可靠度相关MTBF计算

,,,,,,,,,,6000,10,30,,

,,"6000台产品,每天工作10小时,工作一个月后有6台失效,MTBF是30W小时",,,,,,,,,,1800000,,

,,"1000台产品,每天工作24小时,工作一个月后有0.5台失效,MTBF是144W小时",,,,,,,,,,6,300000,2.920%

,,"即当1000台产品,每天工作24小时,连续工作一个月,要使其MTBF为30W时,需使其失效率高于2.4台",,,,,,,,,,,,使用一年100台有2.92台故障

计算方法一:,,,,,,,,,,1000,24,30,,

,,,,,,,,,,,,720000,,

,1Fit=1/109小时,,意为：109小时坏了1台，失效率为1Fit,,,,,,,,,0.5,1440000,0.608%

,,,,,,,,,,,,,,使用一年100台有0.608台故障

1）,6000台*10小时*30天=1800000台时，一个月内坏了6台,,,,,,,,,,,,,

,λ=6/180W,,MTBF=180W/6=30W小时,,,,,,,,,,,

2）,1000台*24小时*30天=720000台时，一个月内坏了0.5台,,,,,,,,,,,,,

,λ=0.5/72W,,MTBF=72W/0.5=144W小时,,,,,,,,,,,

,,,,,,,,,,,,3.1%,,

3),6/180==2.4/72,,,,,,,,,,,,,

,也就是说180W台时内坏了6台与72W内坏了2.4台是等效的.,,,,,,,,,,,,,

计算方法二:,,,,,,,,,,,,,,

,,,㈠,,,,㈡,,,,,㈢,,

,,n=,6000,,,n=,1000,,,,n=,1000,,

,,t*=,300,,,t*=,720,,,,t*=,720,,

,,r=,6,,,r=,0.5,,,,r=,2.4,,

,,,,公式：,,,,,,,,,,

,可靠度：,R（t)=,0.999,=(6000-6)/6000,,R（t)=,0.9995,=(1000-0.5)/1000,,,R（t)=,0.9976,,

,,,,,,,,,,,,,,,

,,,0.9990005,R(t)=e-λt,,,0.999500125,R(t)=e-λt,,,,0.997602878,,

,,,,,,,,,,,,,,,

,,MTBF=,300000,,,MTBF=,1440000,,,,MTBF=,300000,,

,,即当MTBF=30W时，上面两个相等）,,,,即当MTBF=144W时，上面两个相等）,,,,,"即当1000台工作坏了2.4台时,MTBF=30W",,,

计算方法三:,,,,,,,,,,,,,,

,"有20件产品经受有更换试验,试验一直进行到发生10次故障,第10次在第80小时发生,试确定MTBF值？",,,,,,,,,,,,,

,的95%单侧和双侧置信区间?,,,,,,,,,,,,,

,,,,,,㈠,,,,㈡,,,㈢,

,例：,n=,20,,n=,6000,,,n=,1000,,n=,1000,

,,t*=,80,,t*=,300,,,t*=,720,,t*=,720,

,,r=,10,,r=,6,,,r=,0.5,,r=,2.4,

,,置信水平:,0.95,,置信水平:,0.95,,,置信水平:,0.95,,置信水平:,0.95,

,,a=,0.05,,a=,0.05,,,a=,0.05,,a=,0.05,

,,2r=,20,,2r=,12,,,2r=,1,,2r=,4.8,

,,T=nt*,1600,,T=nt*,1800000,,,T=nt*,720000,,T=nt*,720000,

,解:,,,,,,,,,,,,,

,,MTBF=nt*/r=,160,小时,MTBF=nt*/r=,300000,小时,,MTBF=nt*/r=,1440000,小时,MTBF=nt*/r=,300000,

,双侧置信下限=,,93.65047743,,,154263.6932,,,,286630.6971,,,129225.7866,

,双侧置信上限=,,333.6538707,,,817477.9498,,,,1466291908,,,2972635.914,

,,,,,即我们有95%的把握确保真实的MTBF处于15W及81W之间,,,,即我们有95%的把握确保真实的MTBF处于28W及146W之间,,,,,

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,,横线之上为338计算，横线之下为cliffcrag验证。,,,,,,,,,,,,

,338计算方法三的第㈠点,,,㈠0.6双侧置信限,,,,㈠0.6单侧置信限,,,,,,

,n=,6000,,n=,6000,,n=,6000,,,,,,

,t*=,300,,t*=,300,,t*=,300,,,,,,

,r=,6,,r=,6,,r=,6,,,,,,

,置信水平:,0.95,,置信水平:,0.6,,置信水平:,0.6,,,,,,

,a=,0.05,,a=,0.4,,a=,0.4,,,,,,

,2r=,12,,2r=,12,,2r=,12,,,,,,

,T=nt*,1800000,,T=nt*,1800000,,T=nt*,1800000,,,,,,

,,,,,,,,,,,,,,,

,MTBF=nt*/r=,300000,小时,MTBF=nt*/r=,300000,小时,MTBF=nt*/r=,300000,小时,,,,,

双侧置信下限=,,154263.6932,,,227675.3818,,单侧置信限MTBF：,245143.1982,λ=,4079.248405,,,,

,,,,,,,上面的MTBF和λ正好验证了eifer001的计算。,,,,,,,

双侧置信上限=,,8174