* td *β

(D-4)

α

where time *t *is in years. The Weibull hazard function becomes

β -1

β *td *

(D-5)

α α

(4) For this example, the electric motors were considered electrical devices and are not included in

this reliability analysis. They are evaluated in the electrical analysis. The mechanical system was

considered to begin at the first coupling. The reliability for the miter gate machinery model of Figure D-4

at time *t *is calculated as

RSYS(*t*) = RA(*t*)3 * RB(*t*)2 * RC(*t*) * RD(*t*) * RE(*t*)2 * RF(*t*)2 * RG(*t*)2

(D-6)

(5) The reliability for the tainter valve machinery model of Figure D-5 is calculated as

RSYS(*t*) = RA(*t*)4* RB(*t*)2* RC(*t*) * RD(*t*) * RE(*t*)4 * RF(*t*)3

(D-7)

The tainter valve hoist drums and wire rope were not modeled because no failure data were available.

Also, these items are organized in parallel so their combined reliability value is much higher than the

other components.

system was considered a series model since the unreliability of one component will cause the entire

system to be inoperable. The duty factor for dam equipment is not directly related to the number of

lockages. The duty factor was determined as follows:

Assume 2 gate changes per day at 5 min each.

d = (2*5)min/day*365 days/year/60/8760 hrs/year = 0.007

The dam gate system reliability calculation is similar to that for the lock machinery:

RSYS(*t*) = RA(*t*) * RB(*t*)10 * RC(*t*) * RD(*t*)4 * RE(*t*)16 * RF(*t*)6 * RG(*t*)4

(D-8)

systems for 50 years of service are contained in spreadsheet format in Tables D-5 and D-6, respectively.

The values in the tables are shown rounded to the nearest four decimal places; however, they are not

rounded for the mathematical analysis. As a result, some components show a reliability value of 1.0 in

future years when their hazard rates are nonzero. The system reliability for the miter gate and valve

machinery drops to 41 and 33 percent, respectively, after 50 years. It should be noted that the brakes and

the gear reducers have the highest hazard rates, which indicates a higher susceptibility to failure. The

electric motors for this analysis were considered electrical equipment and are not included in the

mechanical analyses.