CN103995970A - Ion thrustor minimum subsample reliability assessment method - Google Patents

Abstract

An ion thrustor minimum subsample reliability assessment method comprises the following steps that first, according to the failure and structure features of an ion thrustor, a service life distribution model is selected; second, according to the ground service life verification test results of the ion thrustor, a reliability analyzing method is selected, if a subsample is non-failure data, an ion thrustor non-failure data reliability analyzing method is selected, and if the subsample is minimum failure data, an ion thrustor minimum failure data reliability analyzing method is selected; third, the service life dispersibility of the ion thrustor non-failure data is determined; fourth, the parameter values of the ion thrustor minimum failure data service life distribution model are computed; and fifth, the reliability lower confidence limit of the given service life of the ion thrustor and the service life lower confidence limit of the given reliability are computed. The reliability assessment method for ion thrustor non-failure data and minimum failure data is established, reliability assessment accuracy is improved, and a foundation is provided for reliability assessment of the ion thrustor in the future.

Description

The minimum increment reliability estimation method of a kind of ion thruster

Technical field

The present invention relates to the minimum increment reliability estimation method of a kind of ion thruster, relating in particular to ion thruster testing data of life-span is the analysis method for reliability of no-failure, few fail data.Belong to space flight reliability analysis technology field.

Background technology

Ion thruster is the one of electric propulsion, and it utilizes the ionization of medium xenon-133 gas to generate charged ion, accelerates ejection under the effect of electrostatic field, produces thrust, so claim again static to advance.There is high specific impulse compared with traditional chemical thruster, high-level efficiency, the feature that thrust is little.Can be used for carrying out the space tasks such as position, north and south guarantor, lifting track and survey of deep space.Because ion thruster thrust is smaller, this just requires to move the requirement that the longer time just can reach sweay.Therefore, ion thruster device is as long-life equipment General Requirements reliability service thousands of hours even up to ten thousand hours in-orbit.So the fail-safe analysis to ion thruster service life is significant.

The basic module of ion thruster subsystem has hollow cathode, arc chamber, grid system and neutralizer etc., as shown in Figure 1.In ion gun, make it ionization by hollow cathode ejected electron collision propellant atom, enter arc chamber, the ionization in ion chamber under the effect of hollow cathode ejected electron of actuating medium xenon-133 gas, the ion-optic system (screen and accelerating grid) that the ion being ionized is contained electric potential difference produces thrust with very high speed ejection engine under accelerating.Ion is accelerated to after desired exhaust velocity, because material is with ionic species ejection, carries clean positive charge, and neutralizer is guaranteed equalizing charge by the electronics of transmitting equivalent in ion beam.

Before ion thruster flies in-orbit, in order to find out the critical failure pattern of ion thruster and to its life reliability analysis, need to carry out ground life-span confirmatory experiment and assess its performance and whether meet the demands.Wherein, 30cm NSTAR (Solar Electric Propulsion Technology Application Readiness) the thruster ground life-span expanding test cumulative time that U.S. NASA is applied to Deep Space 1 reaches 30352h, and the improved ion thruster NEXT that is applied to dawn number (NASA ' s Evolutionary Xenon Thruster) has created the New World record that continuous operation surpasses 48000 hours on the basis of NSTAR; The life-span of the final checking of radio frequency ion thruster RIT-10 of Germany is greater than 20000h; The 10cm microwave plasma thruster ground experiment life-span to 2003 year of Japan reaches 18000h.And the life requirements of the LIPS-200 ion thruster of China is 10000～15000 hours.Because the feature of ion thruster long-life, high reliability is brought certain difficulty to fail-safe analysis.

Due to the manufacturing cost costliness of ion thruster, the restriction of the condition that is simultaneously put to the test, at every turn can only 1～2 tests, and causes reliability assessment test sample limited, belongs to minimum increment category; Be subject to urgent impact of lead time, its durability test often cannot be carried out for a long time simultaneously, and test findings mostly is no-failure data or few fail data. and for the very limited situation of this Test Information amount, fail-safe analysis difficulty is larger.And the inventive method can provide certain foundation to its reliability assessment.

Summary of the invention

The object of this invention is to provide the minimum increment reliability estimation method of a kind of ion thruster, quantity of information that ion thruster ground testing data of life-span comprises that what it will solve is is few, the technical barrier of fail-safe analysis difficulty, a kind of minimum increment reliability estimation method of ion thruster with few fail data for no-failure data is respectively proposed, the method is chosen rational Lifetime Distribution Model according to the main failure mode of ion thruster and design feature thereof, fully develop its testing data of life-span information, obtain conservative life dispersivity, realize the reliability assessment to the minimum increment of ion thruster, there is convenience of calculation, analysis result precision high, can be generalized to and there is the long-life, the fail-safe analysis of the product of the same type of high reliability feature.

The minimum increment reliability estimation method of a kind of ion thruster of the present invention, it comprises the following steps:

Step 1: choose suitable Lifetime Distribution Model according to the main inefficacy of ion thruster and design feature, Lifetime Distribution Model comprises that weibull distributes, normal distribution etc.; Its method of choosing is as follows: all will cause the inefficacy of whole ion thruster because any one weak part loses efficacy, the weibull that this meets the most weak Link Model of basis or the model of connecting obtains distributes, therefore the present invention supposes that the life-span distribution obedience two parameter weibull of ion thruster no-failure data distribute, and distribution function is:

$F\left(t\right)=1-\exp [-{\left(\frac{t}{\mathrm{\β}}\right)}^{\mathrm{\α}}],t>0---\left(1\right)$

In formula, α is form parameter, and β is that characteristics life is location parameter, and α has reflected the dispersiveness in life-span;

Step 2: select analysis method for reliability according to ion thruster ground life-span demonstration test result, if increment is no-failure data selection ion thruster no-failure reliability analysis of data method, if being few fail data, increment selects the few fail data analysis method for reliability of ion thruster;

Step 3: the life dispersivity α that determines ion thruster no-failure data;

Step 4: the parameter value that calculates the few fail data Lifetime Distribution Model of ion thruster;

Step 5: according to the analysis method for reliability of selecting in step 2, calculate the fiduciary level confidence lower limit of ion thruster Given Life and the life-span confidence lower limit of given fiduciary level.

Wherein, " selecting ion thruster no-failure reliability analysis of data method " described in step 2, the specific implementation process of its selection is as follows:

1. according to ion thruster Censoring no-failure lifetime data t ₀, select weibull to distribute as its Lifetime Distribution Model as formula (1).

2. determining of life dispersivity α.There is scholar to study dispersed α=0.7～0.8 of the C material of ion thruster grid assembly, dispersed α=0.9 of molybdenum structure material; Life dispersivity α=2.196 that the present invention goes out SERTII ion thruster according to the estimation of test data of U.S. NASA in addition taking and the dispersiveness of hollow cathode heater as 51.19; Below all can be used as the foundation of intermediate ion thruster no-failure data reliability assessment of the present invention.

3. according to above weibull distributed model and dispersed according to calculating for given fiduciary level R, the Q-percentile life t of ion thruster _rconfidence level be γ one-sided confidence lower limit is:

$t_{\mathrm{RL}}=t_0{[-\frac{\ln R}{\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\γ}}\left(\mathrm{2,2}(n+1)\right)]}]}^{1/\mathrm{\α}}---\left(2\right)$

F in formula _1-γ(2,2 (n+1)) is that degree of freedom is the 1-γ upside quantile of the F distribution of 2 and 2 (n+1), and n is sample size.

