2024设备可靠性试验第4部分指数分布情况下的点估计、置信区间、预测区间和容许区间统计方法

设备可靠性试验4PAGE\*ROMANPAGE\*ROMANIII目 次前 言 III范围 1规范性引用文件 1定义和符号 1定义 1符号 2假设和要求 3计算点估计和置信区间所需的假设和信息 4计算预测区间所需的假设和必要信息 4计算容许区间所需的假设和必要信息 4点估计和置信区间的计算方法 5定时截尾试验 5点估计 5置信限 6定数截尾试验 9点估计 9置信区间 9未来时间段内失效数的预测区间 11双边预测区间2和2 11单边预测区间 11容许区间的确定 11泊松容许上界 11泊松容许下界 12附 录 A （资料性）实例 13MTTF的点估计 13MTTF的置信水平为90%的单边置信下限 13MTTF的置信水平为90%的双边置信限的应用 13置信水平为90%的双边预测区间的应用 14置信水平为95%的90%容许上界的应用 14置信水平为95%的90%容许下界的应用 14附 录 B （资料性）置信区间、预测区间和容许区间之间的关系 15置信区间 15预测区间 15容许区间 15附 录 C 规性）积验间T计算 17情形1：单个可修复产品（具有恒定失效强度） 17情形2：多个可修复产品（具有相同的恒定失效强度） 17情形3：不可修复产品 18附录D（规范性）卡方分布分位数表 19附录E（规范性）卡方分布和渐增泊松分布的积分 22附录F（规范性）F分布的95%分位数表 26GB/T5080《设备可靠性试验》分为六个部分：——第1部分：试验条件和统计检验原理；——第2部分：试验周期统计；——第4部分：指数分布情况下的点估计、置信区间、预测区间和容许区间统计方法；——第5部分：成功率的验证试验方案；——第6部分：恒定失效率假设的有效性检验；——第7部分：恒定失效率假设下的失效率与平均无故障时间的验证试验方案。PAGEPAGE10设备可靠性试验4范围GB/T50805080.6-1996）。只要对产品的随机样本进行了失效时间试验,也可用本部分评估其可靠性指标。规范性引用文件下列文件中的条款通过GB/T5080的本部分的引用成为本部分的条款。凡是注日期的引用文件，其（不包括勘误的内容GB/T3187-1994可靠性、维修性术语GB/T5080.6-1996设备可靠性试验恒定失效率假设的有效性检验GB/T3385.1-1993统计学术语第一部分一般统计术语GB/T3385.2-1993统计学第二部分统计质量控制术语定义和符号GB/T3187-1994GB/T3385.1-1993GB/T3385.2-1993确立的以及下列术语和定义适用于GB/T5080的本部分。3.1.1双边置信区间twosidesconfidenceinterval（见GB/T3385.1-1993）L2和U2使得概率Pr(L2mU2)至少为1m是待估1mL22m的置信水平为1的双边置信区间。3.1.2单边置信区间onesidesconfidenceinterval（见GB/T3385.1-1993）如果关于观测值的函数1（mL1）Pr(am1)Pr(mL1mb)]至少为1m是待估的未知总体参数，11a和bm的最小可能值和最大可能取值，则称a,U1或1,b是m的置信水平为1注：进一步的讨论可参阅附录B。3.1.3容许限tolerancelimits关于观测到的失效数的下限L2和上限U2，使得可以用概率1保证总体落入它们构成的区间的比例至少为P。注：由L2和U2所构成的区间即为容许区间。3.1.4容许量tolerance容许上限和下限之差。注：上述量的更详细描述性定义和它们之间的关系参见附录B。符号MTTF 平均故障前时间，即故障前时间的数学期望cl 可信性参数（MTTF、失效率、可靠度等）的置信上限或下限 L1,U1L2,U

信水平给出的置信水平为100(1)%的单边容许下限和上限置信水平为100(1/2)%的双边容许下限和上限 恒定失效率真值ˆ1,U1

恒定失效率估计值失效率真值的单边置信下限或上限L2,U2

失效率真值的双边置信下限或上限MTTFˆmL1,

MTTF估计值MTTF的单边置信区间下限和上限mL2,

MTTF的双边置信区间下限和上限试验产品总数P 未来总体所占的比例（用于确定容许区间）r 观察到的失效次数,12,

置信水平为)%的单边预测区间下限和上限置信水平为的双边预测区间下限和上限t 试验截止时间T*wfwp12Poiss(J:wfR(t)

