Results  Existing Method [7]  Proposed Method  
Data Sets  Data Set I  Data Set II  Data Set I  Data Set II 
Fitted Probability Distribution for failure times  …  …  Smallest Extreme Value (or Gumbel) with: $\begin{array}{l}\mu =34.25888\\ \sigma =34.11878\end{array}$  Laplace with: $\begin{array}{l}\theta =5183.0120\\ \varphi =94.2625\end{array}$ 
Fitted Distribution for Individual Replacement Cost  …  …  Gamma with: $\begin{array}{l}\alpha =13.68094\\ \beta =42.42969\end{array}$  Largest Extreme Value with: $\begin{array}{l}\mu =501.57496\\ \sigma =55.02559\end{array}$ 
Fitted Distribution for Group Replacement Cost  …  …  Lognormal with: $\begin{array}{l}\mu =5.76867\\ \sigma =0.16455\end{array}$  Weibull with: $\begin{array}{l}\alpha =159.14436\\ \beta =1.68840\end{array}$ 
Expected Cost of Replacement  ${C}_{i}$ = ${C}_{g}$ =  ${C}_{i}$ = ${C}_{g}$ =  $E\left({C}_{V}^{i}\right)$ = $E\left({C}_{V}^{g}\right)$ =  $E\left({C}_{V}^{i}\right)=533.34$ $E\left({C}_{V}^{g}\right)=354.76$ 
Average Cost of Individual Repl. Policy per period  ${A}_{\left(n\right)}^{i}$ =  ${A}_{\left(n\right)}^{i}$ =  $E\left[{A}_{\left(n\right)}^{i}\right]$ =  $E\left[{A}_{\left(n\right)}^{i}\right]$ = 
Average Cost of Group Repl. Policy per period  ${A}_{\left(n\right)}^{g}$ =  ${A}_{\left(n\right)}^{g}$ =  $E\left[{A}_{\left(n\right)}^{g}\right]$ =  $E\left[{A}_{\left(n\right)}^{g}\right]$ = 
Appropriate time to replace failed LED bulbs  After every 8^{th} period (i.e., after every 39,420 burning hours)  After every 6^{th} period (i.e., after every 30,660 burning hours)  After every 7^{th} period (i.e., after every 35,040 burning hours)  After every 6^{th} period (i.e., after every 30,660 burning hours) 
Expected Life of an LED bulb  9.1109 hours  7.5307 hours  9.03971 hours  7.53074 hours 
Average No. of replaced bulbs  79 bulbs  78 bulbs  80 bulbs  78 bulbs 
Average cost of individual replacement per hour 