For ion thruster life dispersivity α, can prove as α>=α ₀time, if given fiduciary level R meets:

$R\≥\frac{1}{1+\frac{1}{n+1}{F}_{1-\mathrm{\γ}}\left(\mathrm{2,2}(n+1)\right)}---\left(3\right)$

The Q-percentile life t of ion thruster _rconfidence level be γ one-sided confidence lower limit is calculated by following formula:

$t_{\mathrm{RL}}^{*}=t_0{[-\frac{\ln R}{\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\γ}}\left(\mathrm{2,2}(n+1)\right)]}]}^{1/{\mathrm{\α}}_0}---\left(4\right)$

4. calculate for Given Life t according to above weibull distributed model and dispersed foundation, in like manner, as dispersed α>=α ₀and given life-span t meets:

t≤t ₀ (5)

Time, the one-sided confidence lower limit that the confidence level of the fiduciary level R (t) of ion thruster is γ is:

$R_L^{*}\left(t\right)=\exp \{-\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\γ}}\left(\mathrm{2,2}(n+1)\right)\left]{\left(\frac{t}{t_0}\right)}^{{\mathrm{\α}}_0}\right\}---\left(6\right)$

Wherein, " selecting the few fail data analysis method for reliability of ion thruster " described in step 2, the specific implementation process of its selection is as follows:

1. according to the few burn-out life data of ion thruster Censoring, select weibull to distribute as its Lifetime Distribution Model as formula (1).

2. distribute according to the weibull in the few fail data of ion thruster life-span, be translated into the extreme value distribution E (μ, σ), embodiment is as follows:

Make Y=lnt, and have

$\left\{\begin{array}{c}\mathrm{\μ}=\ln /\mathrm{\β}\\ \mathrm{\σ}=1/\mathrm{\α}\end{array}\right.---\left(7\right)$

Y obeys the extreme value distribution, and its distribution function is:

$F\left(y\right)=1-\exp [-\exp \left(\frac{Y-\mathrm{\μ}}{\mathrm{\σ}}\right)]---\left(8\right)$

3. according to the few fail data t of Censoring ₁≤ t ₂≤ ...≤t _r<t ^*, wherein t ^*for truncation no-failure data, total r (1≤r<n) platform lost efficacy, and μ and σ was carried out to Best Linear Unbiased Estimate below, and concrete mode is as follows:

1), from y=lnt, y is about t monotonically increasing, has y ₁≤ y ₂≤ ...≤y _rcan regard front r the order statistic Y from the big or small sample for n of the extreme value distribution as ₁≤ Y ₂≤ ... ,≤Y _ra value.Order

$\begin{array}{cc}{Y}_i^0=\frac{Y_i-\mathrm{\&mu;}}{\mathrm{\&sigma;}}& i=\mathrm{1,2},...,r---\left(9\right)\end{array}$

2) Y ⁰follow standard the extreme value distribution, its distribution function F (Y ⁰) and probability density function f (y ⁰) do not rely on any unknown parameter. for front r the order statistic that the sample size from standard the extreme value distribution is n, its average and covariance are respectively:

$\left\{\begin{array}{c}E\left(Y_i^0\right)={\mathrm{\&mu;}}_i\\ \mathrm{Cov}(Y_i^0,Y_j^0)=v_{\mathrm{ij}}=E(Y_i^0,Y_j^0)-{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_j\end{array}\right.i,j=\mathrm{1,2}...,r---\left(10\right)$

μ in formula _iwith can calculate by following formula

$\begin{array}{cc}{\mathrm{\&mu;}}_i=\frac{n!}{(i-1)!(n-i)!}{\&Integral;}_{-\&infin;}^{\&infin;}{y}_i^{0}f\left(y_i^0\right){\left[F\left(y_i^0\right)\right]}^{i-1}{[1-F\left(y_i^0\right)]}^{n-i}d{y}_i^0& i=\mathrm{1,2},...r---\left(11\right)\end{array}$

$\begin{array}{c}E(Y_i^0,Y_j^0)=\frac{n!}{(i-1)!(j-i-1)!(n-j)!}{\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}{y}_i^0{y}_j^{0}f\left(y_i^0\right)f\left(y_j^0\right)\\ {\left[F\left(y_i^0\right)\right]}^{i-1}{[F\left(y_j^0\right)-F\left(y_i^0\right)]}^{j-i-1}{[1-F\left(y_j^0\right)]}^{n-j}d{y}_i^{0}d{y}_j^0\end{array}---\left(12\right)$

3) make truncation moment t ^*r+1 the moment of losing efficacy is t afterwards _r+1, t _r+1r+1 the order statistic that correspondence is n from the sample size of standard the extreme value distribution therefore truncation moment t ^*corresponding y ^*, y ^*corresponding (y ^*) ⁰r Interval Statistic of corresponding same sample can prove r the Interval Statistic that is n from the sample size of standard the extreme value distribution average μ _r+1with variance ν _{(r+1) (r+1)}average and the variance of r+1 the order statistic that is n+1 with the sample size from standard the extreme value distribution are identical, its covariance ν _{(r+1) i}r+1 the order statistic that is n+1 with the sample size from standard the extreme value distribution is identical with the covariance of i order statistic, and formula is as follows, also can table look-up:

$E\left({\left(Y_{r+1}^{*}\right)}^0\right)={\mathrm{\&mu;}}_{r+1}=\frac{(n+1)!}{\left(r\right)!(n-r)!}{\&Integral;}_{-\&infin;}^{\&infin;}{\left(y^{*}\right)}^{0}f\left({\left(y^{*}\right)}^0\right){\left[F\left({\left(y^{*}\right)}^0\right)\right]}^r{[1-F\left({\left(y^{*}\right)}^0\right)]}^{n-r}d{\left(y^{*}\right)}^0---\left(13\right)$

$\left\{\begin{array}{c}\mathrm{Var}\left({\left(Y_{r+1}^{*}\right)}^0\right)=v_{(r+1)(r+1)}=E\left[{\left({\left(Y_{r+1}^{*}\right)}^0\right)}^2\right]-{\mathrm{\&mu;}}_{(r+1)}^2\\ \mathrm{Cov}({\left(Y_{r+1}^{*}\right)}^0,Y_i^0)=v_{(r+1)i}=E({\left(Y_{r+1}^{*}\right)}^0,Y_i^0)-{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_{(r+1)}\end{array}\right.---\left(14\right)$

Wherein,

$E\left[{\left({\left(Y_{r+1}^{*}\right)}^0\right)}^2\right]=\frac{(n+1)!}{\left(r\right)!(n-r)!}{\&Integral;}_{-\&infin;}^{+\&infin;}{\left({\left(y^{*}\right)}^0\right)}^{2}f\left({\left(y^{*}\right)}^0\right){\left[F\left({\left(y^{*}\right)}^0\right)\right]}^r{[1-F\left({\left(y^{*}\right)}^0\right)]}^{n-r}d{\left(y^{*}\right)}^0---\left(15\right)$

