{"id":41,"date":"2015-02-12T15:34:00","date_gmt":"2015-02-12T14:34:00","guid":{"rendered":"https:\/\/caipirinha.spdns.org\/wp\/financial-risk-calculation\/"},"modified":"2020-12-30T18:38:04","modified_gmt":"2020-12-30T17:38:04","slug":"financial-risk-calculation","status":"publish","type":"post","link":"https:\/\/caipirinha.spdns.org\/wp\/?p=41","title":{"rendered":"Financial Risk Calculation"},"content":{"rendered":"<h2><span id=\"ms-rterangecursor-start\"><\/span><span style=\"font-family: Arial, Helvetica, sans-serif;\">Problem Statement<\/span><\/h2>\n<p><span style=\"font-family: Arial, Helvetica, sans-serif;\">We now build up on our knowledge from the blog entry <\/span><a href=\"https:\/\/pm-gabriel.blogspot.de\/2014\/12\/delay-propagation-in-sequential-task.html\"><span style=\"font-family: Arial, Helvetica, sans-serif;\">Delay Propagation in a Sequential Task Chain<\/span><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\">\u00a0and use the knowledge as well as the C code that was developed in that blog post in order to tackle a problem from project risk management. We want to examine which outcomes are possible based on a set of risks and their possible monetary impact on our project. The assumption in our example is though that all risks are independent from each other.<\/span><br \/>\n<span style=\"font-family: Arial, Helvetica, sans-serif;\">The questions we are going to ask are of the type:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: Arial, Helvetica, sans-serif;\">What is the probability that our overall damage is less than <i>x<\/i> \u20ac?<\/span><\/li>\n<li><span style=\"font-family: Arial, Helvetica, sans-serif;\">What is the probability that our overall damage is higher than\u00a0<i>x<\/i> \u20ac?<\/span><\/li>\n<li><span style=\"font-family: Arial, Helvetica, sans-serif;\">&#8230;<\/span><\/li>\n<\/ul>\n<h2><span style=\"font-family: Arial, Helvetica, sans-serif;\">Source Data<\/span><\/h2>\n<p><span style=\"font-family: Arial, Helvetica, sans-serif;\">We use the following risks below. Different from traditional risk tables, we do not have only 2 outcomes per risk (&#8220;Risk does not materialize.&#8221; and &#8220;Risk materializes.&#8221;), but we have an n-ary discrete outcome for each risk (&#8220;Risk does not materialize.&#8221;, &#8220;Risk materializes with damage A and probability a%&#8221;, &#8220;Risk materializes with damage\u00a0B and probability b%&#8221;, &#8230;). This allows a finer grained monetary allocation of each risk.<\/span><\/p>\n<table style=\"border-collapse: collapse; width: 866px;\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr style=\"height: 30.75pt;\">\n<td class=\"xl84\" style=\"background-color: transparent; border-color: windowtext black windowtext windowtext; border-style: solid none solid solid; border-width: 1pt 0px 1pt 1pt; height: 30.75pt; width: 214pt;\" width=\"285\" height=\"41\"><b><span style=\"color: black; font-family: Calibri;\">Risk<\/span><\/b><\/td>\n<td class=\"xl85\" style=\"background-color: transparent; border-color: windowtext black; border-style: solid none; border-width: 1pt 0px; width: 214pt;\" width=\"285\"><b><span style=\"color: black; font-family: Calibri;\">Consequence<\/span><\/b><\/td>\n<td class=\"xl85\" style=\"background-color: transparent; border-color: windowtext black; border-style: solid none; border-width: 1pt 0px; width: 67pt;\" width=\"89\"><b><span style=\"color: black; font-family: Calibri;\">Probability<\/span><\/b><\/td>\n<td class=\"xl85\" style=\"background-color: transparent; border-color: windowtext black; border-style: solid none; border-width: 1pt 0px; width: 67pt;\" width=\"89\"><b><span style=\"color: black; font-family: Calibri;\">Damage<\/span><\/b><\/td>\n<td class=\"xl86\" style=\"background-color: transparent; border-color: windowtext windowtext windowtext black; border-style: solid solid solid none; border-width: 1pt 1pt 1pt 0px; width: 89pt;\" width=\"118\"><b><span style=\"color: black; font-family: Calibri;\">Expected Damage<\/span><\/b><\/td>\n<\/tr>\n<tr style=\"height: 15pt;\">\n<td class=\"xl77\" style=\"background-color: transparent; border-color: black black black windowtext; border-style: none none solid solid; border-width: 0px 0px 1pt 1pt; height: 60.75pt; width: 214pt;\" rowspan=\"4\" width=\"285\" height=\"81\"><span style=\"color: black; font-family: Calibri;\">No internal resources available.<\/span><\/td>\n<td class=\"xl65\" style=\"background-color: #a9d08e; border-color: black windowtext windowtext; border-style: none solid solid; border-width: 0px 0.5pt 0.5pt;\"><span style=\"background-color: #a9d08e; color: black; font-family: Calibri;\">Risk does not materialize.