{"id":16325,"date":"2016-11-16T03:26:02","date_gmt":"2016-11-16T03:26:02","guid":{"rendered":"http:\/\/www.safetyangel.com\/recdev\/?page_id=16325"},"modified":"2016-11-16T04:19:05","modified_gmt":"2016-11-16T04:19:05","slug":"example-r-2-reliability-considering-both-failure-and-usage-distributions","status":"publish","type":"page","link":"http:\/\/www.safetyangel.com\/recdev\/example-r-2-reliability-considering-both-failure-and-usage-distributions\/","title":{"rendered":"Example R-2 &#8211; Reliability Considering Both Failure and Usage Distributions"},"content":{"rendered":"<div id=\"dt_row_1177728673886\" class=\"clearfix dt_row\"><div id=\"dt_column_2\" class=\"dt_column col-sm-12\"><div id=\"dt_row_3177728673866\" class=\"row dt_row\"><div id=\"dt_column_4\" class=\"dt_column col-sm-6\"><div id=\"dt_row_5177728673817\" class=\"row dt_row title-blck\"><div id=\"dt_column_6\" class=\"dt_column col-sm-12\"><div id=\"dt-section-head-7\" class=\"dt-section-head center  size-custom\">\r\n              <div><h2 style=\"color:#ffffff;font-size:35px\" class=\"section-main-title\">Example R-2 - Reliability Considering Both Failure and Usage Distributions<\/h2><\/div><\/div><\/div><\/div><\/div><div id=\"dt_column_8\" class=\"dt_column col-sm-6\"><\/div><\/div><div id=\"dt_row_9177728673817\" class=\"row dt_row\"><div id=\"dt_column_10\" class=\"dt_column col-sm-5\"><\/div><div id=\"dt_column_11\" class=\"dt_column col-sm-7\"><div id=\"dt_row_12177728673867\" class=\"row dt_row\"><div id=\"dt_column_13\" class=\"dt_column col-sm-12\"><div id=\"dt_text14177728673875\" class=\"dt_text\">\n<h3><span style=\"color: #000000; font-size: 1em;\">Examples provided here are purely for illustrating software features and functionality.<\/span><\/h3>\n<\/div><\/div><\/div><\/div><\/div><\/div><\/div><div id=\"dt_row_15177728673868\" class=\"clearfix dt_row\"><div id=\"dt_column_16\" class=\"dt_column col-sm-12\"><div id=\"dt_row_17177728673820\" class=\"row dt_row\"><div id=\"dt_column_18\" class=\"dt_column col-sm-12\"><div id=\"dt_row_19177728673869\" class=\"row dt_row\"><div id=\"dt_column_20\" class=\"dt_column col-sm-1\"><\/div><div id=\"dt_column_21\" class=\"dt_column col-sm-5\"><div id=\"dt_text22177728673854\" class=\"dt_text\">\n<h3><span style=\"color: #0093d5;\">Example R-2 &#8211; Reliability Considering Both Failure and Usage Distributions<\/span><\/h3>\n<p>Software Used: <b>Software Used: ALTA PRO<\/b><\/p>\n<p><b>Download Example File for <a href=\"http:\/\/www.reliasoft.com\/alta\/examples\/rc1\/alta_example_1_V10.rsgz10\" download=\"\">Version 10 (*.rsgz10)<\/a> or <a href=\"http:\/\/www.reliasoft.com\/alta\/examples\/rc1\/alta_example_1_V9.rsr9\" download=\"\">Version 9 (*.rsr9)<\/a><\/b><\/p>\n<h3><span style=\"color: #0093d5;\">Problem Statement:<\/span><\/h3>\n<p>Consider the case of a washing machine that can have varied loads:<\/p>\n<ul class=\"normal\">\n<li>Using a 10-pound load, the washing machine fails according to a Weibull distribution with beta = 3 and eta = 2,500 hours.<\/li>\n<li>Using a 5-pound load, the washing machine fails according to a Weibull distribution with beta = 3 and eta = 10,000 hours.<\/li>\n<\/ul>\n<p>Assuming that customer loads vary from 2 to 8 pounds, the expected load in the field can be described by a normal distribution with mean = 5 and std = 1 pound.<\/p>\n<h3><span style=\"color: #0093d5;\">Objectives<\/span><\/h3>\n<ul class=\"normal\">\n<li>Estimate the reliability of the washing machine for 2,000 hours of operation in the field.<\/li>\n<li>Create a plot of the expected reliability vs. time from 1,000 to 10,000 hours (using 1,000 hour increments).<\/li>\n<li>Generate a data set of times to failure for subsequent life data analysis in Weibull++.<\/li>\n<\/ul>\n<\/div><\/div><div id=\"dt_column_23\" class=\"dt_column col-sm-5\"><div id=\"dt_text24177728673882\" class=\"dt_text\">\n<h3><span style=\"color: #0093d5;\">Define the Resources<\/span><\/h3>\n<p>Let us assume that the effect of load weight on the life of the washing machine is described by an inverse power life-stress relationship:<\/p>\n<\/div><div id=\"dt_image25\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/renoexr2_1.png\" alt=\"\"\/><\/div><\/div><div id=\"dt_text26177728673899\" class=\"dt_text\">\n<p>where <i>L<\/i> is the life of the machine and <i>V<\/i> is the load. The constants <i>K<\/i> and <i>n<\/i> can be obtained by solving for the equation based on the given conditions: L(V=5) = 10,000 and L(V=10) = 2,500. Therefore, K = 0.000004 and n = 2.