On the Use of the K-Chart for Phase II Monitoring of Simple Linear Profiles

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left">Control chart </td><td align="center"><svg height="0.125" id="M157" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 5.7874999 0.125" width="5.7874999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
</svg>Number of OOC profiles </td><td align="center"> Performance rate </td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left"> K-chart</td><td align="center"> 6 </td><td align="center"> 66.67<svg height="11.75" id="M158" style="vertical-align:-0.4368pt" version="1.1" viewbox="0 0 12.975 11.75" width="12.975" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.15)"><path d="M594 629l-404 -661l-31 23l402 661zM194 635q70 0 107 -56t37 -125t-37.5 -125.5t-107.5 -56.5t-107 56.5t-37 124.5q0 70 37.5 126t107.5 56zM193 605q-28 0 -45 -29t-21.5 -59.5t-4.5 -62.5t4.5 -63t22 -60t45.5 -29q22 0 37.5 16t22 42t9 48t2.5 45q0 152 -72 152z
M567 351q69 0 106 -56t37 -125t-37 -125.5t-107 -56.5t-107.5 56.5t-37.5 124.5q0 43 14.5 83t49 69.5t82.5 29.5zM566 322q-28 0 -45 -28.5t-22 -59.5t-5 -64q0 -23 3 -46t10.5 -48.5t23 -41.5t36.5 -16q28 0 45 29.5t21 59.5t4 62q0 24 -2.5 46.5t-9.5 48.5t-22 42t-37 16
z" id="x25"></path></g>
</svg></td></tr><tr><td align="left"><svg height="15.8375" id="M159" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 17.775 15.8375" width="17.775" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z" id="x1D447"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.388,7.613)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg> chart</td><td align="center"> 1</td><td align="center"> 11.11<svg height="11.75" id="M160" style="vertical-align:-0.4368pt" version="1.1" viewbox="0 0 12.975 11.75" width="12.975" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.15)"><path d="M594 629l-404 -661l-31 23l402 661zM194 635q70 0 107 -56t37 -125t-37.5 -125.5t-107.5 -56.5t-107 56.5t-37 124.5q0 70 37.5 126t107.5 56zM193 605q-28 0 -45 -29t-21.5 -59.5t-4.5 -62.5t4.5 -63t22 -60t45.5 -29q22 0 37.5 16t22 42t9 48t2.5 45q0 152 -72 152z
M567 351q69 0 106 -56t37 -125t-37 -125.5t-107 -56.5t-107.5 56.5t-37.5 124.5q0 43 14.5 83t49 69.5t82.5 29.5zM566 322q-28 0 -45 -28.5t-22 -59.5t-5 -64q0 -23 3 -46t10.5 -48.5t23 -41.5t36.5 -16q28 0 45 29.5t21 59.5t4 62q0 24 -2.5 46.5t-9.5 48.5t-22 42t-37 16
z" id="x25"></path></g>
</svg></td></tr><tr><td align="left">R-chart</td><td align="center"> 1 </td><td align="center"> 11.11<svg height="11.75" id="M161" style="vertical-align:-0.4368pt" version="1.1" viewbox="0 0 12.975 11.75" width="12.975" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.15)"><path d="M594 629l-404 -661l-31 23l402 661zM194 635q70 0 107 -56t37 -125t-37.5 -125.5t-107.5 -56.5t-107 56.5t-37 124.5q0 70 37.5 126t107.5 56zM193 605q-28 0 -45 -29t-21.5 -59.5t-4.5 -62.5t4.5 -63t22 -60t45.5 -29q22 0 37.5 16t22 42t9 48t2.5 45q0 152 -72 152z
M567 351q69 0 106 -56t37 -125t-37 -125.5t-107 -56.5t-107.5 56.5t-37.5 124.5q0 43 14.5 83t49 69.5t82.5 29.5zM566 322q-28 0 -45 -28.5t-22 -59.5t-5 -64q0 -23 3 -46t10.5 -48.5t23 -41.5t36.5 -16q28 0 45 29.5t21 59.5t4 62q0 24 -2.5 46.5t-9.5 48.5t-22 42t-37 16
z" id="x25"></path></g>
</svg></td></tr><tr><td align="left">EWMA chart</td><td align="center"> 0 </td><td align="center"> 0.00<svg height="11.75" id="M162" style="vertical-align:-0.4368pt" version="1.1" viewbox="0 0 12.975 11.75" width="12.975" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.15)"><path d="M594 629l-404 -661l-31 23l402 661zM194 635q70 0 107 -56t37 -125t-37.5 -125.5t-107.5 -56.5t-107 56.5t-37 124.5q0 70 37.5 126t107.5 56zM193 605q-28 0 -45 -29t-21.5 -59.5t-4.5 -62.5t4.5 -63t22 -60t45.5 -29q22 0 37.5 16t22 42t9 48t2.5 45q0 152 -72 152z
M567 351q69 0 106 -56t37 -125t-37 -125.5t-107 -56.5t-107.5 56.5t-37.5 124.5q0 43 14.5 83t49 69.5t82.5 29.5zM566 322q-28 0 -45 -28.5t-22 -59.5t-5 -64q0 -23 3 -46t10.5 -48.5t23 -41.5t36.5 -16q28 0 45 29.5t21 59.5t4 62q0 24 -2.5 46.5t-9.5 48.5t-22 42t-37 16
z" id="x25"></path></g>
</svg></td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Performance evaluation of control charts in detecting OOC profiles.

Journal of Quality and Reliability Engineering

tab2

Table 2

Table 2: On the Use of the K-Chart for Phase II Monitoring of Simple Linear Profiles 