設(shè)備可靠性試驗4PAGE\*ROMANPAGE\*ROMANIII目 次前 言 III范圍 1規(guī)范性引用文件 1定義和符號 1定義 1符號 2假設(shè)和要求 3計算點估計和置信區(qū)間所需的假設(shè)和信息 4計算預(yù)測區(qū)間所需的假設(shè)和必要信息 4計算容許區(qū)間所需的假設(shè)和必要信息 4點估計和置信區(qū)間的計算方法 5定時截尾試驗 5點估計 5置信限 6定數(shù)截尾試驗 9點估計 9置信區(qū)間 9未來時間段內(nèi)失效數(shù)的預(yù)測區(qū)間 11雙邊預(yù)測區(qū)間2和2 11單邊預(yù)測區(qū)間 11容許區(qū)間的確定 11泊松容許上界 11泊松容許下界 12附 錄 A （資料性）實例 13MTTF的點估計 13MTTF的置信水平為90%的單邊置信下限 13MTTF的置信水平為90%的雙邊置信限的應(yīng)用 13置信水平為90%的雙邊預(yù)測區(qū)間的應(yīng)用 14置信水平為95%的90%容許上界的應(yīng)用 14置信水平為95%的90%容許下界的應(yīng)用 14附 錄 B （資料性）置信區(qū)間、預(yù)測區(qū)間和容許區(qū)間之間的關(guān)系 15置信區(qū)間 15預(yù)測區(qū)間 15容許區(qū)間 15附 錄 C 規(guī)性）積驗間T計算 17情形1：單個可修復(fù)產(chǎn)品（具有恒定失效強度） 17情形2：多個可修復(fù)產(chǎn)品（具有相同的恒定失效強度） 17情形3：不可修復(fù)產(chǎn)品 18附錄D（規(guī)范性）卡方分布分位數(shù)表 19附錄E（規(guī)范性）卡方分布和漸增泊松分布的積分 22附錄F（規(guī)范性）F分布的95%分位數(shù)表 26GB/T5080《設(shè)備可靠性試驗》分為六個部分：——第1部分：試驗條件和統(tǒng)計檢驗原理；——第2部分：試驗周期統(tǒng)計；——第4部分：指數(shù)分布情況下的點估計、置信區(qū)間、預(yù)測區(qū)間和容許區(qū)間統(tǒng)計方法；——第5部分：成功率的驗證試驗方案；——第6部分：恒定失效率假設(shè)的有效性檢驗；——第7部分：恒定失效率假設(shè)下的失效率與平均無故障時間的驗證試驗方案。PAGEPAGE10設(shè)備可靠性試驗4范圍GB/T50805080.6-1996）。只要對產(chǎn)品的隨機樣本進行了失效時間試驗,也可用本部分評估其可靠性指標(biāo)。規(guī)范性引用文件下列文件中的條款通過GB/T5080的本部分的引用成為本部分的條款。凡是注日期的引用文件，其（不包括勘誤的內(nèi)容GB/T3187-1994可靠性、維修性術(shù)語GB/T5080.6-1996設(shè)備可靠性試驗恒定失效率假設(shè)的有效性檢驗GB/T3385.1-1993統(tǒng)計學(xué)術(shù)語第一部分一般統(tǒng)計術(shù)語GB/T3385.2-1993統(tǒng)計學(xué)第二部分統(tǒng)計質(zhì)量控制術(shù)語定義和符號GB/T3187-1994GB/T3385.1-1993GB/T3385.2-1993確立的以及下列術(shù)語和定義適用于GB/T5080的本部分。3.1.1雙邊置信區(qū)間twosidesconfidenceinterval（見GB/T3385.1-1993）L2和U2使得概率Pr(L2mU2)至少為1m是待估1mL22m的置信水平為1的雙邊置信區(qū)間。3.1.2單邊置信區(qū)間onesidesconfidenceinterval（見GB/T3385.1-1993）如果關(guān)于觀測值的函數(shù)1（mL1）Pr(am1)Pr(mL1mb)]至少為1m是待估的未知總體參數(shù)，11a和bm的最小可能值和最大可能取值，則稱a,U1或1,b是m的置信水平為1注：進一步的討論可參閱附錄B。3.1.3容許限tolerancelimits關(guān)于觀測到的失效數(shù)的下限L2和上限U2，使得可以用概率1保證總體落入它們構(gòu)成的區(qū)間的比例至少為P。注：由L2和U2所構(gòu)成的區(qū)間即為容許區(qū)間。3.1.4容許量tolerance容許上限和下限之差。注：上述量的更詳細描述性定義和它們之間的關(guān)系參見附錄B。符號MTTF 平均故障前時間，即故障前時間的數(shù)學(xué)期望cl 可信性參數(shù)（MTTF、失效率、可靠度等）的置信上限或下限 L1,U1L2,U

