An automatic machine turns out round$-$head bolts with a specified shank diameter of $9\mathrm{.}00+-0\mathrm{.}04$ mm$.$ The process has been operating in control at an estimated $\backslash$mu $($Average$)$ of $9\mathrm{.}0$ mm and an $($R$-$bar$)$ of $0\mathrm{.}0206$ mm$.$ The subgroup size is four. Calculate the control limits for R chart.

R$-$chart

UCL $=$ D$4$ x R$-$bar

LCL $=$ D$3$ x R$-$bar

a$.$ UCL is $0\mathrm{.}0529$ mm and LCL is $0\mathrm{.}0000$ mm

b$.$ UCL is $0\mathrm{.}0435$ mm and LCL is $0\mathrm{.}0016$ mm

c$.$ UCL is $0\mathrm{.}0673$ mm and LCL is $0\mathrm{.}0029$ mm

d$.$ UCL is $0\mathrm{.}0469$ mm and LCL is $0\mathrm{.}0000$ mm