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

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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

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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

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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 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

N 12.63

N 12.47

N 10.60

N 9.50