信水平給出的置信水平為100(1)%的單邊容許下限和上限置信水平為100(1/2)%的雙邊容許下限和上限 恒定失效率真值?1,U1

恒定失效率估計值失效率真值的單邊置信下限或上限L2,U2

失效率真值的雙邊置信下限或上限MTTF?mL1,

MTTF估計值MTTF的單邊置信區(qū)間下限和上限mL2,

MTTF的雙邊置信區(qū)間下限和上限試驗產(chǎn)品總數(shù)P 未來總體所占的比例（用于確定容許區(qū)間）r 觀察到的失效次數(shù),12,

置信水平為)%的單邊預(yù)測區(qū)間下限和上限置信水平為的雙邊預(yù)測區(qū)間下限和上限t 試驗截止時間T*wfwp12Poiss(J:wfR(t)

累積試驗時間（見附錄C）未來時間段的長度（用于確定預(yù)測區(qū)間）過去時間段的長度（用于確定預(yù)測區(qū)間）F分布的12wf的泊松分布的前J1項之和R(t)2分布的分位數(shù)，自由度為假設(shè)和要求本部分中所描述的統(tǒng)計方法僅在所涉及到的產(chǎn)品失效率（1）關(guān)于時間為常數(shù)的條件下是GB5080.6-1996。計算點估計和置信區(qū)間所需的假設(shè)和信息假設(shè)由n個產(chǎn)品構(gòu)成的樣本是從恒定失效率的母體中隨機抽出的。試驗可以是同時也可以是不同T*時，試驗將被停止；而在定數(shù)截尾試驗中，當(dāng)累積的失效產(chǎn)品數(shù)達到預(yù)設(shè)值r驗時間，都會被用于計算。III產(chǎn)品全部失效是沒有必要的，可以提前停止。試驗可以在所有產(chǎn)品都失效前停止。下面是一些必要的信息（AB）：——與數(shù)據(jù)分析相關(guān)的置信水平(1)；——試驗中觀察到的累積試驗時間（見附錄C）；——試驗中觀察到的產(chǎn)品失效數(shù)；——關(guān)于試驗是定數(shù)截尾試驗還是定時截尾試驗的信息。計算預(yù)測區(qū)間所需的假設(shè)和必要信息計算預(yù)測區(qū)間的假設(shè)與4.1的假設(shè)有微小的差異。其中的一條是：已有一定數(shù)量的產(chǎn)品在時間段wp內(nèi)“處于風(fēng)險中”，現(xiàn)想在未來時間段wf內(nèi)建立一個預(yù)測區(qū)間。因此，下列一些信息是必要的：——與數(shù)據(jù)分析相關(guān)的置信水平；——在時間段wp內(nèi)發(fā)生的失效次數(shù)r；wfwp的值。計算容許區(qū)間所需的假設(shè)和必要信息計算容許區(qū)間時，假設(shè)與求預(yù)測區(qū)間類似，所需信息如下：——與數(shù)據(jù)分析相關(guān)的置信水平；——預(yù)測的失效產(chǎn)品在母體中所占的比例P；——累計試驗時間T*：試驗截止時所有產(chǎn)品的工作總時間（見附錄C）1)。在產(chǎn)品失效服從指數(shù)分布假設(shè)下，累計試驗時間可以由一個產(chǎn)品運行較長時間得到，也可以由許多產(chǎn)品運行較短時間得到，然而，在實際試驗中最好避免這兩種極端。點估計和置信區(qū)間的計算方法本章用于下述各項試驗：——定時截尾試驗；——定數(shù)截尾試驗；——無替換試驗；——有替換試驗；——點估計的試驗；——單邊置信限的試驗；圖1 第5章的結(jié)構(gòu)圖定時截尾試驗點估計計算點估計時，采用下述方法（對有替換和無替換試驗均有效）：r，以及累積試驗時間T*失效率的點估計為：MTTF的點估計：