$\begin{array}{c}E(Y_i^0,{\left(Y_{r+1}^{*}\right)}^0)=\frac{(n+1)!}{(i-1)!(r-i)!(n-r)!}{\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}{y}_i^0{\left(y^{*}\right)}^{0}f\left(y_i^0\right)f\left({\left(y^{*}\right)}^0\right){\left[F\left(y_i^0\right)\right]}^{i-1}\\ {[F\left({\left(y^{*}\right)}^0\right)-F\left(y_i^0\right)]}^{r-1}{[1-F\left({\left(y^{*}\right)}^0\right)]}^{n-r}d{y}_i^{0}d{\left(y^{*}\right)}^0\end{array}---\left(16\right)$

Order ${\left(y^{*}\right)}^0=y_{r+1}^0,{\left(Y_{r+1}^{*}\right)}^0=Y_{r+1}^0$ Can be derived by (9)

$\left\{\begin{array}{c}{Y}_i=\mathrm{\&mu;}+\mathrm{\&sigma;}{Y}_i^0\\ \begin{array}{cc}E\left(Y_i\right)=\mathrm{\&mu;}+\mathrm{\&sigma;}{\mathrm{\&mu;}}_i& i,j=\mathrm{1,2},...,r+1---\left(17\right)\end{array}\\ \mathrm{Cov}(Y_i,Y_j)=\mathrm{\&sigma;}{v}_{\mathrm{ij}}\end{array}\right.$

4), according to weighted least require method, residual sum of squares (RSS) Q is

$Q=\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}(y_i-\mathrm{\&mu;}-\mathrm{\&sigma;}{\mathrm{\&mu;}}_i)v_{\mathrm{ij}}(y_j-\mathrm{\&mu;}-\mathrm{\&sigma;}{\mathrm{\&mu;}}_j)---\left(18\right)$

Respectively to μ and σ differentiate

$\left\{\begin{array}{c}\frac{\&PartialD;Q}{\&PartialD;\mathrm{\&mu;}}=0\\ \frac{\&PartialD;Q}{\&PartialD;\mathrm{\&sigma;}}=0\end{array}\right.---\left(19\right)$

Solve and can obtain

$\widehat{\mathrm{\&mu;}}=\frac{1}{\mathrm{\&Delta;}}[\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_j\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{y}_i\right)-\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_j{y}_i\right)]---\left(20\right)$

$\widehat{\mathrm{\&sigma;}}=\frac{1}{\mathrm{\&Delta;}}[\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}\right)\left(\underset{i.j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_j{y}_i\right)-\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{y}_i\right)]---\left(21\right)$

Wherein,

${\left[v^{\mathrm{ij}}\right]}_{(r+1)\&times;(r+1)}={\left[v_{\mathrm{ij}}\right]}_{(r+1)\&times;(r+1)}^{-1}---\left(22\right)$

$\mathrm{\&Delta;}=\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_j\right)-{\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i\right)}^2---\left(23\right)$

4. the location parameter and the form parameter that distribute according to formula (7), (21), (22) two parameter weibull are respectively

$\left\{\begin{array}{c}\widehat{\mathrm{\&beta;}}=\exp \left(\widehat{\mathrm{\&mu;}}\right)\\ \widehat{\mathrm{\&alpha;}}=1/\widehat{\mathrm{\&sigma;}}\end{array}\right.---\left(24\right)$

5. the one-sided confidence lower limit formula of the Q-percentile life that is γ according to exponential distribution confidence level is known, for Weibull distribution variables t, the Q-percentile life t of its given fiduciary level R _rLconfidence level is that the one-sided confidence lower limit of γ is:

$t_{\mathrm{RL}}={[-\frac{2\ln R}{{\mathrm{\&chi;}}_{1-\mathrm{\&gamma;}}^2(2r+2)}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^{\mathrm{\&alpha;}}]}^{1/\mathrm{\&alpha;}}---\left(25\right)$

6. according to Weibull distribution variables t, the Q-percentile life t of its given fiduciary level R _rLconfidence level is that the one-sided confidence lower limit of γ is known, and the one-sided confidence lower limit that fiduciary level R (t) confidence level of Given Life t is γ is:

$R_L\left(t\right)=\exp [-\frac{t^{\mathrm{\&alpha;}}{\mathrm{\&chi;}}_{1-\mathrm{\&gamma;}}^2(2r+2)}{2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^{\mathrm{\&alpha;}}}]---\left(26\right)$

Determine the life dispersivity α of ion thruster no-failure data.

Wherein, at " determining the life dispersivity α of ion thruster no-failure data " described in step 3, its definite method is mainly dispersed as determining foundation according to the structured material of the life dispersivity lower limit of material and ion thruster parts, mainly contains aluminium alloy structure α >=4; Titanium alloy structure α >=3; Steel construction α >=2.2, the structured material dispersiveness of ion thruster parts mainly contains carbon structure α=0.7～0.8 of grid and cathode assembly, molybdenum structure α=0.9.

Wherein, " calculating the parameter value of the few fail data Lifetime Distribution Model of ion thruster " described in step 4, be the parameter value that estimates Lifetime Distribution Model according to testing data of life-span, this parameter value can be tried to achieve by formula (20), (21), (24).

Wherein, at " according to the analysis method for reliability of selecting in step 2; calculate the fiduciary level confidence lower limit of ion thruster Given Life and the life-span confidence lower limit of given fiduciary level " described in step 5, the process of its calculating is: the life-span confidence lower limit of the given fiduciary level of ion thruster no-failure data and the fiduciary level confidence lower limit of Given Life are tried to achieve by formula (4) and formula (6) respectively; The life-span confidence lower limit of the given fiduciary level of the few fail data of ion thruster and the fiduciary level confidence lower limit of Given Life are tried to achieve by formula (25) and formula (26) respectively.

Advantage of the present invention and good effect are:

1. carry out durability test for ion thruster and only have the situation of minimum increment to set up respectively the reliability estimation method of ion thruster no-failure data and few fail data, solved minimum this difficult problem of increment reliability assessment of ion thruster.

2) for the situation of few fail data, on the basis of Interval Statistic theory, make full use of to continue to be tested to from a fail data this important tests information of product failure does not occur, expanded quantity of information, improved ion thruster reliability assessment precision.

3) the present invention has provided the life-span confidence lower limit of ion thruster Given Life fiduciary level and given fiduciary level, for fiduciary level and the life-span foundation that provides whether up to standard of thruster are provided later.

Brief description of the drawings

Fig. 1 is ion thruster structural representation;

Fig. 2 is the flow chart of steps of appraisal procedure of the present invention;

Fig. 3 is the inventive method intermediate ion thruster no-failure reliability analysis of data method flow schematic diagram;

Fig. 4 is the few fail data analysis method for reliability of the inventive method intermediate ion thruster schematic flow sheet;

Symbol description in Fig. 3:

N is the ion thruster number of units of testing;

F _1-γ(2,2 (n+1)) is that degree of freedom is the 1-γ upside quantile of the F distribution of 2 and 2 (n+1);

T ₀for Censoring no-failure data;

Symbol description in Fig. 4:

μ is the location parameter of the extreme value distribution;

σ is the form parameter of the extreme value distribution;

Embodiment

Below in conjunction with accompanying drawing and example, the present invention is described in further detail.

