Results Existing Method  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 ${C}_{i}$ = N 700.00 ${C}_{g}$ = N 400.00 ${C}_{i}$ = N 700.00 ${C}_{g}$ = N 400.00 $E\left({C}_{V}^{i}\right)$ = N 580.38 $E\left({C}_{V}^{g}\right)$ = N 324.47 $E\left({C}_{V}^{i}\right)=533.34$ $E\left({C}_{V}^{g}\right)=354.76$ Average Cost of Individual Repl. Policy per period ${A}_{\left(n\right)}^{i}$ = N55,300.00 ${A}_{\left(n\right)}^{i}$ = N 54,600.00 $E\left[{A}_{\left(n\right)}^{i}\right]$ = N 46,427.20 $E\left[{A}_{\left(n\right)}^{i}\right]$ = N 41,600.52 Average Cost of Group Repl. Policy per period ${A}_{\left(n\right)}^{g}$ = N 57,000.00 ${A}_{\left(n\right)}^{g}$ = N 54,450.00 $E\left[{A}_{\left(n\right)}^{g}\right]$ = N 49,4538.00 $E\left[{A}_{\left(n\right)}^{g}\right]$ = N 50,441.00 Appropriate time to replace failed LED bulbs After every 8th period (i.e., after every 39,420 burning hours) After every 6th period (i.e., after every 30,660 burning hours) After every 7th period (i.e., after every 35,040 burning hours) After every 6th 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 N 12.63 N 12.47 N 10.60 N 9.50