?rTT*

…………（1）? （2）r注：式（2）r值（10）r1代rr值，偏差可以忽略。MTTFMTTF置信限要得到定時截尾試驗的置信限，需要知道試驗是有替換的（有替換的見5.1.2.1），還是無替換的（無替換的見5.1.2.2）。m的單邊置信下限給定置信水平為1rT*U1U1

21

2r2T*

…………………(3)其中為給定的置信水平（例如：0.9090%）2r2的值可通過查的分位數(shù)表（見D）獲得。取U1MTFm1：mL1 2

2T* 2r2如果沒有觀測到失效，則只能得到的單邊置信上限U1和mm1。m的單邊置信上限失效率的置信下限可用以下公式計算：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如果沒有觀測到失效，則只能定義置信下限。無替換如果產(chǎn)品失效時不進行替換，則采用以下估計方法。

/2λm給定置信水平為1001%r,T*U12

2r

……(10)U1 *其中為置信水平（例如：0.9090%）2r1的值可通過查的分位數(shù)表（D）獲得。取U1MTFm1：mL12

2T*2r1

…………………(11)1λm置信水平為1001%時，失效率的置信下限122r1同時還有

1

*

…………………(12a)2T*12r1

…………………(12b)λmL2和U2

L2

2 22

2r12T*2r

………………(13)U2

1/2

………………(14)利用取倒數(shù)的方法，可獲得MTTF的置信限：mL22

2T*2r1

…………………(15)1/22 2/2

2T*2r1

…………………(16)Rm如果從無替換的壽命試驗中獲得的數(shù)據(jù)只有下面的信息：a）試驗開始時的產(chǎn)品數(shù)n；b）試驗過程中出現(xiàn)的失效數(shù)r；c）試驗的持續(xù)時間t。則應(yīng)選用下述的統(tǒng)計方法。第一步，計算可靠度的雙邊置信上、下限如下： r 121nrF 2n2r2r

……(17) /2 rF 2r;2n2r1RL2

1/2nr

…(18)/212可從表F.1第二步，將(17)式求出的RU2代入到下式，計算MTTF的雙邊置信上限mU2。mU2

rln1/2

…………… (19)第三步，將(18)式求出的RL2代入到下式，計算MTTF的雙邊置信下限mL2。1：等式(19)和(20

mL

rln1/RL2

………………(20)Rtexpr/m(21)2：在等式(17)和(18)中，用替換2，可以得到單側(cè)置信上下限1RL1，并可相應(yīng)地1mL1。定數(shù)截尾試驗點估計$類似地，MTTF

?rTT*

………(22)? (23)r(22r（可以用r1r來減r，偏差被認為是可忽略的。如果在試驗過程中沒觀察到失效，將不能得到失效率的點估計值，因為此時的定數(shù)截尾試驗是無意義的。置信區(qū)間對于定數(shù)截尾試驗，在計算置信限時，無須知道試驗過程中是否進行了產(chǎn)品替換。因此，對有替換和無替換的試驗都可使用下述方法。CT*

(方法對有替換和無替換的試驗是同樣適用的)。λmr

T*，使用下式計算U1：2

2rU1

1

……(24)1其中10.0或90，22r的值可通過查2見附錄D1得。取U1MTFm1：mL12

2T* 2r1λmr

T*，使用下式計算1：1

2r*

……(26)其中1為置信水平（例如：0.90或90%），22r的值可通過查2的分位數(shù)表（見附錄D）獲得。取U1MTF的單邊置信上限U1：2T*mU122r

……(27)λm計算上限的公式

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未來時間段內(nèi)失效數(shù)的預(yù)測區(qū)間2和222分別表示置信水平為100r表示（過去）失效數(shù)。估計方法如下。2：wf

wpF

2r

2r(32)r 1

r

2 L2L2 第二步，尋找滿足下式的最小整數(shù)rU2：2r1F

2r

………(33)ww wwf p

2 U2單邊預(yù)測區(qū)間要獲得單邊預(yù)測區(qū)間的下限和上限，只需在式（32）和式（33）中用替換/2。容許區(qū)間的確定泊松容許上界wfP的時間段（或系統(tǒng)）r的一個可能上界U1，由J給出：PrrJPoissJ;wfP% (34)其中的記號PrrJJPoissJwfwf的泊松分布的累積和。注：量PoissJwf與分布的關(guān)系：JPoissJ;wfJ