累积试验时间（见附录C）未来时间段的长度（用于确定预测区间）过去时间段的长度（用于确定预测区间）F分布的12wf的泊松分布的前J1项之和R(t)2分布的分位数，自由度为假设和要求本部分中所描述的统计方法仅在所涉及到的产品失效率（1）关于时间为常数的条件下是GB5080.6-1996。计算点估计和置信区间所需的假设和信息假设由n个产品构成的样本是从恒定失效率的母体中随机抽出的。试验可以是同时也可以是不同T*时，试验将被停止；而在定数截尾试验中，当累积的失效产品数达到预设值r验时间，都会被用于计算。III产品全部失效是没有必要的，可以提前停止。试验可以在所有产品都失效前停止。下面是一些必要的信息（AB）：——与数据分析相关的置信水平(1)；——试验中观察到的累积试验时间（见附录C）；——试验中观察到的产品失效数；——关于试验是定数截尾试验还是定时截尾试验的信息。计算预测区间所需的假设和必要信息计算预测区间的假设与4.1的假设有微小的差异。其中的一条是：已有一定数量的产品在时间段wp内“处于风险中”，现想在未来时间段wf内建立一个预测区间。因此，下列一些信息是必要的：——与数据分析相关的置信水平；——在时间段wp内发生的失效次数r；wfwp的值。计算容许区间所需的假设和必要信息计算容许区间时，假设与求预测区间类似，所需信息如下：——与数据分析相关的置信水平；——预测的失效产品在母体中所占的比例P；——累计试验时间T*：试验截止时所有产品的工作总时间（见附录C）1)。在产品失效服从指数分布假设下，累计试验时间可以由一个产品运行较长时间得到，也可以由许多产品运行较短时间得到，然而，在实际试验中最好避免这两种极端。点估计和置信区间的计算方法本章用于下述各项试验：——定时截尾试验；——定数截尾试验；——无替换试验；——有替换试验；——点估计的试验；——单边置信限的试验；图1 第5章的结构图定时截尾试验点估计计算点估计时，采用下述方法（对有替换和无替换试验均有效）：r，以及累积试验时间T*失效率的点估计为：MTTF的点估计：

ˆrTT*

…………（1）ˆ （2）r注：式（2）r值（10）r1代rr值，偏差可以忽略。MTTFMTTF置信限要得到定时截尾试验的置信限，需要知道试验是有替换的（有替换的见5.1.2.1），还是无替换的（无替换的见5.1.2.2）。m的单边置信下限给定置信水平为1rT*U1U1

21

2r2T*

…………………(3)其中为给定的置信水平（例如：0.9090%）2r2的值可通过查的分位数表（见D）获得。取U1MTFm1：mL1 2

2T* 2r2如果没有观测到失效，则只能得到的单边置信上限U1和mm1。m的单边置信上限失效率的置信下限可用以下公式计算：MTTF1：

1

2r*

……(5a)2T*mU122r

……(5b)λm置信下限L2

2 2

2r

……(6)置信上限U2

L2 *2r2U2

1/2

…………………(7)U2MTTF法：mL22

2T* 2r 21/2以及mU22

2T* 2r如果没有观测到失效，则只能定义置信下限。无替换如果产品失效时不进行替换，则采用以下估计方法。

/2λm给定置信水平为1001%r,T*U12

2r

……(10)U1 *其中为置信水平（例如：0.9090%）2r1的值可通过查的分位数表（D）获得。取U1MTFm1：mL12

2T*2r1

…………………(11)1λm置信水平为1001%时，失效率的置信下限122r1同时还有

1

*

…………………(12a)2T*12r1

…………………(12b)λmL2和U2

L2

2 22

2r12T*2r

………………(13)U2

1/2

………………(14)利用取倒数的方法，可获得MTTF的置信限：mL22

2T*2r1

…………………(15)1/22 2/2

2T*2r1

…………………(16)Rm如果从无替换的寿命试验中获得的数据只有下面的信息：a）试验开始时的产品数n；b）试验过程中出现的失效数r；c）试验的持续时间t。则应选用下述的统计方法。第一步，计算可靠度的双边置信上、下限如下： r 121nrF 2n2r2r

……(17) /2 rF 2r;2n2r1RL2

1/2nr

…(18)/212可从表F.1第二步，将(17)式求出的RU2代入到下式，计算MTTF的双边置信上限mU2。mU2

rln1/2

…………… (19)第三步，将(18)式求出的RL2代入到下式，计算MTTF的双边置信下限mL2。1：等式(19)和(20

mL

rln1/RL2

………………(20)Rtexpr/m(21)2：在等式(17)和(18)中，用替换2，可以得到单侧置信上下限1RL1，并可相应地1mL1。定数截尾试验点估计$类似地，MTTF

