Civil cost Optimization of Risk Reduction (Step 12)

The study is carried out in 2005
A maintenance scenario A comprises of one task that is executed every 3 years, starting in 2006.
If carried out in 2005 the task would cost 10 kUSD
The estimated annual inflation rate is 2% (this is an example)
The maintenance plan is optimized over 13 years up to 2019

The table below gives the expected cost for each year that the task is conducted.

Expected Task cost for first maintenance scenario:

Year	Cost (USD)	Discount Factor (-)	Discount Cost (USD)	Cumulative Discount Cost (USD)
2006	10,000	0.93	9,300	9,300
2009	10,000	0.76	7,600	16,900
2012	10,000	0.62	6,200	23,100
2015	10,000	0.51	5,100	28,200
2018	10,000	0.41	4,100	32,300

A second maintenance scenario comprises of one task that is executed every 6 years, starting in 2006 so that the asset can realize its remnant life of 13 years.
If carried out in 2005 the task would cost 65 kUSD
The estimated annual inflation rate is 2% (this is an example)
The maintenance plan is optimized over 14 years up to 2019

The following table gives the expected cost for each year that the task is conducted.

Expected Task cost for second maintenance scenario:

Year	Cost (USD)	Discount Factor (-)	Discount Cost (USD)	Cumulative Discount Cost (USD)
2006	45,000	0.93	41,850	41,850
2012	45,000	0.62	27,900	69,750
2018	45,000	0.41	18,450	88,200

The total cost of the damages caused by the age-related failure are estimated in the range of 1M to 10M USD, this means that 1M USD is taken for calculation purposes
The remnant life is 10 – 15 years, this means that 13 years is taken as the remnant life for calculation purposes.
The likelihood of failure is estimated in the range of 0.1 to 1% (a likelihood rating of C) this means that 1% is taken for calculation purposes.

Likelihood Matrix - to calculate Risk Likelihood class for AR FMs.

Likelihood vs probability of the design condition:

A	B	C	D	E
Never heard of in the industry	Heard of in the industry	Has happened in the organization or more than once in the industry	Has happened at the location or more than once in the organization	Has happened more than once in the location
< 0.01%	< 0.1%	<1%	<10%	<100%
Less than once in 10,000 yrs	One in 1,000 to one in 10,000 yrs	One in 100 to one in 1,000 yrs	One in 10 to one in 100 yrs	Annually to once in 10 yrs
We would be greatly amazed to see it happen	We would think it unusual	We would not be surprised to see it happen

The following table gives an overview of the Consequence of Failure for the likelihood rating C that is cumulatively discounted cost over time.

Consequence of Failure for the likelihood rating C:

Year	Consequence of Failure (USD)	Likelihood of Failure (%)	Annual Cost (USD)	Discount Factor (-)	Discount Annual Cost (USD)	Cumulative Discount Cost (USD)
2006	1,300,000	1	13,000	0.93	12,090	12,090
2007	1,300,000	1	13,000	0.87	11,310	23,400
2008	1,300,000	1	13,000	0.82	10,660	34,060
2009	1,300,000	1	13,000	0.76	9,880	43,940
2010	1,300,000	1	13,000	0.71	9,230	53,170
2011	1,300,000	1	13,000	0.67	8,710	61,880
2012	1,300,000	1	13,000	0.62	8,060	69,940
2013	1,300,000	1	13,000	0.58	7,540	77,480
2014	1,300,000	1	13,000	0.54	7,020	84,500
2015	1,300,000	1	13,000	0.51	6,630	91,130
2016	1,300,000	1	13,000	0.48	6,240	97,370
2017	1,300,000	1	13,000	0.44	5,720	103,090
2018	1,300,000	1	13,000	0.41	5,330	108,420
2019	1,300,000	1	13,000	0.39	5,070	113,490

The maintenance scenario A improves the likelihood rating to B while the maintenance scenario B can improve the likelihood rating to A.

The table gives an overview of the Consequence of Failure for the likelihood rating B in the range of 0.01% to 0.1% that is cumulatively discounted cost over time. For calculation purposes, 0.1% is used.

Consequence of Failure for the likelihood rating B:

Year	Consequence of Failure (USD)	Likelihood of Failure (%)	Annual Cost (USD)	Discount Factor (-)	Discount Annual Cost (USD)	Cumulative Discount Cost (USD)
2006	1,300,000	0.1	1,300	0.93	1,209	1,209
2007	1,300,000	0.1	1,300	0.87	1,131	2,340
2008	1,300,000	0.1	1,300	0.82	1,066	3,406
2009	1,300,000	0.1	1,300	0.76	988	4,394
2010	1,300,000	0.1	1,300	0.71	923	5,317
2011	1,300,000	0.1	1,300	0.67	871	6,188
2012	1,300,000	0.1	1,300	0.62	806	6,994
2013	1,300,000	0.1	1,300	0.58	754	7,748
2014	1,300,000	0.1	1,300	0.54	702	8,450
2015	1,300,000	0.1	1,300	0.51	663	9,113
2016	1,300,000	0.1	1,300	0.48	624	9,737
2017	1,300,000	0.1	1,300	0.44	572	10,309
2018	1,300,000	0.1	1,300	0.41	533	10,842
2019	1,300,000	0.1	1,300	0.39	507	11,349

The RAE for maintenance scenario A = $32, 300

(113,490-11,349)

= 0.316

The table gives an overview of the Consequence of Failure for the likelihood rating A for < 0.01% that is cumulatively discounted cost over time. For calculation purposes, 0.01% is used.

Consequence of Failure for the likelihood rating A:

Year	Consequence of Failure (USD)	Likelihood of Failure (%)	Annual Cost (USD)	Discount Factor (-)	Discount Annual Cost (USD)	Cumulative Discount Cost (USD)
2006	1,300,000	0.01	130	0.93	121	121
2007	1,300,000	0.01	130	0.87	113	234
2008	1,300,000	0.01	130	0.82	107	341
2009	1,300,000	0.01	130	0.76	99	439
2010	1,300,000	0.01	130	0.71	92	532
2011	1,300,000	0.01	130	0.67	87	619
2012	1,300,000	0.01	130	0.62	81	699
2013	1,300,000	0.01	130	0.58	75	775
2014	1,300,000	0.01	130	0.54	70	845
2015	1,300,000	0.01	130	0.51	66	911
2016	1,300,000	0.01	130	0.48	62	974
2017	1,300,000	0.01	130	0.44	57	1,031
2018	1,300,000	0.01	130	0.41	53	1,084
2019	1,300,000	0.01	130	0.39	51	1,135

The RAE for maintenance scenario B = $88,200

(113,490-1,135)

= 0.785

The results show that even though maintenance scenario B would reduce the risk of failure significantly, it is less economical than maintenance scenario A. Note that this does not take management attention, workload of personnel and plant logistics into account.

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