<\/p>\n<p>(See also <a href=\"http:\/\/reliawiki.org\/index.php\/Inverse_Power_Law_Relationship\" target=\"_blank\">http:\/\/reliawiki.org\/index.php\/Inverse_Power_Law_Relationship<\/a> for more information about the inverse power law model.)<\/p>\n<\/div><div id=\"dt_text27177728673857\" class=\"dt_text\">\n<p>Create a model to describe the variations in customer loads, as shown next.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"img-responsive style-default aligncenter\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/Untitled-212.png\" width=\"300\" height=\"300\" \/><\/p>\n<\/div><\/div><div id=\"dt_column_28\" class=\"dt_column col-sm-1\"><\/div><\/div><\/div><\/div><\/div><\/div><div id=\"dt_row_29177728673820\" class=\"clearfix dt_row\"><div id=\"dt_column_30\" class=\"dt_column col-sm-12\"><div id=\"dt_row_31177728673858\" class=\"row dt_row\"><div id=\"dt_column_32\" class=\"dt_column col-sm-12\"><div id=\"dt_row_33177728673815\" class=\"row dt_row\"><div id=\"dt_column_34\" class=\"dt_column col-sm-1\"><\/div><div id=\"dt_column_35\" class=\"dt_column col-sm-5\"><div id=\"dt_image36\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/Untitled-222.png\" alt=\"\"\/><\/div><\/div><div id=\"dt_text37177728673863\" class=\"dt_text\">\n<p class=\"caption\">Create RENO static functions to describe the life-stress relationship (LSR) and the failure time of the washing machine based on this relationship.<\/p>\n<\/div><div id=\"dt_image38\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/Untitled-213.png\" alt=\"\"\/><\/div><\/div><div id=\"dt_text39177728673880\" class=\"dt_text\">\n<p>Here, LSR uses the RENO internal function called &#8220;rvm&#8221; to return a random value based on the UsageLoad model.<\/p>\n<p>FailureTime uses the internal function called &#8220;rv_weibull&#8221; to return a random time to failure based on the washing machine&#8217;s failure distribution. This function returns the inverse of the Weibull cumulative distribution with the specified parameters for the specified probability. In this case, we want the function to return a random value. To do this, we use the predefined function called &#8220;rand&#8221; as the function\u2019s probability value, and then we enter the following parameters for the distribution: 3 (beta), the variable LSR (eta) and 0 (gamma).<\/p>\n<\/div><\/div><div id=\"dt_column_40\" class=\"dt_column col-sm-5\"><div id=\"dt_text41177728673876\" class=\"dt_text\">\n<h3><span style=\"color: #0093d5;\">Estimate the Reliability at 2,000 Hours<\/span><\/h3>\n<p>To estimate the reliability at 2,000 hours, create the flowchart shown below.<\/p>\n<\/div><div id=\"dt_image42\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/Untitled-214.png\" alt=\"\"\/><\/div><\/div><div id=\"dt_text43177728673845\" class=\"dt_text\">\n<p>In this example, the standard block uses FailureTime to obtain a random time to failure based on customer load.<\/p>\n<p>The conditional block evaluates whether the failure time (obtained from the previous block) occurred before the time of interest (the variable called &#8220;Life,&#8221; which was set to 2,000).<\/p>\n<\/div><div id=\"dt_image44\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/Untitled-215.png\" alt=\"\"\/><\/div><\/div><\/div><div id=\"dt_column_45\" class=\"dt_column col-sm-1\"><\/div><\/div><\/div><\/div><\/div><\/div><div id=\"dt_row_46177728673846\" class=\"clearfix dt_row\"><div id=\"dt_column_47\" class=\"dt_column col-sm-12\"><div id=\"dt_row_48177728673830\" class=\"row dt_row\"><div id=\"dt_column_49\" class=\"dt_column col-sm-12\"><div id=\"dt_row_50177728673896\" class=\"row dt_row\"><div id=\"dt_column_51\" class=\"dt_column col-sm-1\"><\/div><div id=\"dt_column_52\" class=\"dt_column col-sm-5\"><div id=\"dt_text53177728673895\" class=\"dt_text\">\n<h3><span style=\"color: #0093d5;\">Create a Plot of the Expected Reliability vs. Time from 1,000 to 10,000 Hours (Using 1,000 Hour Increments)<\/span><\/h3>\n<p>You can use the sensitivity analysis feature to create a plot that shows how the reliability varies over time.