Fig. 1 is ion thruster structural representation; Principle of work in conjunction with Fig. 1 ion thruster is: the basic module of ion thruster subsystem has hollow cathode, arc chamber, grid system and neutralizer etc., in ion gun, make it ionization by hollow cathode ejected electron collision propellant atom, enter arc chamber, the ionization in ion chamber under the effect of hollow cathode ejected electron of actuating medium xenon-133 gas, the ion-optic system (screen and accelerating grid) that the ion being ionized is contained electric potential difference produces thrust with very high speed ejection engine under accelerating.Ion is accelerated to after desired exhaust velocity, because material is with ionic species ejection, carries clean positive charge, and neutralizer is guaranteed equalizing charge by the electronics of transmitting equivalent in ion beam.

The minimum increment reliability estimation method of a kind of ion thruster of the present invention, its reliability estimation method process flow diagram as shown in Figure 2, it comprises the assessment of ion thruster no-failure data reliability and the few fail data reliability assessment of ion thruster, shown in Fig. 2, the minimum increment reliability estimation method of a kind of ion thruster of the present invention, its concrete steps are as follows:

Step 1: choose suitable Lifetime Distribution Model according to the main inefficacy of ion thruster and design feature, Lifetime Distribution Model comprises that weibull distributes, normal distribution etc.Its method of choosing is as follows: all will cause the inefficacy of whole ion thruster because any one weak part loses efficacy, the weibull that this meets the most weak Link Model of basis or the model of connecting obtains distributes, therefore the present invention supposes that the life-span distribution obedience two parameter weibull of ion thruster no-failure data distribute, and distribution function is:

$F\left(t\right)=1-\exp [-{\left(\frac{t}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}],t>0---\left(1\right)$

In formula, α is form parameter, and β is that characteristics life is location parameter, and α has reflected the dispersiveness in life-span.

Step 2: select analysis method for reliability according to ion thruster ground life-span demonstration test result, if increment is no-failure data selection ion thruster no-failure reliability analysis of data method, if being few fail data, increment selects the few fail data analysis method for reliability of ion thruster.

Step 3: the conservative life dispersivity α that determines ion thruster _o.

Step 4: the parameter value that calculates the few fail data Lifetime Distribution Model of ion thruster.

Step 5: according to the analysis method for reliability of selecting in step 2, calculate the fiduciary level confidence lower limit of ion thruster Given Life and the life-span confidence lower limit of given fiduciary level.

First we illustrate a kind of ion thruster no-failure reliability analysis of data in conjunction with Fig. 3 below, and concrete implementation step is as follows:

Step 1. is according to ion thruster Censoring no-failure lifetime data t ₀, select suitable Lifetime Distribution Model, embodiment is as follows:

1) ion thruster complex structure, failure mode is many, the crucial parts that affects ion thruster operation life is grid system and cathode assembly, its main failure mode has that electronics backflows, accelerating grid structural failure, emitter exhaust, heater strip fuses and touches and hold utmost point wearing and tearing etc., and wherein any one weak part lost efficacy and all will cause the inefficacy of whole ion thruster.Because Weibull distribution obtains according to the most weak Link Model or series connection model, can fully reflect the impact of fault in material, wearing and tearing and fatigue lifetime.A large amount of practice explanations, every because a certain partial failure or fault will cause that the life-span of overall function components and parts, equipment etc. out of service can be regarded as or the approximate Weibull that regards as distributes.

2) there is lot of documents to distribute the reliability of service life of ion thruster and parts thereof is studied by weibull, therefore the present invention supposes that the life-span distribution obedience two parameter weibull of ion thruster no-failure data distribute, and distribution function is as formula (1)

Step 2. life dispersivity α determines.There is scholar to study dispersed α=0.7～0.8 of the C material of ion thruster grid assembly, dispersed α=0.9 of molybdenum structure material; Life dispersivity α=2.196 that the present invention goes out SERT II ion thruster according to the estimation of test data of U.S. NASA in addition taking and the dispersiveness of hollow cathode heater as 51.19; Below all can be used as the foundation of intermediate ion thruster no-failure data reliability assessment of the present invention.

Step 3. is according to above weibull distributed model and dispersed according to calculating for given fiduciary level R, the Q-percentile life t of ion thruster _rconfidence level be γ one-sided confidence lower limit is:

$t_{\mathrm{RL}}=t_0{[-\frac{\ln R}{\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)]}]}^{1/\mathrm{\&alpha;}}---\left(2\right)$

F in formula _1-γ(2,2 (n+1)) is that degree of freedom is the 1-γ upside quantile of the F distribution of 2 and 2 (n+1), and n is sample size.

For ion thruster life dispersivity α, can prove as α>=α ₀time, if given fiduciary level R meets:

$R\&GreaterEqual;\frac{1}{1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)}---\left(3\right)$

The Q-percentile life t of ion thruster _rconfidence level be γ one-sided confidence lower limit is calculated by following formula:

$t_{\mathrm{RL}}^{*}=t_0{[-\frac{\ln R}{\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)]}]}^{1/{\mathrm{\&alpha;}}_0}---\left(4\right)$

Step 4. calculates for Given Life t according to above weibull distributed model and dispersed foundation, in like manner, and as dispersed α>=α ₀and given life-span t meets:

t≤t ₀ (5)

Time, the one-sided confidence lower limit that the confidence level of the fiduciary level R (t) of ion thruster is γ is:

$R_L^{*}\left(t\right)=\exp \{-\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)\left]{\left(\frac{t}{t_0}\right)}^{{\mathrm{\&alpha;}}_0}\right\}---\left(6\right)$

Wherein, at " life dispersivity α determines " described in step 2, its definite method is: because the main failure mode of ion thruster is the sputtering etching of grid system, and current most of ion thruster grid structure material is molybdenum, therefore, the conservative selected shape parameter lower limit α>=α of the present invention ₀=0.9.

The minimum increment reliability estimation method of a kind of ion thruster of the present invention, it comprises the assessment of ion thruster no-failure data reliability and the few fail data reliability assessment of ion thruster, first we illustrate the few fail data reliability estimation method of a kind of ion thruster in conjunction with Fig. 4 below, and concrete implementation step is as follows:

Step 1. is according to the few burn-out life data of ion thruster Censoring, select suitable Lifetime Distribution Model, embodiment is with the step 1 in Fig. 3, the present invention supposes that the life-span distribution obedience two parameter weibull of the few fail data of ion thruster distribute, and distribution function is as formula (1).

Step 2. distributes according to the weibull in the few fail data of ion thruster life-span, is translated into the extreme value distribution E (μ, σ), and embodiment is as follows:

Make Y=lnt, and have

$\left\{\begin{array}{c}\mathrm{\&mu;}=\ln /\mathrm{\&beta;}\\ \mathrm{\&sigma;}=1/\mathrm{\&alpha;}\end{array}\right.---\left(7\right)$

Y obeys the extreme value distribution, and its distribution function is:

$F\left(y\right)=1-\exp [-\exp \left(\frac{Y-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\right)]---\left(8\right)$

Step 3. is according to the few fail data t of Censoring ₁≤ t ₂≤ ...≤t _r<t ^*, wherein t ^*for truncation no-failure data, total r (1≤r<n) platform lost efficacy, and μ and σ was carried out to Best Linear Unbiased Estimate below, and concrete mode is as follows:

1. from y=lnt, y is about t monotonically increasing, has y ₁≤ y ₂≤ ...≤y _rcan regard front r the order statistic Y from the big or small sample for n of the extreme value distribution as ₁≤ Y ₂≤ ... ,≤Y _ra value.Order