<\/span><\/td>\n<td class=\"xl66\" style=\"background-color: #a9d08e; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #a9d08e; color: black; font-family: Calibri;\">60%<\/span><\/td>\n<td class=\"xl67\" style=\"background-color: #a9d08e; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #a9d08e; color: black; font-family: Calibri;\">0 \u20ac<\/span><\/td>\n<td class=\"xl80\" style=\"background-color: transparent; border-color: black windowtext; border-style: none solid solid; border-width: 0px 1pt 1pt 0.5pt; width: 89pt;\" rowspan=\"4\" align=\"right\" width=\"118\"><span style=\"color: black; font-family: Calibri;\">16.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15pt;\">\n<td class=\"xl68\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext; border-style: none solid solid; border-width: 0px 0.5pt 0.5pt; height: 15pt;\" height=\"20\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">Hire external 1 staff.<\/span><\/td>\n<td class=\"xl69\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">20%<\/span><\/td>\n<td class=\"xl70\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">10.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15pt;\">\n<td class=\"xl68\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext; border-style: none solid solid; border-width: 0px 0.5pt 0.5pt; height: 15pt;\" height=\"20\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">Hire external 5 staff.<\/span><\/td>\n<td class=\"xl69\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">10%<\/span><\/td>\n<td class=\"xl70\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">50.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15.75pt;\">\n<td class=\"xl71\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext; border-style: none solid solid; border-width: 0px 0.5pt 1pt; height: 15.75pt;\" height=\"21\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">Hire external 9 staff.<\/span><\/td>\n<td class=\"xl72\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 1pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">10%<\/span><\/td>\n<td class=\"xl73\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 1pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">90.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15pt;\">\n<td class=\"xl74\" style=\"background-color: transparent; border-color: black windowtext; border-style: none solid solid; border-width: 0px 0.5pt 1pt 1pt; height: 45.75pt; width: 214pt;\" rowspan=\"3\" width=\"285\" height=\"61\"><span style=\"color: black; font-family: Calibri;\">Design does not fulfil specification.<\/span><\/td>\n<td class=\"xl65\" style=\"background-color: #a9d08e; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\"><span style=\"background-color: #a9d08e; color: black; font-family: Calibri;\">Risk does not materialize.<\/span><\/td>\n<td class=\"xl66\" style=\"background-color: #a9d08e; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #a9d08e; color: black; font-family: Calibri;\">40%<\/span><\/td>\n<td class=\"xl67\" style=\"background-color: #a9d08e; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #a9d08e; color: black; font-family: Calibri;\">0 \u20ac<\/span><\/td>\n<td class=\"xl80\" style=\"background-color: transparent; border-color: black windowtext; border-style: none solid solid; border-width: 0px 1pt 1pt 0.5pt; width: 89pt;\" rowspan=\"3\" align=\"right\" width=\"118\"><span style=\"color: black; font-family: Calibri;\">800.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15pt;\">\n<td class=\"xl68\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px; height: 15pt;\" height=\"20\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">Partial redesign of unit.<\/span><\/td>\n<td class=\"xl69\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">40%<\/span><\/td>\n<td class=\"xl70\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">1.000.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15.75pt;\">\n<td class=\"xl71\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 1pt 0px; height: 15.75pt;\" height=\"21\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">Complete redesign of unit.<\/span><\/td>\n<td class=\"xl72\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 1pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">20%<\/span><\/td>\n<td class=\"xl73\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 1pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">2.000.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15pt;\">\n<td class=\"xl74\" style=\"background-color: transparent; border-color: black windowtext; border-style: none solid solid; border-width: 0px 0.5pt 1pt 1pt; height: 75.75pt; width: 214pt;\" rowspan=\"5\" width=\"285\" height=\"101\"><span style=\"color: black; font-family: Calibri;\">Cost target cannot be achieved.<\/span><\/td>\n<td class=\"xl65\" style=\"background-color: #a9d08e; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\"><span style=\"background-color: #a9d08e; color: black; font-family: Calibri;\">Risk does not materialize.