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===ACME Example===
<noinclude>{{Banner ALTA Examples}}</noinclude>
ACME manufacturing has implemented an accelerated testing program for their new design. A total of 40 units were tested at four different pressure levels. The operating stress level is 170 psi.
ACME manufacturing has implemented an accelerated life testing program for their new product design. A total of 40 units were tested at four different pressure levels. The operating stress level is 170 psi. The following table shows the data from the test. Determine the parameters of the inverse power law Weibull model and obtain the use level probability plot with 90% 2-sided confidence bounds on time.


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!Stress Level, psi
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Do the following:
1) Determine the parameters of the inverse power law Weibull model.
2) Obtain the use level probability plot with 90% 2-sided confidence bounds on time.
3) Obtain the Life vs. Stress plot with 90% 2-sided confidence bounds.
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====Solution====




1) The parameters of the IPL-Weibull model are estimated to be:  
The parameters of the IPL-Weibull model are estimated to be:  




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2) The use level probability plot is shown next.
The use level probability plot is shown next.
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[[Image:new_7.gif|thumb|center|500px|The probability plot at a use stress level.]]
[[Image:new_7.gif|center|550px|The probability plot at a use stress level.]]
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The confidence bounds on time are the Type 1 bounds (Time Bounds) in ALTA.


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In ALTA, the confidence bounds on time are the Type 1 bounds (Time Bounds).
[[Image:new_9.gif|thumb|center|500px|The probability plot at a use stress level with 90% Type I confidence bounds.]]
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3) Similarly, the Life vs. Stress plot with the confidence bounds can be obtained.


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[[Image:new_9.gif|center|550px|The probability plot at a use stress level with 90% Type I confidence bounds.]]

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ACME manufacturing has implemented an accelerated life testing program for their new product design. A total of 40 units were tested at four different pressure levels. The operating stress level is 170 psi. The following table shows the data from the test. Determine the parameters of the inverse power law Weibull model and obtain the use level probability plot with 90% 2-sided confidence bounds on time.


Stress Level, psi 220 psi 230 psi 240 psi 250 psi
165 93 72 26
177 106 73 44
238 156 99 63
290 170 124 68
Times-to-failure, hr 320 185 134 69
340 214 150 72
341 220 182 77
380 236 186 96
449 252 190 131
544 288 228 140


The parameters of the IPL-Weibull model are estimated to be:


[math]\displaystyle{ \begin{align} \beta =\ & 3.009236 \\ K=\ & 3.267923E-27 \\ n=\ & 10.218104 \end{align} }[/math]


The use level probability plot is shown next.


The probability plot at a use stress level.


In ALTA, the confidence bounds on time are the Type 1 bounds (Time Bounds).


The probability plot at a use stress level with 90% Type I confidence bounds.
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