$\begin{array}{cc}{Y}_i^0=\frac{Y_i-\mathrm{\&mu;}}{\mathrm{\&sigma;}}& i=\mathrm{1,2},...,r---\left(9\right)\end{array}$

2.Y ⁰follow standard the extreme value distribution, its distribution function F (Y ⁰) and probability density function f (y ⁰) do not rely on any unknown parameter. for front r the order statistic that the sample size from standard the extreme value distribution is n, its average and covariance are respectively:

$\left\{\begin{array}{c}E\left(Y_i^0\right)={\mathrm{\&mu;}}_i\\ \mathrm{Cov}(Y_i^0,Y_j^0)=v_{\mathrm{ij}}=E(Y_i^0,Y_j^0)-{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_j\end{array}\right.i,j=\mathrm{1,2}...,r---\left(10\right)$

μ in formula _iwith can calculate by following formula

$\begin{array}{cc}{\mathrm{\&mu;}}_i=\frac{n!}{(i-1)!(n-i)!}{\&Integral;}_{-\&infin;}^{\&infin;}{y}_i^{0}f\left(y_i^0\right){\left[F\left(y_i^0\right)\right]}^{i-1}{[1-F\left(y_i^0\right)]}^{n-i}d{y}_i^0& i=\mathrm{1,2},...r---\left(11\right)\end{array}$

$\begin{array}{c}E(Y_i^0,Y_j^0)=\frac{n!}{(i-1)!(j-i-1)!(n-j)!}{\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}{y}_i^0{y}_j^{0}f\left(y_i^0\right)f\left(y_j^0\right)\\ {\left[F\left(y_i^0\right)\right]}^{i-1}{[F\left(y_j^0\right)-F\left(y_i^0\right)]}^{j-i-1}{[1-F\left(y_j^0\right)]}^{n-j}d{y}_i^{0}d{y}_j^0\end{array}---\left(12\right)$

3. make truncation moment t ^*r+1 the moment of losing efficacy is t afterwards _r+1, t _r+1r+1 the order statistic that correspondence is n from the sample size of standard the extreme value distribution therefore truncation moment t ^*corresponding y ^*, y ^*corresponding (y ^*) ⁰r Interval Statistic of corresponding same sample can prove r the Interval Statistic that is n from the sample size of standard the extreme value distribution average μ _r+1with variance ν _{(r+1) (r+1)}average and the variance of r+1 the order statistic that is n+1 with the sample size from standard the extreme value distribution are identical, its covariance ν _{(r+1) i}r+1 the order statistic that is n+1 with the sample size from standard the extreme value distribution is identical with the covariance of i order statistic, and formula is as follows, also can table look-up:

$E\left({\left(Y_{r+1}^{*}\right)}^0\right)={\mathrm{\&mu;}}_{r+1}=\frac{(n+1)!}{\left(r\right)!(n-r)!}{\&Integral;}_{-\&infin;}^{\&infin;}{\left(y^{*}\right)}^{0}f\left({\left(y^{*}\right)}^0\right){\left[F\left({\left(y^{*}\right)}^0\right)\right]}^r{[1-F\left({\left(y^{*}\right)}^0\right)]}^{n-r}d{\left(y^{*}\right)}^0---\left(13\right)$

$\left\{\begin{array}{c}\mathrm{Var}\left({\left(Y_{r+1}^{*}\right)}^0\right)=v_{(r+1)(r+1)}=E\left[{\left({\left(Y_{r+1}^{*}\right)}^0\right)}^2\right]-{\mathrm{\&mu;}}_{(r+1)}^2\\ \mathrm{Cov}({\left(Y_{r+1}^{*}\right)}^0,Y_i^0)=v_{(r+1)i}=E({\left(Y_{r+1}^{*}\right)}^0,Y_i^0)-{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_{(r+1)}\end{array}\right.---\left(14\right)$

Wherein,

$E\left[{\left({\left(Y_{r+1}^{*}\right)}^0\right)}^2\right]=\frac{(n+1)!}{\left(r\right)!(n-r)!}{\&Integral;}_{-\&infin;}^{+\&infin;}{\left({\left(y^{*}\right)}^0\right)}^{2}f\left({\left(y^{*}\right)}^0\right){\left[F\left({\left(y^{*}\right)}^0\right)\right]}^r{[1-F\left({\left(y^{*}\right)}^0\right)]}^{n-r}d{\left(y^{*}\right)}^0---\left(15\right)$

$\begin{array}{c}E(Y_i^0,{\left(Y_{r+1}^{*}\right)}^0)=\frac{(n+1)!}{(i-1)!(r-i)!(n-r)!}{\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}{y}_i^0{\left(y^{*}\right)}^{0}f\left(y_i^0\right)f\left({\left(y^{*}\right)}^0\right){\left[F\left(y_i^0\right)\right]}^{i-1}\\ {[F\left({\left(y^{*}\right)}^0\right)-F\left(y_i^0\right)]}^{r-1}{[1-F\left({\left(y^{*}\right)}^0\right)]}^{n-r}d{y}_i^{0}d{\left(y^{*}\right)}^0\end{array}---\left(16\right)$

Order ${\left(y^{*}\right)}^0=y_{r+1}^0,{\left(Y_{r+1}^{*}\right)}^0=Y_{r+1}^0$ Can be derived by (9)

$\left\{\begin{array}{c}{Y}_i=\mathrm{\&mu;}+\mathrm{\&sigma;}{Y}_i^0\\ \begin{array}{cc}E\left(Y_i\right)=\mathrm{\&mu;}+\mathrm{\&sigma;}{\mathrm{\&mu;}}_i& i,j=\mathrm{1,2},...,r+1---\left(17\right)\end{array}\\ \mathrm{Cov}(Y_i,Y_j)=\mathrm{\&sigma;}{v}_{\mathrm{ij}}\end{array}\right.$

4. according to weighted least require method, residual sum of squares (RSS) Q is

$Q=\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}(y_i-\mathrm{\&mu;}-\mathrm{\&sigma;}{\mathrm{\&mu;}}_i)v_{\mathrm{ij}}(y_j-\mathrm{\&mu;}-\mathrm{\&sigma;}{\mathrm{\&mu;}}_j)---\left(18\right)$

Respectively to μ and σ differentiate

$\left\{\begin{array}{c}\frac{\&PartialD;Q}{\&PartialD;\mathrm{\&mu;}}=0\\ \frac{\&PartialD;Q}{\&PartialD;\mathrm{\&sigma;}}=0\end{array}\right.---\left(19\right)$

Solve and can obtain

$\widehat{\mathrm{\&mu;}}=\frac{1}{\mathrm{\&Delta;}}[\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_j\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{y}_i\right)-\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_j{y}_i\right)]---\left(20\right)$

$\widehat{\mathrm{\&sigma;}}=\frac{1}{\mathrm{\&Delta;}}[\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}\right)\left(\underset{i.j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_j{y}_i\right)-\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{y}_i\right)]---\left(21\right)$

Wherein,

${\left[v^{\mathrm{ij}}\right]}_{(r+1)\&times;(r+1)}={\left[v_{\mathrm{ij}}\right]}_{(r+1)\&times;(r+1)}^{-1}---\left(22\right)$

$\mathrm{\&Delta;}=\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_j\right)-{\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i\right)}^2---\left(23\right)$

Location parameter and form parameter that step 4. distributes according to formula (7), (21), (22) two parameter weibull are respectively