ˆrTT*

………(22)ˆ (23)r(22r（可以用r1r来减r，偏差被认为是可忽略的。如果在试验过程中没观察到失效，将不能得到失效率的点估计值，因为此时的定数截尾试验是无意义的。置信区间对于定数截尾试验，在计算置信限时，无须知道试验过程中是否进行了产品替换。因此，对有替换和无替换的试验都可使用下述方法。CT*

(方法对有替换和无替换的试验是同样适用的)。λmr

T*，使用下式计算U1：2

2rU1

1

……(24)1其中10.0或90，22r的值可通过查2见附录D1得。取U1MTFm1：mL12

2T* 2r1λmr

T*，使用下式计算1：1

2r*

……(26)其中1为置信水平（例如：0.90或90%），22r的值可通过查2的分位数表（见附录D）获得。取U1MTF的单边置信上限U1：2T*mU122r

……(27)λm计算上限的公式

2 2

2r

……(28)以及下限的公式

L2 *2rU2

1/2

……(29)MTTFmL22：mL22

2T* 2r1/2以及mU22

2T* 2r/2未来时间段内失效数的预测区间2和222分别表示置信水平为100r表示（过去）失效数。估计方法如下。2：wf

wpF

2r

2r(32)r 1

r

2 L2L2 第二步，寻找满足下式的最小整数rU2：2r1F

2r

………(33)ww wwf p

2 U2单边预测区间要获得单边预测区间的下限和上限，只需在式（32）和式（33）中用替换/2。容许区间的确定泊松容许上界wfP的时间段（或系统）r的一个可能上界U1，由J给出：PrrJPoissJ;wfP% (34)其中的记号PrrJJPoissJwfwf的泊松分布的累积和。注：量PoissJwf与分布的关系：JPoissJ;wfJ

wrfr!f

ewf1

2

f(x)dx2(J1)

w2()/2

0 02()其中 , f

，10

f(

的取值见附录E。式(34)中是未知的，U1可由下面两个步骤求得：(3(10)或(24)之一求出的置信水平为1001%的置信上限U1。第二步，将此值作为代入到公式(34)JJ即为所要得到的容许上界U1。100wfP的区间，在其中发生至多U1P的系统中发生至多U1次失效”。泊松容许下界wfP的时间段内（或系统）r的一个可能下界L1，J给出：PrrJ1PoissJwfP% (35)其中记号PrrJJPoissJwfwf的泊松分布的累积和。式(35)中L1可由下面两个步骤求得：第1(5a(12)或(26)之一求出的置信水平为1001%的置信下限1。2代入到式(35)JJ即为所要得到的容许下界L1。因此，供方可以有1001%的把握认为“对一个特定的系统来说，在长度为wf的众多未来时间段内，至少P%的时间段里发生至少L1次失效”或者“在一个长度为wf的未来时间段内，至少P%的系统中里发生至少L1次失效”。附 录 A（资料性）实例330811—每台设备的失效率关于时间是常数；—每台设备在失效之后立刻被相同的设备替换；—试验是定时截尾试验。MTTF由式(2ˆ=1a330设备数）/1失效数即301（706h。MTTF的置信水平为90的单边置信下限由式(4)：

mL12

2T*24即同样地，由式(21)得到

mL1

90%213308199.3a33.2RL1

exptm例如，当任务的时间为10a时，RL10.9511。MTTF的置信水平为90的双边置信限的应用

L1由式(8)和(9)，得到计算双边置信下限的表达式：m 213308182a以及双边置信上限的表达式：

L2 20.95

24m 213308536aU2 20.05

22于是，未知的MTTF真值的双边置信下限和上限分别为182a和536a。置信水平为90的双边预测区间的应用rwp1wf利用式(32)和式(33)，得到rL24和rU222。

1。因此，供方有90%的把握认为：在即将到来的一年中，失效数的真值会落在区间4,22之内。置信水平为95的90容许上界的应用由式(3)得到失效率的置信水平为95%的单边置信上限为：2

24U1 213308即每件产品每年平均发生36.4/（2×1×3308）=0.0055次失效。9533818.(34)和表E.1，得到满足Poiss(J;18.20.90J24。90%的单边容许上界rU124。有95%的把握认为：未来至少有90%的年份不会超过24次失效。置信水平为95的90容许下界的应用由等式(5a)得到失效率的置信度为95%单边置信下限为：2