wrfr!f

ewf1

2

f(x)dx2(J1)

w2()/2

0 02()其中 , f

，10

f(

的取值見附錄E。式(34)中是未知的，U1可由下面兩個步驟求得：(3(10)或(24)之一求出的置信水平為1001%的置信上限U1。第二步，將此值作為代入到公式(34)JJ即為所要得到的容許上界U1。100wfP的區(qū)間，在其中發(fā)生至多U1P的系統(tǒng)中發(fā)生至多U1次失效”。泊松容許下界wfP的時間段內(nèi)（或系統(tǒng)）r的一個可能下界L1，J給出：PrrJ1PoissJwfP% (35)其中記號PrrJJPoissJwfwf的泊松分布的累積和。式(35)中L1可由下面兩個步驟求得：第1(5a(12)或(26)之一求出的置信水平為1001%的置信下限1。2代入到式(35)JJ即為所要得到的容許下界L1。因此，供方可以有1001%的把握認為“對一個特定的系統(tǒng)來說，在長度為wf的眾多未來時間段內(nèi)，至少P%的時間段里發(fā)生至少L1次失效”或者“在一個長度為wf的未來時間段內(nèi)，至少P%的系統(tǒng)中里發(fā)生至少L1次失效”。附 錄 A（資料性）實例330811—每臺設(shè)備的失效率關(guān)于時間是常數(shù)；—每臺設(shè)備在失效之后立刻被相同的設(shè)備替換；—試驗是定時截尾試驗。MTTF由式(2?=1a330設(shè)備數(shù)）/1失效數(shù)即301（706h。MTTF的置信水平為90的單邊置信下限由式(4)：

mL12

2T*24即同樣地，由式(21)得到

mL1

90%213308199.3a33.2RL1

exptm例如，當(dāng)任務(wù)的時間為10a時，RL10.9511。MTTF的置信水平為90的雙邊置信限的應(yīng)用

L1由式(8)和(9)，得到計算雙邊置信下限的表達式：m 213308182a以及雙邊置信上限的表達式：

L2 20.95

24m 213308536aU2 20.05

22于是，未知的MTTF真值的雙邊置信下限和上限分別為182a和536a。置信水平為90的雙邊預(yù)測區(qū)間的應(yīng)用rwp1wf利用式(32)和式(33)，得到rL24和rU222。

1。因此，供方有90%的把握認為：在即將到來的一年中，失效數(shù)的真值會落在區(qū)間4,22之內(nèi)。置信水平為95的90容許上界的應(yīng)用由式(3)得到失效率的置信水平為95%的單邊置信上限為：2

24U1 213308即每件產(chǎn)品每年平均發(fā)生36.4/（2×1×3308）=0.0055次失效。9533818.(34)和表E.1，得到滿足Poiss(J;18.20.90J24。90%的單邊容許上界rU124。有95%的把握認為：未來至少有90%的年份不會超過24次失效。置信水平為95的90容許下界的應(yīng)用由等式(5a)得到失效率的置信度為95%單邊置信下限為：2