$\left\{\begin{array}{c}\widehat{\mathrm{\&beta;}}=\exp \left(\widehat{\mathrm{\&mu;}}\right)\\ \widehat{\mathrm{\&alpha;}}=1/\widehat{\mathrm{\&sigma;}}\end{array}\right.---\left(24\right)$

The one-sided confidence lower limit formula of Q-percentile life that step 5. is γ according to exponential distribution confidence level is known, for Weibull distribution variables t, the Q-percentile life t of its given fiduciary level R _rLconfidence level is that the one-sided confidence lower limit of γ is:

$t_{\mathrm{RL}}={[-\frac{2\ln R}{{\mathrm{\&chi;}}_{1-\mathrm{\&gamma;}}^2(2r+2)}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^{\mathrm{\&alpha;}}]}^{1/\mathrm{\&alpha;}}---\left(25\right)$

Step 6. is according to Weibull distribution variables t, the Q-percentile life t of its given fiduciary level R _rLconfidence level is that the one-sided confidence lower limit of γ is known, and the one-sided confidence lower limit that fiduciary level R (t) confidence level of Given Life t is γ is:

$R_L\left(t\right)=\exp [-\frac{t^{\mathrm{\&alpha;}}{\mathrm{\&chi;}}_{1-\mathrm{\&gamma;}}^2(2r+2)}{2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^{\mathrm{\&alpha;}}}]---\left(26\right)$

Wherein, at " the one-sided confidence lower limit formula of Q-percentile life that is γ according to exponential distribution confidence level " described in step 5, its specific implementation process is as follows:

Weibull is distributed and carried out as down conversion

$\left\{\begin{array}{c}z=t^{\mathrm{\&alpha;}}\\ \mathrm{\&theta;}={\mathrm{\&beta;}}^{\mathrm{\&alpha;}}\end{array}\right.---\left(27\right)$

Weibull distributes and is converted into exponential distribution, i.e. z=t ^αobeys index distribution

$F\left(z\right)=1-\exp (-\frac{z}{\mathrm{\&theta;}})---\left(28\right)$

Below by ion thruster test figure, the present invention is carried out to experimental verification:

1. ion thruster no-failure data reliability assessment checking

Be 8000h the former designed life of the 30cm NSTAR thruster of U.S. NASA, consumes xenon propellant 83kg.Launch Deep Space 1 (DS-1) in October, 1998 and carried out planetary detection, engineering prototype (EMT) to NSTAR before transmitting has carried out the life-span demonstration test of ground 8000h, from test, find the main failure mode of NSTAR and to its improvement, produce again 2 NSTAR thrusters on the basis of EMT, one (DS1) is arranged on DS-1 spacecraft, another (FT1) carries out life-span expanding test on ground as backup machine, within 2004, FT1 ground life-span expanding test people is for stopping, cumulative time reaches 30352h, consume propellant 235kg.We are for the no-failure data t of FT1 below ₀=30352h carries out reliability assessment:

Fiduciary level R=0.87 under confidence level γ=0.6 meets:

$R\&GreaterEqual;\frac{1}{1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)}=0.63$

The Q-percentile life t of ion thruster _rconfidence level be γ one-sided confidence lower limit is

$t_{\mathrm{RL}}^{*}=t_0{[-\frac{\ln R}{\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)]}]}^{1/{\mathrm{\&alpha;}}_0}=8082.64h$

Meeting its designed life is 8000h.

Meet for given life-span t=8000h:

t≤t ₀＝30352h

Fiduciary level confidence lower limit under confidence level γ=0.6 is

$R_L^{*}\left(t\right)=\exp \{-\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)\left]{\left(\frac{t}{t_0}\right)}^{{\mathrm{\&alpha;}}_0}\right\}=0.8712$

2. the few fail data reliability assessment checking of ion thruster

The ion thruster propulsion system that the model of U.S. NASA development is XIPS-13 is mainly used in HS-601HP telstar platform, for whether the life-span of verifying this model 13cm ion thruster can meet the ability with telstar task with adequate allowance, U.S. NASA chooses 2 XIPS-13 ion thrusters and carries out life-span ground validation test.One lost efficacy at 16146h, and one is to end 21058h people, and the requirements for life of XIPS-13 ion thruster is about to 10000h, considers after 2 times of margins of safety, and ground durability test checking target is work 21000h.

The estimates of parameters that is drawn the extreme value distribution after conversion by the method for the step 3 in Fig. 4 is

$\begin{array}{cc}\widehat{\mathrm{\&mu;}}=10.1055& \widehat{\mathrm{\&sigma;}}=0.327548\end{array}$

Location parameter and form parameter estimated value that substitution formula (25) obtains weibull distribution are

$\left\{\begin{array}{c}\widehat{\mathrm{\&beta;}}=\exp \left(\widehat{\mathrm{\&mu;}}\right)=24477.33\\ \widehat{\mathrm{\&alpha;}}=1/\widehat{\mathrm{\&sigma;}}=3.052987\end{array}\right.$

The one-sided confidence lower limit of fiduciary level R (t) that is γ=0.6 in confidence level for the requirements for life t=10000h of XIPS-13cm ion thruster by formula (27) calculate into

$R_L\left(10000\right)=\exp [-\frac{t^{\widehat{\mathrm{\&alpha;}}}{\mathrm{\&chi;}}_{1-\mathrm{\&gamma;}}^2(2r+2)}{2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^{\widehat{\mathrm{\&alpha;}}}}]=0.87$

Suppose XIPS-13cm ion thruster in confidence level γ=0.6 time fiduciary level require R=0.9 life-span confidence lower limit can by formula (26) calculate into

$t_{\mathrm{RL}}={[-\frac{2\ln R}{{\mathrm{\&chi;}}_{1-\mathrm{\&gamma;}}^2(2r+2)}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^{\widehat{\mathrm{\&alpha;}}}]}^{1/\widehat{\mathrm{\&alpha;}}}=9024.6h$

The above the present invention has provided the minimum increment reliability assessment of ion thruster, but protection scope of the present invention is not limited to this, and method provided by the invention can also expand in the product of other long-life, high reliability and apply.

Claims (6)

1. the minimum increment reliability estimation method of ion thruster, is characterized in that: it comprises the following steps:

Step 1: choose suitable Lifetime Distribution Model according to the main inefficacy of ion thruster and design feature, Lifetime Distribution Model comprises that weibull distributes, normal distribution; Its method of choosing is as follows: all will cause the inefficacy of whole ion thruster because any one weak part loses efficacy, the weibull that this meets the most weak Link Model of basis or the model of connecting obtains distributes, therefore the life-span distribution obedience two parameter weibull that suppose ion thruster no-failure data distribute, and distribution function is:

$F\left(t\right)=1-\exp [-{\left(\frac{t}{\mathrm{\&beta;}}\right)}^{\mathrm{\&alpha;}}],t>0---\left(1\right)$

In formula, α is form parameter, and β is that characteristics life is location parameter, and α has reflected the dispersiveness in life-span;

Step 2: select analysis method for reliability according to ion thruster ground life-span demonstration test result, if increment is no-failure data selection ion thruster no-failure reliability analysis of data method, if being few fail data, increment selects the few fail data analysis method for reliability of ion thruster;

Step 3: the life dispersivity α that determines ion thruster no-failure data;

Step 4: the parameter value that calculates the few fail data Lifetime Distribution Model of ion thruster;

Step 5: according to the analysis method for reliability of selecting in step 2, calculate the fiduciary level confidence lower limit of ion thruster Given Life and the life-span confidence lower limit of given fiduciary level.