<\/span><\/td>\n<td class=\"xl66\" style=\"background-color: #a9d08e; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #a9d08e; color: black; font-family: Calibri;\">60%<\/span><\/td>\n<td class=\"xl67\" style=\"background-color: #a9d08e; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #a9d08e; color: black; font-family: Calibri;\">0 \u20ac<\/span><\/td>\n<td class=\"xl80\" style=\"background-color: transparent; border-color: black windowtext windowtext; border-style: none solid solid; border-width: 0px 1pt 0.5pt 0.5pt; width: 89pt;\" rowspan=\"5\" align=\"right\" width=\"118\"><span style=\"color: black; font-family: Calibri;\">210.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15pt;\">\n<td class=\"xl68\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px; height: 15pt;\" height=\"20\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">Redesign component #1.<\/span><\/td>\n<td class=\"xl69\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">10%<\/span><\/td>\n<td class=\"xl70\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">200.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15pt;\">\n<td class=\"xl68\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px; height: 15pt;\" height=\"20\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">Redesign component #1, #2.<\/span><\/td>\n<td class=\"xl69\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">10%<\/span><\/td>\n<td class=\"xl70\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">300.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15pt;\">\n<td class=\"xl68\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px; height: 15pt;\" height=\"20\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">Redesign component #1, #2, #3.<\/span><\/td>\n<td class=\"xl69\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">20%<\/span><\/td>\n<td class=\"xl70\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 0.5pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">400.000 \u20ac<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15.75pt;\">\n<td class=\"xl71\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 1pt 0px; height: 15.75pt;\" height=\"21\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">Redesign component #1, #2, #3, #4.<\/span><\/td>\n<td class=\"xl72\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 1pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">10%<\/span><\/td>\n<td class=\"xl73\" style=\"background-color: #f8cbad; border-color: black windowtext windowtext black; border-style: none solid solid none; border-width: 0px 0.5pt 1pt 0px;\" align=\"right\"><span style=\"background-color: #f8cbad; color: black; font-family: Calibri;\">800.000 \u20ac<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-family: Arial, Helvetica, sans-serif;\">We can calulate that the expected value of the damage is <b>1,026,000 \u20ac<\/b> by adding up the expected damages of the individual, independent risks.<\/span><\/p>\n<h2><span style=\"font-family: Arial, Helvetica, sans-serif;\">Solution<\/span><\/h2>\n<p><span style=\"font-family: Arial, Helvetica, sans-serif;\">Our approach will use the <\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/Convolution#Discrete_convolution\"><b><span style=\"font-family: Arial, Helvetica, sans-serif;\">discrete convolution<\/span><\/b><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\"> and take leverage of the C file <\/span><a href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/faltung.c\"><b><span style=\"font-family: Arial, Helvetica, sans-serif;\">faltung.c<\/span><\/b><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\">. However, in contrast to the example in the blog entry <\/span><a href=\"https:\/\/pm-gabriel.blogspot.de\/2014\/12\/delay-propagation-in-sequential-task.html\"><span style=\"font-family: Arial, Helvetica, sans-serif;\">Delay Propagation in a Sequential Task Chain<\/span><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\">, we face the problem that our possible outcomes (the individual damage values) are a few discrete values spread over a large interval. Hence, the program <\/span><a href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/faltung.c\"><b><span style=\"font-family: Arial, Helvetica, sans-serif;\">faltung.c<\/span><\/b><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\">. must be modified unless we want to eat up the whole system memory with unnecessarily large arrays of float numbers. Therefore, the upgraded version (<b><a href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/faltung2.c\">faltung2.c<\/a><\/b>) uses a struct to capture our input and output vectors, and the modified sub-routine <i><b>convolution()<\/b><\/i> iterates through all possible combinations of input vectors and stores the resulting struct elements in the output vector. We also need a helper funtion that checks if a struct with a certain damage value already exists (function <i><b>exists()<\/b><\/i>). We do not sort our output vector until before printing it out where we use <i><b>qsort()<\/b><\/i> in connection with <i><b>compare_damage()<\/b><\/i> to get an output with increasing damage values. In addition to the probability distribution, we now generate values for a probability curve (accumulated probabilities) which will help us to answer the questions of the problem statement.