2221即每件產(chǎn)品每年平均發(fā)生12.3/（2×1×3308）=0.00186次失效。953386.1(35)和表E.1，得到滿足1Poiss(J0.90J12。90%的單邊容許下界rL13。有95%的把握認為：未來至少有90%年份至少出現(xiàn)3次失效。附 錄 B（資料性）置信區(qū)間、預(yù)測區(qū)間和容許區(qū)間之間的關(guān)系MTTFm有初步判斷，盡可能使得累積的試驗時間T*相對m充分大（m的三倍）。當(dāng)試驗的產(chǎn)品數(shù)量太少時，這些產(chǎn)品很可能不具有代表性。不應(yīng)對Hahn&Meeker(1991[1]置信區(qū)間與預(yù)測區(qū)間和容許區(qū)間相比而言，用于總體均值上的置信區(qū)間這一概念被各種文獻更多提及。但（未知）90%的雙邊置信限（90%作例子）n個樣本，并采用前面所敘述的方法安排壽命試驗.LCLUCLLCL90%UCL90%的雙邊置信上限。這9090%的置信區(qū)間包含未10%的置信區(qū)間不包含真值。因此，構(gòu)造置信區(qū)間時要限定置信水平。LCLUCLLCLUCL01預(yù)測區(qū)間在一般文獻中出現(xiàn)的預(yù)測區(qū)間有許多種類型。例如，有的預(yù)測區(qū)間只含有一個未來事件，有的含r（6（例如失效）的次數(shù)。這要根據(jù)之前時間段內(nèi)事件發(fā)生的次數(shù)為依據(jù)得出。（單邊或雙邊都有一個與之對應(yīng)的置信水平。與前面一樣，置信水平與計算預(yù)測區(qū)間的方法相關(guān)聯(lián)。容許區(qū)間B.2P。9095（由以往經(jīng)驗生成應(yīng)當(dāng)指出，在表述容許區(qū)間時，用到了兩個百分?jǐn)?shù)，而在置信區(qū)間和預(yù)測區(qū)間時只有一個。對這指的是與陳述有關(guān)的置信程度。附 錄 C（規(guī)范性）*的計算圖C.1到圖C.3通過三個一般的情形，說明了在各種試驗方案下，累積的相關(guān)試驗時間的計算方法。1：單個可修復(fù)產(chǎn)品（具有恒定失效強度）（不包括修復(fù)時間和其它中斷的時間）。見圖C.1。圖C.1單個可修復(fù)產(chǎn)品情形試驗總時間2：多個可修復(fù)產(chǎn)品（具有相同的恒定失效強度）（不包括被修復(fù)或中斷的情形。C.2。其中假設(shè)所有產(chǎn)品是相同的，而且在相同的條件下工作（例如相同的環(huán)境和負載）。圖C.2多個可修復(fù)產(chǎn)品情形試驗總時間3：不可修復(fù)產(chǎn)品在產(chǎn)品不可修復(fù)的情況下，每個產(chǎn)品只有一個相關(guān)試驗時間，即失效前時間。在這種情況下，且僅在此情形下，累積相關(guān)試驗時間為各產(chǎn)品試驗時間之和。圖C.3不可修復(fù)產(chǎn)品情形的試驗總時間附 錄 D（規(guī)范性）卡方分布分位數(shù)表表D.1卡方分布分位數(shù)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