2. the minimum increment reliability estimation method of a kind of ion thruster according to claim 1, is characterized in that: " selecting ion thruster no-failure reliability analysis of data method " described in step 2, the specific implementation process of its selection is as follows:

1.. according to ion thruster Censoring no-failure lifetime data t ₀, select weibull to distribute as its Lifetime Distribution Model as formula (1);

2.. life dispersivity α determines: have dispersed α=0.7～0.8 of the C material of ion thruster grid assembly, dispersed α=0.9 of molybdenum structure material; Life dispersivity α=2.196 that go out SERT II ion thruster according to the estimation of test data of U.S. NASA in addition taking and the dispersiveness of hollow cathode heater as 51.19; The foundation of all assessing as ion thruster no-failure data reliability above;

3.. according to above weibull distributed model and dispersed according to calculating for given fiduciary level R, the Q-percentile life t of ion thruster _rconfidence level be γ one-sided confidence lower limit is:

$t_{\mathrm{RL}}=t_0{[-\frac{\ln R}{\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)]}]}^{1/\mathrm{\&alpha;}}---\left(2\right)$

F in formula _1-γ(2,2 (n+1)) is that degree of freedom is the 1-γ upside quantile of the F distribution of 2 and 2 (n+1), and n is sample size;

For ion thruster life dispersivity α, prove as α>=α ₀time, if given fiduciary level R meets:

$R\&GreaterEqual;\frac{1}{1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)}---\left(3\right)$

The Q-percentile life t of ion thruster _rconfidence level be γ one-sided confidence lower limit is calculated by following formula:

$t_{\mathrm{RL}}^{*}=t_0{[-\frac{\ln R}{\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)]}]}^{1/{\mathrm{\&alpha;}}_0}---\left(4\right)$

4.. according to above weibull distributed model and dispersed according to calculating for Given Life t, in like manner, as dispersed α>=α ₀and given life-span t meets:

t≤t ₀ (5)

Time, the one-sided confidence lower limit that the confidence level of the fiduciary level R (t) of ion thruster is γ is:

$R_L^{*}\left(t\right)=\exp \{-\ln [1+\frac{1}{n+1}{F}_{1-\mathrm{\&gamma;}}\left(\mathrm{2,2}(n+1)\right)\left]{\left(\frac{t}{t_0}\right)}^{{\mathrm{\&alpha;}}_0}\right\}---\left(6\right)$

。

3. the minimum increment reliability estimation method of a kind of ion thruster according to claim 1, is characterized in that: " selecting the few fail data analysis method for reliability of ion thruster " described in step 2, the specific implementation process of its selection is as follows:

(1). according to the few burn-out life data of ion thruster Censoring, select weibull to distribute as its Lifetime Distribution Model as formula (1);

(2). distribute according to the weibull in the few fail data of ion thruster life-span, be translated into the extreme value distribution E (μ, σ), embodiment is as follows:

Make Y=lnt, and have

$\left\{\begin{array}{c}\mathrm{\&mu;}=\ln /\mathrm{\&beta;}\\ \mathrm{\&sigma;}=1/\mathrm{\&alpha;}\end{array}\right.---\left(7\right)$

Y obeys the extreme value distribution, and its distribution function is:

$F\left(y\right)=1-\exp [-\exp \left(\frac{Y-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\right)]---\left(8\right)$

(3). according to the few fail data t of Censoring ₁≤ t ₂≤ ...≤t _r<t ^*, wherein t ^*for truncation no-failure data, total r (1≤r<n) platform lost efficacy, and μ and σ was carried out to Best Linear Unbiased Estimate below, and concrete mode is as follows:

1), from y=lnt, y is about t monotonically increasing, has y ₁≤ y ₂≤ ...≤y _rcan regard front r the order statistic Y from the big or small sample for n of the extreme value distribution as ₁≤ Y ₂≤ ... ,≤Y _ra value, order

$\begin{array}{cc}{Y}_i^0=\frac{Y_i-\mathrm{\&mu;}}{\mathrm{\&sigma;}}& i=\mathrm{1,2},...,r---\left(9\right)\end{array}$

2) Y ⁰follow standard the extreme value distribution, its distribution function F (Y ⁰) and probability density function f (y ⁰) do not rely on any unknown parameter, for front r the order statistic that the sample size from standard the extreme value distribution is n, its average and covariance are respectively:

$\left\{\begin{array}{c}E\left(Y_i^0\right)={\mathrm{\&mu;}}_i\\ \mathrm{Cov}(Y_i^0,Y_j^0)=v_{\mathrm{ij}}=E(Y_i^0,Y_j^0)-{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_j\end{array}\right.i,j=\mathrm{1,2}...,r---\left(10\right)$

μ in formula _iwith calculate by following formula

$\begin{array}{cc}{\mathrm{\&mu;}}_i=\frac{n!}{(i-1)!(n-i)!}{\&Integral;}_{-\&infin;}^{\&infin;}{y}_i^{0}f\left(y_i^0\right){\left[F\left(y_i^0\right)\right]}^{i-1}{[1-F\left(y_i^0\right)]}^{n-i}d{y}_i^0& i=\mathrm{1,2},...r---\left(11\right)\end{array}$

$\begin{array}{c}E(Y_i^0,Y_j^0)=\frac{n!}{(i-1)!(j-i-1)!(n-j)!}{\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}{y}_i^0{y}_j^{0}f\left(y_i^0\right)f\left(y_j^0\right)\\ {\left[F\left(y_i^0\right)\right]}^{i-1}{[F\left(y_j^0\right)-F\left(y_i^0\right)]}^{j-i-1}{[1-F\left(y_j^0\right)]}^{n-j}d{y}_i^{0}d{y}_j^0\end{array}---\left(12\right)$

3) make truncation moment t ^*r+1 the moment of losing efficacy is t afterwards _r+1, t _r+1r+1 the order statistic that correspondence is n from the sample size of standard the extreme value distribution therefore truncation moment t ^*corresponding y ^*, y ^*corresponding (y ^*) ⁰r Interval Statistic of corresponding same sample r the Interval Statistic that is n from the sample size of standard the extreme value distribution average μ _r+1with variance ν _{(r+1) (r+1)}average and the variance of r+1 the order statistic that is n+1 with the sample size from standard the extreme value distribution are identical, its covariance ν _{(r+1) i}r+1 the order statistic that is n+1 with the sample size from standard the extreme value distribution is identical with the covariance of i order statistic, and formula is as follows, also can table look-up:

$E\left({\left(Y_{r+1}^{*}\right)}^0\right)={\mathrm{\&mu;}}_{r+1}=\frac{(n+1)!}{\left(r\right)!(n-r)!}{\&Integral;}_{-\&infin;}^{\&infin;}{\left(y^{*}\right)}^{0}f\left({\left(y^{*}\right)}^0\right){\left[F\left({\left(y^{*}\right)}^0\right)\right]}^r{[1-F\left({\left(y^{*}\right)}^0\right)]}^{n-r}d{\left(y^{*}\right)}^0---\left(13\right)$