<\/span><br \/>\n<span style=\"font-family: Arial, Helvetica, sans-serif;\">Our input values now are reflected in 3 input vectors in the file <\/span><a href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/input_monetary.dat\"><b><span style=\"font-family: Arial, Helvetica, sans-serif;\">input_monetary.dat<\/span><\/b><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\"> and looks like this:<\/span><\/p>\n<div><span class=\"ms-rteFontFace-2 ms-rteFontSize-1\"><span style=\"font-family: 'Courier New', Courier, monospace; font-size: x-small;\"># Distribution of the Monetary Damages of Risks A, B, and C<br \/>\n# START<br \/>\n0\u00a0\u00a0\u00a0 0.6<br \/>\n10000\u00a0\u00a0\u00a0 0.20<br \/>\n50000\u00a0\u00a0\u00a0 0.10<br \/>\n90000\u00a0\u00a0\u00a0 0.10<br \/>\n# STOP<\/p>\n<p># START<br \/>\n0\u00a0 0.4<br \/>\n1000000\u00a0 0.40<br \/>\n2000000\u00a0 0.20<br \/>\n# STOP<\/p>\n<p># START<br \/>\n0\u00a0\u00a0 0.5<br \/>\n200000\u00a0\u00a0 0.1<br \/>\n300000\u00a0\u00a0 0.1<br \/>\n400000\u00a0\u00a0 0.2<br \/>\n800000\u00a0\u00a0 0.1<br \/>\n# STOP<\/span><\/span><\/div>\n<p><span style=\"font-family: Arial, Helvetica, sans-serif;\">When we evaluate this input with our C program, we get the following output:<\/span><\/p>\n<div><\/div>\n<div><span class=\"ms-rteFontFace-2 ms-rteFontSize-1\"><span style=\"font-family: 'Courier New', Courier, monospace; font-size: x-small;\"># Convolution Batch Processing Utility (only for demonstration purposes)<br \/>\n# The resulting propability density vector is of size: 60<br \/>\n# START<br \/>\n0\u00a0\u00a0 0.1200<br \/>\n10000\u00a0\u00a0 0.0400<br \/>\n50000\u00a0\u00a0 0.0200<br \/>\n90000\u00a0\u00a0 0.0200<br \/>\n200000\u00a0\u00a0 0.0240<br \/>\n210000\u00a0\u00a0 0.0080<br \/>\n250000\u00a0\u00a0 0.0040<br \/>\n290000\u00a0\u00a0 0.0040<br \/>\n300000\u00a0\u00a0 0.0240<br \/>\n310000\u00a0\u00a0 0.0080<br \/>\n350000\u00a0\u00a0 0.0040<br \/>\n390000\u00a0\u00a0 0.0040<br \/>\n400000\u00a0\u00a0 0.0480<br \/>\n410000\u00a0\u00a0 0.0160<br \/>\n450000\u00a0\u00a0 0.0080<br \/>\n490000\u00a0\u00a0 0.0080<br \/>\n800000\u00a0\u00a0 0.0240<br \/>\n810000\u00a0\u00a0 0.0080<br \/>\n850000\u00a0\u00a0 0.0040<br \/>\n890000\u00a0\u00a0 0.0040<br \/>\n1000000\u00a0\u00a0 0.1200<br \/>\n1010000\u00a0\u00a0 0.0400<br \/>\n1050000\u00a0\u00a0 0.0200<br \/>\n1090000\u00a0\u00a0 0.0200<br \/>\n1200000\u00a0\u00a0 0.0240<br \/>\n1210000\u00a0\u00a0 0.0080<br \/>\n1250000\u00a0\u00a0 0.0040<br \/>\n1290000\u00a0\u00a0 0.0040<br \/>\n1300000\u00a0\u00a0 0.0240<br \/>\n1310000\u00a0\u00a0 0.0080<br \/>\n1350000\u00a0\u00a0 0.0040<br \/>\n1390000\u00a0\u00a0 0.0040<br \/>\n1400000\u00a0\u00a0 0.0480<br \/>\n1410000\u00a0\u00a0 0.0160<br \/>\n1450000\u00a0\u00a0 0.0080<br \/>\n1490000\u00a0\u00a0 0.0080<br \/>\n1800000\u00a0\u00a0 0.0240<br \/>\n1810000\u00a0\u00a0 0.0080<br \/>\n1850000\u00a0\u00a0 0.0040<br \/>\n1890000\u00a0\u00a0 0.0040<br \/>\n2000000\u00a0\u00a0 0.0600<br \/>\n2010000\u00a0\u00a0 0.0200<br \/>\n2050000\u00a0\u00a0 0.0100<br \/>\n2090000\u00a0\u00a0 0.0100<br \/>\n2200000\u00a0\u00a0 0.0120<br \/>\n2210000\u00a0\u00a0 0.0040<br \/>\n2250000\u00a0\u00a0 0.0020<br \/>\n2290000\u00a0\u00a0 0.0020<br \/>\n2300000\u00a0\u00a0 0.0120<br \/>\n2310000\u00a0\u00a0 0.0040<br \/>\n2350000\u00a0\u00a0 0.0020<br \/>\n2390000\u00a0\u00a0 0.0020<br \/>\n2400000\u00a0\u00a0 0.0240<br \/>\n2410000\u00a0\u00a0 0.0080<br \/>\n2450000\u00a0\u00a0 0.0040<br \/>\n2490000\u00a0\u00a0 0.0040<br \/>\n2800000\u00a0\u00a0 0.0120<br \/>\n2810000\u00a0\u00a0 0.0040<br \/>\n2850000\u00a0\u00a0 0.0020<br \/>\n2890000\u00a0\u00a0 0.0020<br \/>\n# STOP<\/span><\/span><\/div>\n<div><span class=\"ms-rteFontFace-2\"><span style=\"font-family: 'Courier New', Courier, monospace;\"><span style=\"font-size: x-small;\"><span class=\"ms-rteFontSize-1\"># The propability values are:<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 0.1200<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0\u00a0 10000\u00a0\u00a0 0.1600<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0\u00a0 50000\u00a0\u00a0 0.1800<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0\u00a0 90000\u00a0\u00a0 0.2000<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 