2221即每件产品每年平均发生12.3/（2×1×3308）=0.00186次失效。953386.1(35)和表E.1，得到满足1Poiss(J0.90J12。90%的单边容许下界rL13。有95%的把握认为：未来至少有90%年份至少出现3次失效。附 录 B（资料性）置信区间、预测区间和容许区间之间的关系MTTFm有初步判断，尽可能使得累积的试验时间T*相对m充分大（m的三倍）。当试验的产品数量太少时，这些产品很可能不具有代表性。不应对Hahn&Meeker(1991[1]置信区间与预测区间和容许区间相比而言，用于总体均值上的置信区间这一概念被各种文献更多提及。但（未知）90%的双边置信限（90%作例子）n个样本，并采用前面所叙述的方法安排寿命试验.LCLUCLLCL90%UCL90%的双边置信上限。这9090%的置信区间包含未10%的置信区间不包含真值。因此，构造置信区间时要限定置信水平。LCLUCLLCLUCL01预测区间在一般文献中出现的预测区间有许多种类型。例如，有的预测区间只含有一个未来事件，有的含r（6（例如失效）的次数。这要根据之前时间段内事件发生的次数为依据得出。（单边或双边都有一个与之对应的置信水平。与前面一样，置信水平与计算预测区间的方法相关联。容许区间B.2P。9095（由以往经验生成应当指出，在表述容许区间时，用到了两个百分数，而在置信区间和预测区间时只有一个。对这指的是与陈述有关的置信程度。附 录 C（规范性）*的计算图C.1到图C.3通过三个一般的情形，说明了在各种试验方案下，累积的相关试验时间的计算方法。1：单个可修复产品（具有恒定失效强度）（不包括修复时间和其它中断的时间）。见图C.1。图C.1单个可修复产品情形试验总时间2：多个可修复产品（具有相同的恒定失效强度）（不包括被修复或中断的情形。C.2。其中假设所有产品是相同的，而且在相同的条件下工作（例如相同的环境和负载）。图C.2多个可修复产品情形试验总时间3：不可修复产品在产品不可修复的情况下，每个产品只有一个相关试验时间，即失效前时间。在这种情况下，且仅在此情形下，累积相关试验时间为各产品试验时间之和。图C.3不可修复产品情形的试验总时间附 录 D（规范性）卡方分布分位数表表D.1卡方分布分位数表：2()10.000.022.713.8420.100.214.615.9930.350.586.257.8140.711.067.789.4951.151.619.2411.0761.642.2010.6412.5972.172.8312.0214.0782.733.4913.3615.5193.334.1714.6816.92103.944.8715.9918.31114.575.5817.2819.68125.236.3018.5521.03135.897.0419.822.36146.577.7921.0623.68157.268.5522.3125.00167.969.3123.5426.30178.6710.0924.7727.59189.3910.8625.9928.871910.1211.6527.2030.142010.8512.4428.4131.412111.5913.2429.6232.672212.3414.0430.8133.922313.0914.8532.0135.172413.8515.6633.2036.422514.6116.4734.3837.652615.3817.2935.5638.892716.1518.1136.7440.112816.9318.9437.9241.342917.7119.7739.0942.563018.4920.6040.2643.773119.2821.4341.4244.993220.0722.2742.5846.193320.8723.1143.7547.403421.6623.9544.9048.603522.4724.8046.0649.80D.1

(续)3623.2725.6447.2151.003724.0726.4948.3652.193824.8827.3449.5153.383925.7028.2050.6654.574026.5129.0551.8155.764127.3329.9152.9556.944228.1430.7754.0958.124328.9631.6355.2359.304429.7932.4956.3760.484530.6133.3557.5161.664631.4434.2258.6462.834732.2735.0859.7764.004833.1035.9560.9165.174933.9336.8262.0466.345034.7637.6963.1767.505135.6038.5664.3068.675236.4439.4365.4269.835337.2840.3166.5570.995438.1241.1867.6772.155538.9642.0668.8073.315639.8042.9469.9274.475740.6543.8271.0475.625841.4944.7072.1676.785942.3445.5873.2877.936043.1946.4674.4079.086144.0447.3475.5180.236244.8948.2376.6381.386345.7449.1177.7582.536446.5950.0078.8683.686547.4550.8879.9784.826648.3151.7781.0985.966749.1652.6682.2087.116850.0253.5583.3188.256950.8854.4484.4289.397051.7455.3385.5390.537152.6056.2286.6491.677253.4657.1187.7492.817354.3358.0188.8593.957455.1958.9089.9695.087556.0559.7991.0696.22D.1