$\left\{\begin{array}{c}\mathrm{Var}\left({\left(Y_{r+1}^{*}\right)}^0\right)=v_{(r+1)(r+1)}=E\left[{\left({\left(Y_{r+1}^{*}\right)}^0\right)}^2\right]-{\mathrm{\&mu;}}_{(r+1)}^2\\ \mathrm{Cov}({\left(Y_{r+1}^{*}\right)}^0,Y_i^0)=v_{(r+1)i}=E({\left(Y_{r+1}^{*}\right)}^0,Y_i^0)-{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_{(r+1)}\end{array}\right.---\left(14\right)$

Wherein,

$E\left[{\left({\left(Y_{r+1}^{*}\right)}^0\right)}^2\right]=\frac{(n+1)!}{\left(r\right)!(n-r)!}{\&Integral;}_{-\&infin;}^{+\&infin;}{\left({\left(y^{*}\right)}^0\right)}^{2}f\left({\left(y^{*}\right)}^0\right){\left[F\left({\left(y^{*}\right)}^0\right)\right]}^r{[1-F\left({\left(y^{*}\right)}^0\right)]}^{n-r}d{\left(y^{*}\right)}^0---\left(15\right)$

$\begin{array}{c}E(Y_i^0,{\left(Y_{r+1}^{*}\right)}^0)=\frac{(n+1)!}{(i-1)!(r-i)!(n-r)!}{\&Integral;}_{-\&infin;}^{+\&infin;}{\&Integral;}_{-\&infin;}^{+\&infin;}{y}_i^0{\left(y^{*}\right)}^{0}f\left(y_i^0\right)f\left({\left(y^{*}\right)}^0\right){\left[F\left(y_i^0\right)\right]}^{i-1}\\ {[F\left({\left(y^{*}\right)}^0\right)-F\left(y_i^0\right)]}^{r-1}{[1-F\left({\left(y^{*}\right)}^0\right)]}^{n-r}d{y}_i^{0}d{\left(y^{*}\right)}^0\end{array}---\left(16\right)$

Order ${\left(y^{*}\right)}^0=y_{r+1}^0,{\left(Y_{r+1}^{*}\right)}^0=Y_{r+1}^0$ Can be derived by (9)

$\left\{\begin{array}{c}{Y}_i=\mathrm{\&mu;}+\mathrm{\&sigma;}{Y}_i^0\\ \begin{array}{cc}E\left(Y_i\right)=\mathrm{\&mu;}+\mathrm{\&sigma;}{\mathrm{\&mu;}}_i& i,j=\mathrm{1,2},...,r+1---\left(17\right)\end{array}\\ \mathrm{Cov}(Y_i,Y_j)=\mathrm{\&sigma;}{v}_{\mathrm{ij}}\end{array}\right.$

4), according to weighted least require method, residual sum of squares (RSS) Q is

$Q=\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}(y_i-\mathrm{\&mu;}-\mathrm{\&sigma;}{\mathrm{\&mu;}}_i)v_{\mathrm{ij}}(y_j-\mathrm{\&mu;}-\mathrm{\&sigma;}{\mathrm{\&mu;}}_j)---\left(18\right)$

Respectively to μ and σ differentiate

$\left\{\begin{array}{c}\frac{\&PartialD;Q}{\&PartialD;\mathrm{\&mu;}}=0\\ \frac{\&PartialD;Q}{\&PartialD;\mathrm{\&sigma;}}=0\end{array}\right.---\left(19\right)$

Solve

$\widehat{\mathrm{\&mu;}}=\frac{1}{\mathrm{\&Delta;}}[\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_j\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{y}_i\right)-\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_j{y}_i\right)]---\left(20\right)$

$\widehat{\mathrm{\&sigma;}}=\frac{1}{\mathrm{\&Delta;}}[\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}\right)\left(\underset{i.j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_j{y}_i\right)-\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{y}_i\right)]---\left(21\right)$

Wherein,

${\left[v^{\mathrm{ij}}\right]}_{(r+1)\&times;(r+1)}={\left[v_{\mathrm{ij}}\right]}_{(r+1)\&times;(r+1)}^{-1}---\left(22\right)$

$\mathrm{\&Delta;}=\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}\right)\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i{\mathrm{\&mu;}}_j\right)-{\left(\underset{i,j=1}{\overset{r+1}{\mathrm{\&Sigma;}}}{v}^{\mathrm{ij}}{\mathrm{\&mu;}}_i\right)}^2---\left(23\right)$

(4). the location parameter and the form parameter that distribute according to formula (7), (21), (22) two parameter weibull are respectively

$\left\{\begin{array}{c}\widehat{\mathrm{\&beta;}}=\exp \left(\widehat{\mathrm{\&mu;}}\right)\\ \widehat{\mathrm{\&alpha;}}=1/\widehat{\mathrm{\&sigma;}}\end{array}\right.---\left(24\right)$

(5). the one-sided confidence lower limit formula of the Q-percentile life that is γ according to exponential distribution confidence level is known, for Weibull distribution variables t, the Q-percentile life t of its given fiduciary level R _rLconfidence level is that the one-sided confidence lower limit of γ is:

$t_{\mathrm{RL}}={[-\frac{2\ln R}{{\mathrm{\&chi;}}_{1-\mathrm{\&gamma;}}^2(2r+2)}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^{\mathrm{\&alpha;}}]}^{1/\mathrm{\&alpha;}}---\left(25\right)$

(6). according to Weibull distribution variables t, the Q-percentile life t of its given fiduciary level R _rLconfidence level is that the one-sided confidence lower limit of γ is known, and the one-sided confidence lower limit that fiduciary level R (t) confidence level of Given Life t is γ is:

$R_L\left(t\right)=\exp [-\frac{t^{\mathrm{\&alpha;}}{\mathrm{\&chi;}}_{1-\mathrm{\&gamma;}}^2(2r+2)}{2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i^{\mathrm{\&alpha;}}}]---\left(26\right)$

Determine the life dispersivity α of ion thruster no-failure data.

4. the minimum increment reliability estimation method of a kind of ion thruster according to claim 1, it is characterized in that: at " determining the life dispersivity α of ion thruster no-failure data " described in step 3, its definite method is mainly dispersed as determining foundation according to the structured material of the life dispersivity lower limit of material and ion thruster parts, mainly contains aluminium alloy structure α >=4; Titanium alloy structure α >=3; Steel construction α >=2.2, the structured material dispersiveness of ion thruster parts mainly contains carbon structure α=0.7～0.8 of grid and cathode assembly, molybdenum structure α=0.9.

5. the minimum increment reliability estimation method of a kind of ion thruster according to claim 1, it is characterized in that: " calculating the parameter value of the few fail data Lifetime Distribution Model of ion thruster " described in step 4, be the parameter value that estimates Lifetime Distribution Model according to testing data of life-span, this parameter value is tried to achieve by formula (20), (21), (24).

6. the minimum increment reliability estimation method of a kind of ion thruster according to claim 1, it is characterized in that: at " according to the analysis method for reliability of selecting in step 2; calculate the fiduciary level confidence lower limit of ion thruster Given Life and the life-span confidence lower limit of given fiduciary level " described in step 5, the process of its calculating is: the life-span confidence lower limit of the given fiduciary level of ion thruster no-failure data and the fiduciary level confidence lower limit of Given Life are tried to achieve by formula (4) and formula (6) respectively; The life-span confidence lower limit of the given fiduciary level of the few fail data of ion thruster and the fiduciary level confidence lower limit of Given Life are tried to achieve by formula (25) and formula (26) respectively.