{"id":652,"date":"2012-01-22T00:40:48","date_gmt":"2012-01-22T04:40:48","guid":{"rendered":"http:\/\/www.reliabilityanalytics.com\/blog\/?p=652"},"modified":"2012-09-21T09:18:57","modified_gmt":"2012-09-21T13:18:57","slug":"weibull-prediction-of-future-failures","status":"publish","type":"post","link":"https:\/\/reliabilityanalytics.com\/blog\/2012\/01\/22\/weibull-prediction-of-future-failures\/","title":{"rendered":"Weibull Prediction of Future Failures"},"content":{"rendered":"

This is an example of a recently published in the Reliability Analytics Toolkit called Weibull Prediction of Future Failures<\/a>. This tool is based on work described in references 1 and 2. For a population of N items placed on test, this tool calculates the expected number of failures for some future time interval based on the following two inputs:
\n1. the estimated Weibull shape parameter and
\n2. some number of failures (X>=1) during the initial time interval (t1<\/sub>).<\/p>\n

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

For example, if there are 20,000 items that have started operation at “time 0” and 8 have found to be in a failed state at the 3 year point.\u00a0 It is desired to estimate how many additional items will fail between the 3 and 10 year point.\u00a0 The figure below shows the inputs required.\u00a0 Although a single value could be entered for input #1, beta, three values separated by commas are entered for purposes of performing sensitivity analysis.\u00a0 It is estimated that the Weibull shape parameter is in the range of 3.0 to 3.6, with a typical value of 3.3.<\/p>\n

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

The resulting estimated number of failures is 413, assuming a Weibull shape parameter of 3.3, with a lower 90% bound of 206 failures and an upper bound of 753.\"\"<\/a><\/p>\n

The calculation of confidence limits in the above table depends on p and q being small. If p + q is greater than 0.10, confidence limits are not shown (references provide examples with p+q=0.03). p is the probability of item failure up to t1<\/sub>. Given that an item survives to t1<\/sub>, q is the probability of item failure from t1<\/sub> to t2<\/sub>. r is the probability of item survival to t2<\/sub>.
\np + q + r = 1.0 <\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

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

 <\/p>\n

References:<\/p>\n

    \n
  1. Nordman, D. J., & Meeker, W. Q. (2002). Weibull Prediction Intervals for a Future Number of Failures. Technometrics. 44, 15-23. <\/a>.<\/li>\n
  2. Nelson, W. (2000). Weibull prediction of a future number of failures. Quality and Reliability Engineering International. 16, 23-26. <\/a><\/li>\n
  3. Abernethy, Robert, The New Weibull Handbook Fifth Edition, Reliability and Statistical Analysis for Predicting Life, Safety, Supportability, Risk, Cost and Warranty Claims<\/a>\"\"<\/li>\n
  4. Nelson, Wayne, Applied Life Data Analysis (Wiley Series in Probability and Statistics)<\/a>\"\"<\/li>\n
  5. http:\/\/www.barringer1.com\/wdbase.htm<\/a>, database of typical Weibull shape and characteristic life parameters.<\/li>\n<\/ol>\n

     <\/p>\n","protected":false},"excerpt":{"rendered":"

    This is an example of a recently published in the Reliability Analytics Toolkit called Weibull Prediction of Future Failures. This tool is based on work described in references 1 and 2. For a population of N items placed on test, … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[42,50],"class_list":["post-652","post","type-post","status-publish","format-standard","hentry","category-weibull","tag-toolkit-examples","tag-weibull-distribution"],"_links":{"self":[{"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/posts\/652","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=652"}],"version-history":[{"count":7,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/posts\/652\/revisions"}],"predecessor-version":[{"id":660,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/posts\/652\/revisions\/660"}],"wp:attachment":[{"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/media?parent=652"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/categories?post=652"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/reliabilityanalytics.com\/blog\/wp-json\/wp\/v2\/tags?post=652"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}