(续)7656.9260.6992.1797.357757.7961.5993.2798.487858.6562.4894.3799.627959.5263.3895.48100.758060.3964.2896.58101.888161.2665.1897.68103.018262.1366.0898.78104.148363.0066.9899.88105.278463.8867.88100.98106.398564.7568.78102.08107.528665.6269.68103.18108.658766.5070.58104.28109.778867.3771.48105.37110.908968.2572.39106.47112.029069.1373.29107.57113.159170.0074.20108.66114.279270.8875.10109.76115.399371.7676.01110.85116.519472.6476.91111.94117.639573.5277.82113.04118.759674.4078.73114.13119.879775.2879.63115.22120.999876.1680.54116.32122.119977.0581.45117.41123.2310077.9382.36118.50124.3411086.7991.47129.39135.4812095.70100.62140.23146.57130104.66109.81151.05157.61140113.66119.03161.83168.61150122.69128.28172.58179.58160131.76137.55183.31190.52170140.85146.84194.02201.42180149.97156.15204.70212.30190159.11165.49215.37223.16200168.28174.84226.02233.99z-1.64-1.28+1.64+1.28较用式2)z 12/2中z相的准态布的位在 各列最后给出。可参考Johnson等人的文献（1994）[3]。PAGEPAGE22附 录 E（规范性）Chisq0.0050.0100.0500.100Chisq0.0050.0100.0500.1000.5001.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.0018.0019.00DFJw0.00250.0050.0250.0500.2500.5001.01.52.02.53.03.54.04.55.05.56.06.57.07.58.08.59.09.5200.99750.99500.97530.95120.77880.60650.36790.22310.13530.08210.04980.03020.01830.01110.00670.00410.00250.00150.00090.00060.00030.00020.00010.0001411.00001.00000.99970.99880.97350.90980.73580.55780.40600.28730.19910.13590.09160.06110.04040.02660.01740.01130.00730.00470.00300.00190.00120.0008621.00001.00001.00001.00000.99780.98560.91970.80880.67670.54380.42320.32080.23810.17360.12470.08840.06200.04300.02960.02030.01380.00930.00620.0042831.00001.00001.00001.00000.99990.99820.98100.93440.85710.75760.64720.53660.43350.34230.26500.20170.15120.11180.08180.05910.04240.03010.02120.01491041.00001.00001.00001.00001.00000.99980.99630.98140.94730.89120.81530.72540.62880.53210.44050.35750.28510.22370.17300.13210.09960.07440.05500.04031251.00001.00001.00001.00001.00001.00000.99940.99550.98340.95800.91610.85760.78510.70290.61600.52890.44570.36900.30070.24140.19120.14960.11570.08851461.00001.00001.00001.00001.00001.00000.99990.99910.99550.98580.96650.93470.88930.83110.76220.68600.60630.52650.44970.37820.31340.25620.20680.16491671.00001.00001.00001.00001.00001.00001.00000.99980.99890.99580.98810.97330.94890.91340.86660.80950.74400.67280.59870.52460.45300.38560.32390.26871881.00001.00001.00001.00001.00001.00001.00001.00000.99980.99890.99620.99010.97860.95970.93190.89440.84720.79160.72910.66200.59250.52310.45570.39182091.00001.00001.00001.00001.00001.00001.00001.00001.00000.99970.99890.99670.99190.98290.96820.94620.91610.87740.83050.77640.71660.65300.58740.521822101.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99900.99720.99330.98630.97470.95740.93320.90150.86220.81590.76340.70600.645324111.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99910.99760.99450.98900.97990.96610.94670.92080.88810.84870.80300.752026121.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99920.99800.99550.99120.98400.97300.95730.93620.90910.87580.836428131.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99930.99830.99640.99290.98720.97840.96580.94860.92610.898130141.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99940.99860.99700.99430.98970.98270.97260.95850.940032151.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99950.99880.99760.99540.99180.98620.97800.966534161.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99960.99900.99800.99630.99340.98890.982336171.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99960.99920.99840.99700.99470.991138181.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99970.99930.99870.99760.995740191.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99950.99890.998042201.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99960.999144211.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.999646221.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.999948231.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.999950241.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000052251.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000054261.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000056271.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000058281.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000060291.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000062301.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000064311.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000066321.00001.00001.00001.00001.00001.00001.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