<\/p>\n<p>In the RENO Simulation window, keep the same number of simulations (10,000) and seed (1). Then on the Sensitivity Analysis tab, specify to vary the <b>Life<\/b> variable from <b>1,000<\/b> to <b>10,000 hours<\/b>, with increments of <b>1,000<\/b> hours, as shown below.<\/p>\n<\/div><div id=\"dt_image54\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/renoexr2_7.png\" alt=\"\"\/><\/div><\/div><div id=\"dt_text55177728673814\" class=\"dt_text\">With these settings, RENO will perform 10 runs with 10,000 simulations in each run. The first run will calculate the results with the Life variable set at 1,000 hours, the second at 2,000 hours, and so on.<\/div><\/div><div id=\"dt_column_56\" class=\"dt_column col-sm-5\"><div id=\"dt_text57177728673868\" class=\"dt_text\">\n<p class=\"caption\" style=\"text-align: center;\">The following picture shows a plot of the reliability from 1,000 to 10,000 hours.<\/p>\n<\/div><div id=\"dt_image58\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/Untitled-216.png\" alt=\"\"\/><\/div><\/div><div id=\"dt_text59177728673894\" class=\"dt_text\">\n<h3><span style=\"color: #0093d5;\">Generate a Data Set of Times to Failure for Subsequent Life Data Analysis in Weibull++<\/span><\/h3>\n<p>To generate a set of times-to-failure data that can be used for subsequent life data analysis, construct the flowchart shown below.<\/p>\n<\/div><div id=\"dt_image60\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/renoexr2_9.png\" alt=\"\"\/><\/div><\/div><\/div><div id=\"dt_column_61\" class=\"dt_column col-sm-1\"><\/div><\/div><\/div><\/div><div id=\"dt_row_62177728673885\" class=\"row dt_row\"><div id=\"dt_column_63\" class=\"dt_column col-sm-12\"><div id=\"dt_row_64177728673843\" class=\"row dt_row\"><div id=\"dt_column_65\" class=\"dt_column col-sm-1\"><\/div><div id=\"dt_column_66\" class=\"dt_column col-sm-5\"><div id=\"dt_text67177728673851\" class=\"dt_text\">Here, the result storage block is configured to store an array of the failure times obtained by the standard block, as shown next.<\/div><div id=\"dt_image68\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/Untitled-217.png\" alt=\"\"\/><\/div><\/div><\/div><div id=\"dt_column_69\" class=\"dt_column col-sm-5\"><div id=\"dt_text70177728673824\" class=\"dt_text\">\n<p class=\"caption\" style=\"text-align: left;\">Run 1,000 simulation with a seed of 1 for repeatability. Once the simulation completes, click the <b>Details<\/b> button in the RENO Simulation window to open the Simulation Results Explorer. Select the result storage block to display the stored values, as shown below.<\/p>\n<\/div><div id=\"dt_image71\" class=\"dt_image\"><div class=\"image-align-center\"><img decoding=\"async\"  class=\"img-responsive style-default\" src=\"http:\/\/www.safetyangel.com\/recdev\/wp-content\/uploads\/2016\/11\/Untitled-218.png\" alt=\"\"\/><\/div><\/div><div id=\"dt_text72177728673895\" class=\"dt_text\">You can transfer your data from RENO to a Weibull++ standard folio for further life data analysis by selecting the cells that contain the data and then clicking the <b>Send Selection to Weibull++<\/b> icon on the Ribbon.<\/div><\/div><div id=\"dt_column_73\" class=\"dt_column col-sm-1\"><\/div><\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"fullwidth.php","meta":{"footnotes":""},"class_list":["post-16325","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.safetyangel.com\/recdev\/wp-json\/wp\/v2\/pages\/16325","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.safetyangel.com\/recdev\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.safetyangel.com\/recdev\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.safetyangel.com\/recdev\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.safetyangel.com\/recdev\/wp-json\/wp\/v2\/comments?post=16325"}],"version-history":[{"count":13,"href":"http:\/\/www.safetyangel.com\/recdev\/wp-json\/wp\/v2\/pages\/16325\/revisions"}],"predecessor-version":[{"id":16349,"href":"http:\/\/www.safetyangel.com\/recdev\/wp-json\/wp\/v2\/pages\/16325\/revisions\/16349"}],"wp:attachment":[{"href":"http:\/\/www.safetyangel.com\/recdev\/wp-json\/wp\/v2\/media?parent=16325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}