200000\u00a0\u00a0 0.2240<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 210000\u00a0\u00a0 0.2320<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 250000\u00a0\u00a0 0.2360<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 290000\u00a0\u00a0 0.2400<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 300000\u00a0\u00a0 0.2640<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 310000\u00a0\u00a0 0.2720<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 350000\u00a0\u00a0 0.2760<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 390000\u00a0\u00a0 0.2800<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 400000\u00a0\u00a0 0.3280<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 410000\u00a0\u00a0 0.3440<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 450000\u00a0\u00a0 0.3520<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 490000\u00a0\u00a0 0.3600<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 800000\u00a0\u00a0 0.3840<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 810000\u00a0\u00a0 0.3920<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 850000\u00a0\u00a0 0.3960<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0\u00a0 890000\u00a0\u00a0 0.4000<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1000000\u00a0\u00a0 0.5200<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1010000\u00a0\u00a0 0.5600<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1050000\u00a0\u00a0 0.5800<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1090000\u00a0\u00a0 0.6000<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1200000\u00a0\u00a0 0.6240<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1210000\u00a0\u00a0 0.6320<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1250000\u00a0\u00a0 0.6360<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1290000\u00a0\u00a0 0.6400<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1300000\u00a0\u00a0 0.6640<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1310000\u00a0\u00a0 0.6720<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1350000\u00a0\u00a0 0.6760<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1390000\u00a0\u00a0 0.6800<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1400000\u00a0\u00a0 0.7280<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1410000\u00a0\u00a0 0.7440<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1450000\u00a0\u00a0 0.7520<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1490000\u00a0\u00a0 0.7600<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1800000\u00a0\u00a0 0.7840<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1810000\u00a0\u00a0 0.7920<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1850000\u00a0\u00a0 0.7960<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 1890000\u00a0\u00a0 0.8000<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2000000\u00a0\u00a0 0.8600<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2010000\u00a0\u00a0 0.8800<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2050000\u00a0\u00a0 0.8900<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2090000\u00a0\u00a0 0.9000<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2200000\u00a0\u00a0 0.9120<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2210000\u00a0\u00a0 0.9160<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2250000\u00a0\u00a0 0.9180<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2290000\u00a0\u00a0 0.9200<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2300000\u00a0\u00a0 0.9320<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2310000\u00a0\u00a0 0.9360<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2350000\u00a0\u00a0 0.9380<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2390000\u00a0\u00a0 0.9400<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2400000\u00a0\u00a0 0.9640<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2410000\u00a0\u00a0 0.9720<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2450000\u00a0\u00a0 0.9760<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2490000\u00a0\u00a0 0.9800<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2800000\u00a0\u00a0 0.9920<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2810000\u00a0\u00a0 0.9960<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2850000\u00a0\u00a0 0.9980<\/span><br class=\"ms-rteFontSize-1\" \/><span class=\"ms-rteFontSize-1\">\u00a0\u00a0 2890000\u00a0\u00a0 1.0000<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"ms-rteFontFace-2\"><span class=\"ms-rteThemeFontFace-1\"><span style=\"font-family: Arial, Helvetica, sans-serif;\">and we can see from the header that there are 60 possible outcomes. When we look at the graph, we can see that the <span class=\"ms-rteThemeForeColor-5-3\">blue<\/span> lines representing the probability density curve are not as &#8220;useful&#8221; as the (accumulated) probability curve (showin in <span class=\"ms-rteForeColor-2\">red<\/span>). With the red curve, we can now answer our questions from the first problem statement (&#8220;What is the probability that our overall damage is less than <i>x<\/i> \u20ac?