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<h2 class="hd hd-2 unit-title">5.1 Limitations of mean first order reliability method</h2>
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<h2 class="hd hd-2 unit-title">5.2 Geometry interpretation of the reliability index</h2>
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<h2 class="hd hd-2 unit-title">5.3 Solve reliability index in the u space</h2>
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<h3 class="hd hd-2">Video</h3>
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<h2 class="hd hd-2 unit-title">5.4 Solve reliability index in the n space</h2>
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<h2 class="hd hd-2 unit-title">Chapter 5 Homework</h2>
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<p style="margin: 0in; text-align: justify; text-justify: inter-ideograph;"><b><span style="font-family: 'Times New Roman',serif;">Problem: </span></b><span style="font-family: 'Times New Roman',serif; mso-bidi-font-weight: bold;">Suppose </span><i style="mso-bidi-font-style: normal;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian; mso-bidi-font-weight: bold;">g</span></i><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian; mso-bidi-font-weight: bold;">(<i style="mso-bidi-font-style: normal;">x</i>, <i style="mso-bidi-font-style: normal;">y</i>)</span><span style="font-family: 'Times New Roman',serif; mso-bidi-font-weight: bold;"> is a function of <i style="mso-bidi-font-style: normal;">x</i> and <i style="mso-bidi-font-style: normal;">y</i> as follows:<o:p></o:p></span></p>
<p align="center" style="margin: 0in; text-align: center;"><i style="mso-bidi-font-style: normal;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian; mso-bidi-font-weight: bold;">g</span></i><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian; mso-bidi-font-weight: bold;">(<i style="mso-bidi-font-style: normal;">x</i>, <i style="mso-bidi-font-style: normal;">y</i>) = <i style="mso-bidi-font-style: normal;">x</i><sup>2</sup>+<i style="mso-bidi-font-style: normal;">xy</i>-<i style="mso-bidi-font-style: normal;">y</i><o:p></o:p></span></p>
<p style="margin: 0in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian; mso-bidi-font-weight: bold;">where the mean and standard deviation values of<i> x</i> and <i>y</i> are:<o:p></o:p></span></p>
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<p align="center" style="margin: 0in; text-align: center;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian;"><o:p> </o:p></span></p>
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<p align="center" style="margin: 0in; text-align: center;"><i style="mso-bidi-font-style: normal;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian;">x<o:p></o:p></span></i></p>
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<p align="center" style="margin: 0in; text-align: center;"><i style="mso-bidi-font-style: normal;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian;">y<o:p></o:p></span></i></p>
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<p align="center" style="margin: 0in; text-align: center;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian;">Mean<o:p></o:p></span></p>
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<p align="center" style="margin: 0in; text-align: center;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian;">2<o:p></o:p></span></p>
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<p align="center" style="margin: 0in; text-align: center;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian;">3<o:p></o:p></span></p>
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<p align="center" style="margin: 0in; text-align: center;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian;">Std.<o:p></o:p></span></p>
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<p align="center" style="margin: 0in; text-align: center;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian;">1<o:p></o:p></span></p>
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<p align="center" style="margin: 0in; text-align: center;"><span style="font-family: 'Times New Roman',serif; mso-fareast-font-family: DengXian;">1<o:p></o:p></span></p>
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<p class="MsoNormal" style="text-indent: 24.0pt; mso-char-indent-count: 2.0;">Assume the correlation coefficient between <i style="mso-bidi-font-style: normal;">x</i> and <i style="mso-bidi-font-style: normal;">y</i> is -0.5. Let g(x,y) < 0 denote failure. <span style="mso-spacerun: yes;"> </span>Using AFORM, work out the answers to the following questions<o:p></o:p></p>
<p class="MsoNoSpacing" style="margin-left: 0in; mso-para-margin-left: 0gd; text-indent: 24.0pt; mso-char-indent-count: 2.0; mso-list: l0 level1 lfo1;"><!-- [if !supportLists]--><span style="mso-no-proof: yes;"><span style="mso-list: Ignore;">(1)<span style="font: 7.0pt 'Times New Roman';"> </span></span></span><!--[endif]--><span style="mso-no-proof: yes;">the reliability index<o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left: 0in; mso-para-margin-left: 0gd; text-indent: 24.0pt; mso-char-indent-count: 2.0; mso-list: l0 level1 lfo1;"><!-- [if !supportLists]--><span style="mso-no-proof: yes;"><span style="mso-list: Ignore;">(2)<span style="font: 7.0pt 'Times New Roman';"> </span></span></span><!--[endif]--><span style="mso-no-proof: yes;">failure probability<o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left: 0in; mso-para-margin-left: 0gd; text-indent: 24.0pt; mso-char-indent-count: 2.0; mso-list: l0 level1 lfo1;"><!-- [if !supportLists]--><span style="mso-no-proof: yes;"><span style="mso-list: Ignore;">(3)<span style="font: 7.0pt 'Times New Roman';"> </span></span></span><!--[endif]--><span style="mso-no-proof: yes;">design point in the reduced space<o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left: 0in; mso-para-margin-left: 0gd; text-indent: 24.0pt; mso-char-indent-count: 2.0; mso-list: l0 level1 lfo1;"><!-- [if !supportLists]--><span style="mso-no-proof: yes;"><span style="mso-list: Ignore;">(4)<span style="font: 7.0pt 'Times New Roman';"> </span></span></span><!--[endif]--><span style="mso-no-proof: yes;">design point in the original space<o:p></o:p></span></p>
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