(續(xù))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

(續(xù))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較用式2)z 12/2中z相的準(zhǔn)態(tài)布的位在 各列最后給出。可參考Johnson等人的文獻（1994）[3]。PAGEPAGE22附 錄 E（規(guī)范性）Chisq0.0050.0100.0500.100Chisq0.0050.0100.0500.1000.5001.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.0018.0019.00DFJw0.00250.0050.0250.0500.2500.5001.01.52.02.53.03.54.04.55.05.56.06.57.07.58.08.59.09.5200.99750.99500.97530.95120.77880.60650.36790.22310.13530.08210.04980.03020.01830.01110.00670.00410.00250.00150.00090.00060.00030.00020.00010.0001411.00001.00000.99970.99880.97350.90980.73580.55780.40600.28730.19910.13590.09160.06110.04040.02660.01740.01130.00730.00470.00300.00190.00120.0008621.00001.00001.00001.00000.99780.98560.91970.80880.67670.54380.42320.32080.23810.17360.12470.08840.06200.04300.02960.02030.01380.00930.00620.0042831.00001.00001.00001.00000.99990.99820.98100.93440.85710.75760.64720.53660.43350.34230.26500.20170.15120.11180.08180.05910.04240.03010.02120.01491041.00001.00001.00001.00001.00000.99980.99630.98140.94730.89120.81530.72540.62880.53210.44050.35750.28510.22370.17300.13210.09960.07440.05500.04031251.00001.00001.00001.00001.00001.00000.99940.99550.98340.95800.91610.85760.78510.70290.61600.52890.44570.36900.30070.24140.19120.14960.11570.08851461.00001.00001.00001.00001.00001.00000.99990.99910.99550.98580.96650.93470.88930.83110.76220.68600.60630.52650.44970.37820.31340.25620.20680.16491671.00001.00001.00001.00001.00001.00001.00000.99980.99890.99580.98810.97330.94890.91340.86660.80950.74400.67280.59870.52460.45300.38560.32390.26871881.00001.00001.00001.00001.00001.00001.00001.00000.99980.99890.99620.99010.97860.95970.93190.89440.84720.79160.72910.66200.59250.52310.45570.39182091.00001.00001.00001.00001.00001.00001.00001.00001.00000.99970.99890.99670.99190.98290.96820.94620.91610.87740.83050.77640.71660.65300.58740.521822101.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99900.99720.99330.98630.97470.95740.93320.90150.86220.81590.76340.70600.645324111.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99910.99760.99450.98900.97990.96610.94670.92080.88810.84870.80300.752026121.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99920.99800.99550.99120.98400.97300.95730.93620.90910.87580.836428131.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99930.99830.99640.99290.98720.97840.96580.94860.92610.898130141.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99940.99860.99700.99430.98970.98270.97260.95850.940032151.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99950.99880.99760.99540.99180.98620.97800.966534161.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99960.99900.99800.99630.99340.98890.982336171.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99960.99920.99840.99700.99470.991138181.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99970.99930.99870.99760.995740191.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99970.99950.99890.998042201.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99960.999144211.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.999646221.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.999948231.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.999950241.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000052251.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000054261.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000056271.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000058281.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000060291.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000062301.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000064311.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000066321.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000068331.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000070341.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000072351.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000074361.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000076371.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000078381.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000080391.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000082401.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000084411.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000086421.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000088431.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000090441.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000E.1E.1PAGEPAGE23Chisq0.0050.0100.0500.1000.5001.002.003.004.005.006.007.008.009.0010.0011.0012.0013.0014.0015.0016.0017.0018.0019.00DFJw0.00250.0050.0250.0500.2500.5001.01.52.02.53.03.54.04.55.05.56.06.57.07.58.08.59.09.592451.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000094461.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000096471.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000098481.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000100491.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000102501.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000104511.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000106521.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000108531.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000110541.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000Chisq22.0023.0024.0025.0026.0027.0028.0029.0030.0031.0032.0033.0034.0035.0036.0037.0038.0039.0040.0041.0042.0043.0044.0045.0046.0047.00DFJw11.011.512.012.513.013.514.014.515.015.516.016.517.017.518.018.519.019.520.020.521.021.522.022.523.023.5200.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000410.00020.00010.00010.00010.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000620.00120.00080.00050.00030.00020.00010.00010.00010.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000830.00490.00340.00230.00160.00110.00070.00050.00030.00020.00010.00010.00010.