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The exponential distribution is a commonly used distribution in reliability engineering. Mathematically, it is a fairly simple distribution, which many times leads to its use in inappropriate situations. It is, in fact, a special case of the Weibull distribution where <math>\beta =1</math>. The exponential distribution is used to model the behavior of units that have a constant failure rate (or units that do not degrade with time or wear out). 
#REDIRECT [[The Exponential Distribution]]
{{Exponential Probability Density Function}}
 
{{Exponential Statistical Properties}}
 
{{Characteristics of the Exponential Distribution}}
 
==Estimation of the Exponential Parameters==
{{Probability Plotting Exponential Distribution }}
 
{{Rank Regression on Y for Exponential Distribution}}
 
{{Rank Regression on X for Exponential Distribution}}
 
{{Maximum Likelihood Estimation for Exponential Distribution}}
 
{{Confidence Bounds}}
 
{{Bayesian Confidence Bounds ED}}
 
==General Examples==
 
{{Example 8: Exponential Dstribution for Grouped Data}}
 
===Example 9===
A number of leukemia patients were treated with either drug 6 MP or a placebo, and the times in weeks until cancer symptoms returned were recorded. Analyze each treatment separately. [21, p.175]
 
 
{|align="center" border=1 cellspacing=0
|-
|colspan="4" style="text-align:center"|Table 7.3 - Leukemia Treatment Results
|-
!Time  (weeks)
!Number of Patients
!Treament
!Comments
|-
|1 ||2 ||placebo ||
|-
|2 ||2 ||placebo ||
|-
|3 ||1 ||placebo ||
|-
|4 ||2 ||placebo ||
|-
|5 ||2 ||placebo ||
|-
|6 ||4 ||6MP ||3 patients completed
|-
|7 ||1 ||6MP ||
|-
|8 ||4 ||placebo ||
|-
|9 ||1 ||6MP ||Not completed
|-
|10 ||2 ||6MP ||1 patient completed
|-
|11 ||2 ||placebo ||
|-
|11 ||1 ||6MP ||Not completed
|-
|12 ||2 ||placebo ||
|-
|13 ||1 ||6MP ||
|-
|15 ||1 ||placebo ||
|-
|16 ||1 ||6MP ||
|-
|17 ||1 ||placebo ||
|-
|17 ||1 ||6MP ||Not completed
|-
|19 ||1 ||6MP ||Not completed
|-
|20 ||1 ||6MP ||Not completed
|-
|22 ||1 ||placebo ||
|-
|22 ||1 ||6MP ||
|-
|23 ||1 ||placebo ||
|-
|23 ||1 ||6MP ||
|-
|25 ||1 ||6MP ||Not completed
|-
|32 ||2 ||6MP ||Not completed
|-
|34 ||1 ||6MP ||Not completed
|-
|35 ||1 ||6MP ||Not completed
|}
 
 
'''Solution to Example 9'''
 
Enter the data into Weibull++, by selecting '''Times to Failure, with Right Censored Data (Suspensions)''' and '''with Grouped Observations''. In the first column enter the number of patients. Whenever there are uncompleted tests, enter the number of patients who completed the test separately from the number of patients who did not. In the second column enter F for completed tests and S for uncompleted. In the third column enter the time. In the fourth column (Subset ID) enter the name of the treatment. The title of each column can be changed by double-clicking it and typing the desired name.
 
 
[[Image:weibullplacebofolio.png|thumb|center|400px|]]
 
 
Now click the '''Batch Auto Run''' icon
 
 
[[Image:batchautorun.png|thumb|center|300px|]]
 
::or:
 
[[Image:batchautorunicon.png|thumb|center|300px|]]
 
 
and click Select All Available> > to separate the 6 MP drug from the placebo as shown next.
 
 
[[Image:BARsheet.png|thumb|center|350px|]]
 
 
Click OK and you will get a new Data Sheet for each treatment with the corresponding results, as shown next.
 
 
{|style= align="center" border="1"
|-
|[[Image:BAR6mp.png|thumb|center|400px|]]||[[Image:BARplacebo.png|thumb|center|400px|]]
|}
 
 
Make sure both data sheets are calculated, then from the Life Data tab, click on Insert Additional Plot. Click on the Select Data Sheets button.
 
[[Image:insertadditionalplot.png|thumb|center|300px|]]
 
 
 
[[Image:selectdatasheets.png|thumb|center|300px|]]
 
 
and check the two data sheets under the Folio1 project.
 
 
The plot is shown next,
 
 
[[Image:multipleplotsheet.png|thumb|center|400px|]]

Latest revision as of 10:10, 9 August 2012

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