of an exceptional temperature level. Therefore, a summarization and evaluation of available datasets by using descriptive statistics appears to be a promising approach. Hence, the succeeding subsections will introduce as well basic as special descriptive statistical measures from other already introduced monitoring settings. 45 Moreover, the expected gain of information is evaluated. Descriptive statistics offer some very common measures that can be applied easily to all kinds of numerical data. Most known are: ([Holland01], chapter 4) • Minimum and Maximum • The Mode • The Median • The Mean • The Standard Deviation The first basic descriptive statistical measurements are the minimum and the maximum value. Their determination can be done with very few time and effort. Nevertheless, these values can already indicate uncommon behavior. 46 45 See chapter 4 for details 46 See section 6.2.1 for details 58
The mode is the most frequent value of a dataset. It can be regarded as a kind of center of a sorted dataset ([Eckey02], p. 42). Therefore, the mode is suitable to get a quick overview of the main behavior of large datasets. A disadvantage of the mode is the ignorance of outliers. The median is a value that divides a dataset into two parts of same extend. To calculate the median the single values of the given dataset have to be sorted by size to a row, so that X ( 1) ≤ X (2) ≤K ≤ X ( n) is complied. Afterwards, the value right in the middle is the median. In case of an even number of values, the mean of the two mid values is taken as described by the following Formula 5-1: ([Eckey02], p. 44) X ⎧X (( n+ ⎪ = ⎨1 ⎪ ( X ⎩2 1) / 2) ( n / 2) + X ( n / 2+ 1) ) if n odd if n even Formula 5-1: The Median Formula In case of a normal distribution, mode and median are very similar. This behavior changes, if the most frequent temperature value tends to one of the interval borders. Moreover, the median also ignores outliers. Probably the most common value in statistics is the mean. In fact, several different types of mean values do exist. Talking about the mean generally just denotes the arithmetic mean. It is calculated by just summarizing all values from a dataset and a subsequent division by the dataset’s quantity. Formula 5-2 describes this procedure in mathematical form. In contrast to mode and median, the arithmetic mean does not ignore outliers but weights every single value the same. ([Bourier03], p. 79) X 1 = n n ∑ X i i= 1 Formula 5-2: The Arithmetic Mean Formula As already mentioned, there are several different mean values. Beside the already introduced arithmetic mean, there are the geometric and the harmonic mean. The geometric mean is especially used to analyze growth rates ([Bourier03], p. 84). The harmonic mean is defined to provide mean values of ratios ([Eckey02], p. 54). As monitoring data within the setting of sensor based temperature monitoring is neither faced with growth rates nor ratios these methods will not be presented. 59
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Technische Universität Braunschwei
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4.4 Review of Current State of Rese
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Index of Tables Table 2-1: Error of
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1 Introduction 1.1 Initial Position
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2 Sensor Based Temperature Monitori
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compressor. They are served by a ce
Page 13 and 14: the specified value, it works very
Page 15 and 16: of this, over a hundred irregular p
Page 17 and 18: a centralized one. An isolated appl
Page 19 and 20: Figure 2-8: Lack of Information Pro
Page 21 and 22: Moreover, the fridge’s filling le
Page 23 and 24: store this kind of data but only of
Page 25 and 26: 3 Current Monitoring Systems The la
Page 27 and 28: device’s condition. Especially th
Page 29 and 30: a converter that is also available
Page 31 and 32: To indicate important events within
Page 33 and 34: 1. Display stored data in table for
Page 35 and 36: This way of visualizing data is the
Page 37 and 38: free text. Moreover it is possible
Page 39 and 40: dependent limit and delay settings,
Page 41 and 42: Aside from these functions, the kin
Page 43 and 44: 1. Temperature verification in retr
Page 45 and 46: alarms by the use of additionally a
Page 47 and 48: The third mentioned Centron Environ
Page 49 and 50: 4 Current State of Research As alre
Page 51 and 52: even this improvement is still face
Page 53 and 54: Another current approach is regress
Page 55 and 56: S o n 2 = ∑ Yi −Yi n −1 i= 2
Page 57 and 58: This algorithm returns an upper and
Page 59 and 60: • Critical values • Pre-warning
Page 61 and 62: 5 Possible and Promising Ways of Da
Page 63: could be: “The mean increase of a
Page 67 and 68: Figure 5-1: Two Samples of Regressi
Page 69 and 70: 5.4.2 The Major Problems of Regress
Page 71 and 72: The next section will introduce tim
Page 73 and 74: explained in section 5.4. If such a
Page 75 and 76: pictured in Formula 5-12. Beside a
Page 77 and 78: P ( m) = P ( r ) ⋅ P ( m−r ) wi
Page 79 and 80: But the greatest problem is again t
Page 81 and 82: clustering as well as an analysis o
Page 83 and 84: The general idea of supervised lear
Page 85 and 86: sometimes data of a door opening se
Page 87 and 88: Beside the introduced notification
Page 89 and 90: A classification could be achieved
Page 91 and 92: Table 5-1: Estimated Improvements A
Page 93 and 94: As all these software products fail
Page 95 and 96: 6.2 Case Study The UMC St. Radboud
Page 97 and 98: Figure 6-3: Maximum Values at Dayti
Page 99 and 100: Figure 6-5: Minimum Values at Dayti
Page 101 and 102: Figure 6-9: Standard Deviation at D
Page 103 and 104: Table 6-3: Reported Notifications (
Page 105 and 106: Important for the determination of
Page 107 and 108: Remarkable is a comparison to the a
Page 109 and 110: Interviews with several employees f
Page 111 and 112: 7 Summary Cooling devices within me
Page 113 and 114: Bibliography Books and Articles: [B
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[Wittenberg98] Reinhard Wittenberg,
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Appendix 1 - Implementation of Inte
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%Name and location of the source fi
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Appendix 2 - Implementation of Stat
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dailydate = [dailydate; floor(date(
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%Count Dooropenings per Day dailydo
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xlswrite(strcat(path, 'Excel\', fil
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print('-dtiff', strcat(path, 'Graph
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ar([dailydate(1):dailydate(length(s
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Appendix 3 - Implementation of Data
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Duration = 0; maxtemp = 0; elseif (
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%Contains [Duration, Number of Occu
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disp(strcat('Dooropening
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