&#8221;) by looking for <i>x<\/i> on the axis <i>Damage Value<\/i>, going vertically up until we hit the <span class=\"ms-rteForeColor-2\">red<\/span> curve and then branching to the right until we hit the axis <i>Accumulated Probability<\/i>.<\/span><\/span><\/span><\/div>\n<p><span style=\"font-family: Arial, Helvetica, sans-serif;\">The second problem statement (&#8220;What is the probability that our overall damage is higher than\u00a0<i>x<\/i> \u20ac?&#8221;) is determined with the same approach. However, rather than directly using the value on the axis <i>Accumulated Probability<\/i>, we have to subtract that one from 1.00. The result is then the probability that the\u00a0resulting damage is <i>higher<\/i> than <i>x<\/i>.<\/span><\/p>\n<div class=\"separator\" style=\"clear: both; text-align: center;\"><a style=\"margin-left: 1em; margin-right: 1em;\" href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/Monetary_Risk_Output.jpg\"><img decoding=\"async\" title=\"Probability Density and Accumulated Probability Curve\" src=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/Monetary_Risk_Output.jpg\" alt=\"\" border=\"0\" \/><\/a><\/div>\n<h2><span style=\"font-family: Arial, Helvetica, sans-serif;\">Downloads and Hints<span id=\"ms-rterangepaste-end\"><\/span><\/span><\/h2>\n<ul>\n<li><span style=\"font-family: Arial, Helvetica, sans-serif;\">You can download the source code of <\/span><a href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/faltung2.c\"><span style=\"font-family: Arial, Helvetica, sans-serif;\">faltung2.c<\/span><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\">\u00a0from <\/span><a href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/faltung2.c\"><span style=\"font-family: Arial, Helvetica, sans-serif;\">https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/faltung2.c<\/span><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\">. The source code is in Unix format, hence no CR\/LF, but only LF. It can be compiled with <span class=\"ms-rteFontFace-2 ms-rteThemeForeColor-9-4\">gcc -o {target_name} faltung2.c<\/span>. The C program is a demonstration only; no responsibility is assumed for damages resulting from its usage.<\/span><\/li>\n<li><span style=\"font-family: Arial, Helvetica, sans-serif;\">The sample input file <\/span><a href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/input_monetary.dat\"><span style=\"font-family: Arial, Helvetica, sans-serif;\">input_monetary.dat<\/span><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\"> is available at <\/span><a href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/input_monetary.dat\"><span style=\"font-family: Arial, Helvetica, sans-serif;\">https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/input_monetary.dat<\/span><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\">\u00a0and can be read with a standard text editor. If is also in Unix format (only LF).<\/span><\/li>\n<li><span style=\"font-family: Arial, Helvetica, sans-serif;\">The Excel tables and visualizations are available at <\/span><a href=\"https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/PM%20Blog%20Tables.xlsx\"><span style=\"font-family: Arial, Helvetica, sans-serif;\">https:\/\/caipirinha.spdns.org\/~gabriel\/Blog\/PM%20Blog%20Tables.xlsx<\/span><\/a><span style=\"font-family: Arial, Helvetica, sans-serif;\">.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Problem Statement We now build up on our knowledge from the blog entry Delay Propagation in a Sequential Task Chain\u00a0and use the knowledge as well as the C code that was developed in that blog post in order to tackle a problem from project risk management. We want to examine which outcomes are possible based [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[36],"tags":[],"class_list":["post-41","post","type-post","status-publish","format-standard","hentry","category-pm"],"_links":{"self":[{"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/41","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=41"}],"version-history":[{"count":2,"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/41\/revisions"}],"predecessor-version":[{"id":412,"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/41\/revisions\/412"}],"wp:attachment":[{"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=41"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=41"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/caipirinha.spdns.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}