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00001040.01510.01070.00760.00530.00370.00260.00180.00120.00090.00060.00040.00030.00020.00010.00010.00010.00000.00000.00000.00000.00000.00000.00000.00000.00000.00001250.03750.02770.02030.01480.01070.00770.00550.00390.00280.00200.00140.00100.00070.00050.00030.00020.00020.00010.00010.00000.00000.00000.00000.00000.00000.00001460.07860.06030.04580.03460.02590.01930.01420.01050.00760.00550.00400.00290.00210.00150.00100.00070.00050.00040.00030.00020.00010.00010.00010.00000.00000.00001670.14320.11370.08950.06980.05400.04150.03160.02390.01800.01350.01000.00740.00540.00400.00290.00210.00150.00110.00080.00060.00040.00030.00020.00010.00010.00011880.23200.19060.15500.12490.09980.07900.06210.04840.03740.02880.02200.01670.01260.00950.00710.00520.00390.00280.00210.00150.00110.00080.00060.00040.00030.00022090.34050.28880.24240.20140.16580.13530.10940.08780.06990.05520.04330.03370.02610.02010.01540.01170.00890.00670.00500.00370.00280.00200.00150.00110.00080.000622100.45990.40170.34720.29710.25170.21120.17570.14490.11850.09610.07740.06190.04910.03870.03040.02370.01830.01410.01080.00820.00630.00470.00350.00270.00200.001524110.57930.51980.46160.40580.35320.30450.26000.22010.18480.15380.12700.10410.08470.06840.05490.04380.03470.02730.02140.01670.01290.00990.00760.00580.00440.003326120.68870.63290.57600.51900.46310.40930.35850.31110.26760.22830.19310.16210.13500.11160.09170.07480.06060.04880.03900.03100.02450.01930.01510.01180.00910.007028130.78130.73300.68150.62780.57300.51820.46440.41250.36320.31710.27450.23570.20090.16990.14260.11890.09840.08090.06610.05370.04340.03480.02780.02210.01740.013730140.85400.81530.77200.72500.67510.62330.57040.51760.46570.41540.36750.32250.28080.24260.20810.17710.14970.12570.10490.08690.07160.05860.04770.03860.03110.024932150.90740.87830.84440.80600.76360.71780.66940.61920.56810.51700.46670.41800.37150.32750.28670.24900.21480.18400.15650.13230.11110.09270.07690.06340.05200.042434160.94410.92360.89870.86930.83550.79750.75590.71120.66410.61540.56600.51650.46770.42040.37510.33210.29200.25500.22110.19040.16290.13850.11700.09830.08210.068136170.96780.95420.93700.91580.89050.86090.82720.78970.74890.70520.65930.61200.56400.51600.46860.42260.37840.33640.29700.26050.22700.19650.16900.14450.12280.103738180.98230.97380.96260.94810.93020.90840.88260.85300.81950.78250.74230.69960.65500.60890.56220.51560.46950.42460.38140.34030.30170.26570.23250.20220.17480.150240190.99070.98570.97870.96940.95730.94210.92350.90120.87520.84550.81220.77570.73630.69450.65090.60610.56060.51510.47030.42650.38430.34400.30600.27050.23770.207642200.99530.99250.98840.98270.97500.96490.95210.93620.91700.89440.86820.83850.80550.76940.73070.68980.64720.60340.55910.51480.47100.42820.38690.34740.31010.275144210.99770.99620.99390.99060.98590.97960.97120.96040.94690.93040.91080.88780.86150.83190.79910.76360.72550.68540.64370.60100.55770.51440.47160.42980.38940.350746220.99900.99820.99700.99510.99240.98850.98330.97630.96730.95580.94180.92480.90470.88150.85510.82560.79310.75800.72060.68130.64050.59870.55640.51410.47230.431348230.99950.99920.99850.99750.99600.99380.99070.98630.98050.97300.96330.95130.93670.91930.89890.87550.84900.81960.78750.75280.71600.67740.63740.59650.55510.513850240.99980.99960.99930.99880.99800.99680.99500.99240.98880.98400.97770.96960.95940.94680.93170.91390.89330.86970.84320.81400.78220.74800.71170.67380.63460.594552250.99990.99980.99970.99940.99900.99840.99740.99590.99380.99090.98690.98160.97480.96610.95540.94240.92690.90870.88780.86410.83770.80860.77710.74330.70770.670454261.00000.99990.99990.99970.99950.99920.99870.99790.99670.99500.99250.98920.98480.97910.97180.96260.95140.93800.92210.90370.88260.85880.83240.80350.77230.739056271.00001.00000.99990.99990.99980.99960.99940.99890.99830.99730.99590.99390.99120.98750.98270.97650.96870.95910.94750.93370.91750.89880.87750.85370.82740.798758281.00001.00001.00001.00000.99990.99980.99970.99950.99910.99860.99780.99670.99500.99280.98970.98570.98050.97390.96570.95570.94360.92940.91290.89400.87260.848860291.00001.00001.00001.00001.00000.99990.99990.99980.99960.99930.99890.99820.99730.99590.99410.99150.98820.98380.97820.97120.96260.95220.93980.92530.90850.889462301.00001.00001.00001.00001.00001.00000.99990.99990.99980.99970.99940.99910.99860.99780.99670.99510.99300.99020.98650.98180.97580.96850.95950.94870.93600.921264311.00001.00001.00001.00001.00001.00001.00001.00000.99990.99980.99970.99950.99930.99880.99820.99730.99600.99430.99190.98880.98480.97980.97350.96570.95640.945366321.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99980.99960.99940.99900.99850.99780.99670.99530.99330.99070.98740.98310.97770.97110.963068331.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99980.99970.99950.99920.99880.99820.99730.99610.99450.99230.98950.98590.98130.975670341.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99980.99960.99940.99900.99850.99780.99680.99540.99360.99130.98820.984372351.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99980.99970.99950.99920.99880.99820.99740.99620.99470.99270.990274361.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99980.99970.99960.99930.99900.99850.99780.99690.99560.994076371.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99980.99970.99950.99920.99880.99820.99740.996478381.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99980.99970.99960.99930.99900.99850.997980391.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99990.99980.99960.99950.99920.998882401.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99980.99970.99960.999384411.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.99980.99980.999686421.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.99990.999888431.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.99990.999990441.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.999992451.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000094461.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000096471.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.000098481.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000100491.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.0000102501.00001.00001.00001.0000