{"id":678,"date":"2012-06-14T21:22:45","date_gmt":"2012-06-15T01:22:45","guid":{"rendered":"http:\/\/www.reliabilityanalytics.com\/blog\/?p=678"},"modified":"2014-03-01T11:35:54","modified_gmt":"2014-03-01T15:35:54","slug":"estimating-average-failure-rate-based-on-l10-life","status":"publish","type":"post","link":"https:\/\/reliabilityanalytics.com\/blog\/2012\/06\/14\/estimating-average-failure-rate-based-on-l10-life\/","title":{"rendered":"Estimating MTBF Based on L10 Life"},"content":{"rendered":"

The Reliability Analytics Toolkit L10 to MTBF Conversion tool<\/a>\u00a0provides a quick and easy way to convert a quoted L10%<\/sub>\u00a0life to an average failure rate (or MTBF), provided that an educated guess can be made regarding a Weibull shape parameter\u00a0(\u03b2). For example, an L10%<\/sub>\u00a0life of 15,500 hours is shown in the Weibull probability plot \u00a0below (green line). For a population of these devices, what average failure rate should be used? \u00a0The average failure\u00a0depends on the underlying failure distribution and any renewal that may take place over time. With an\u00a0L10%<\/sub>\u00a0life\u00a0and an estimate for the Weibull shape parameter, \u03b2, the underlying failure distribution is completely defined. \u00a0For example, if the L10%<\/sub>\u00a0life is quoted as 15,500 hours and\u00a0\u03b2 is estimated to be 2.15, the Weibull characteristic life (\u03b7)\u00a0has to be approximately 44,000 hours\u00a0(red dot). This is because defining \u03b2 defines the slope of the line in the Weibull plot below. \u00a0So, if know one point (L10 life) and the slope, you can determine any other point. \u00a0Of special interest is the Weibull characteristic life. \u00a0The characteristic life is the point where 63.2% percent of the population will fail, regardless of the Weibull shape parameter\u00a0\u03b2. Therefore, defining L10% <\/sub>life and \u03b2\u00a0defines \u03b7, and thus the underlying\u00a0Weibull failure distribution.<\/p>\n

\"\"<\/a><\/p>\n

In the\u00a0L10 to MTBF Conversion tool<\/a>, enter the estimated\u00a0\u03b2 value of 2.15, the given\u00a0L10%<\/sub>\u00a0life of 15,500 hours, and any maintenance interval for item renewal. The renewal time is that time when the item is renewed to “as good as new.”<\/p>\n

\"\"<\/a><\/p>\n

The resulting average failure rate is then output, as shown in the picture below. For these inputs, the hazard varies between 0 at “time zero” to approximately 45 at the five year point, with average failure rate of 18.77 FPMH. The item is renewed at five years and the process starts over again.<\/p>\n

\"\"<\/a><\/p>\n

Thus, a 15,500 hour L10%<\/sub>\u00a0life translates into approximately a 50,000 hour MTBF, assuming a \u00a0five year renewal process.<\/p>\n

 <\/p>\n

References:<\/p>\n

    \n
  1. Bazovsky, Igor,\u00a0Reliability Theory and Practice<\/a><\/li>\n
  2. http:\/\/www.barringer1.com\/wdbase.htm<\/a>, database of typical Weibull shape and characteristic life parameters.<\/li>\n
  3. 3. O\u2019Connor, Patrick, D. T.,\u00a0Practical Reliability Engineering<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    The Reliability Analytics Toolkit L10 to MTBF Conversion tool\u00a0provides a quick and easy way to convert a quoted L10%\u00a0life to an average failure rate (or MTBF), provided that an educated guess can be made regarding a Weibull shape parameter\u00a0(\u03b2).<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[59,55],"tags":[56,30,70,26,42,50],"class_list":["post-678","post","type-post","status-publish","format-standard","hentry","category-reliability-modeling","category-system-modeling","tag-failure-modeling","tag-failure-rate","tag-l10-life-mtbf","tag-mtbf","tag-toolkit-examples","tag-weibull-distribution"],"_links":{"self":[{"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/posts\/678","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/comments?post=678"}],"version-history":[{"count":26,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/posts\/678\/revisions"}],"predecessor-version":[{"id":698,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/posts\/678\/revisions\/698"}],"wp:attachment":[{"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/media?parent=678"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/categories?post=678"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/tags?post=678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}