Determining the distribution probability paper* test distribution study to analyze the reliability of power generation, the actual research is to analyze the reliability, maintainability and effectiveness of power generation equipment. The former is generalized reliability, the latter is narrow reliability, a qualitative device state description, and its quantitative description is its relevant reliability index. The use of mathematical statistics method for reliability index prediction, quantitative description of equipment operating conditions, not only can guide the on-site operation and maintenance work, and can provide a scientific basis for equipment condition maintenance. 1 Index prediction method analysis Process probability theory believes that individuals with irrelevant individuals in the population have the same probability, and random samples have the same distribution as the population. We use the sample as the overall observation. The mean and variance of the sample should be the “approximation†of the population mean and variance. Therefore, the distribution function of the sample should approximate the distribution function of the population. The degree of "approximation" can be used to test whether the distribution function of the sample represents the distribution function of the population under a given reliability. Distribution function! The relationship between (") and distribution density (") is a derivable distribution function! ("). Determine the distribution function of the event according to the engineering accuracy (ie reliability), and determine the distribution function of the event. Based on the probability theory, use the mathematical statistics method to predict the reliability. The basic procedure is as follows: Determine the research object! The raw data is collected - a distribution function - a parameter estimate is determined. The steps of determining the distribution function are as shown. ~Data sorting~Putting distribution one column Statistical calculation table drawing histogram *Single logarithm *Lognormal distribution *Kolmolov test hypothesis test method *"2 test method - normal, exponential distribution test method to determine the distribution function The steps of the step interval estimation parameter estimation are as shown. *Distribution parameter I* point estimation L* reliability index parameter estimation distribution parameter reliability index parameter estimation step 2 statistical method application now power generation equipment no fault available time 2TBF Table 1 a hydropower plant 4 units 9> no fault available Time/h year No.1 unit No.2 unit No.3 unit No.4 unit No.4 unit 2.1 Speculation distribution First, data sorting is carried out. The purpose is to regularly organize the chaotic data, and based on this, seek its inherent regularity. The estimated value of the available time of the unit is MTBF. 2.1.1 Determine the number of group groups and the number of group distance groups (based on the empirical formula: 1)05, the above data '6)09, the calculation is rounded (=11. The maximum value in the data group is the minimum value in the data group. The range of the parent value in the above data is larger than the sample size, and the maximum endpoint is 11x800=8800. The statistical table range is calculated according to Table 1, as shown in Table 2. Table 2 Statistical calculation table limit / h frequency frequency / '(' is the total number of samples) 2.1.3 draw a histogram speculation distribution with the group limit as the abscissa, frequency or frequency as the ordinate, according to the statistical calculation table 1 draw the frequency histogram As shown. From the visible, this curve is similar to the exponential distribution probability density curve. It can be inferred that the unit has no fault available time to obey the exponential distribution. The exponential distribution probability density function is as follows: the distribution function is now estimated by the exponential distribution-(x), and the available probability is estimated by the probability. ((xc)=internal frequency; is the total number of samples; % is the number of groups in which the sample is selected. 2.2 Test distribution curve 2.2.1 Visual inspection method, that is, probability paper drawing (!), with the group limit value in the statistical table and the corresponding available probability ((!) constitutes an ordered pair (!',%(!)), statistical drawing data ,as shown in Table 3. Table 3 shows the statistical plot data set limit / h, approximately on a straight line (0,) point, the slope is negative, draw a more reasonable straight line, as shown. 0.368, so 0.368 is intercepted in the vertical axis of the single logarithmic coordinate, that is, 1/" value can be obtained in the horizontal axis; in the single logarithmic relationship curve between the available probability and the available time without failure, 1/"=2110, that is, take" = 2.2.2 The hypothesis test is observed by approximating the exponential distribution, assuming that the exponential distribution is obeyed, that is, obeying the exponential distribution, and the midpoint estimation of the parameter estimation, then there is, the exponential distribution density (!) = the confidence degree a = 0.05, for the hypothesis sample distribution The function tests, that is, whether the test (!) is acceptable. The Kolmogorov threshold test is used. Calculate the available probabilities for less (!), that is, the samples are each! Corresponding to %(!) ze is calculated; Table 4 uses two methods to compare the value of the available probability calculation value / h lov check table, ie table:. n, = 0.39122 > 0.036 = .m, so the sample distribution function is acceptable. 2.2.3 Parameter estimation Various distributions have parameters. After a certain distribution is determined, the parameters are determined accordingly, that is, the parameter estimation. The overall parameter estimation can be divided into two categories: point estimation and interval estimation. If an estimate is used to represent the population parameter, then this method of estimation is called a point estimate. This method of point estimation has the advantages of simple and outstanding features, but its accuracy is difficult to guarantee, and sometimes it may cause large deviation due to the randomness of the sample. Therefore, when estimating the overall parameters, it is more reasonable to establish an interval and determine how likely the overall parameters are in this interval. This method is the interval estimation. For different distribution functions and corresponding standards, the mathematical statistics have given point estimates and interval estimates for common distribution functions, which can be used directly. For ease of application, the point estimation formula of the exponential function is now organized as follows: the point estimator of the parameter: K=r/X, X=! ! The interval estimation formula for the distribution of the full sample exponential function is shown in Table 5. Table 5 The interval estimation formula of the exponential function distribution is “double-sided confidence interval upper limit lower limit timing □ 2 truncation T 2 estimation; for sample sum; 2/2(2r) is 2 distribution, direct table lookup can be calculated. The parameter that satisfies the exponential distribution function for the time-to-failure available time is estimated as follows: Since the water wheel is faulty, when the equipment is not related to the fault time, the timing end model is adopted. Full sample analysis, ie =! Obey the exponential distribution, and the timing end model, that is, there is 2.3 fault-free time distribution function and application 2.3.1 can be determined by the above calculation and test. 2.3.2 Using the distribution function can judge the equipment running status, such as the turbine group running without faults. The normal operation guarantee rate of the unit above 000h is above 80%, and the inspection time should be determined. Within the overhaul, the probability of failure-free availability is above 80%. 3 Conclusions The above is a mathematical analysis of the time available for the failure of power generation equipment. Other indicators such as maintenance time and failure time can also be statistically predicted. Reliability indicators can be derived from the above indicators. In the engineering application, mathematical statistics based on probability theory mainly observes its distribution form through visual map, and combines the normal distribution, 2 distribution and other distribution functions to apply specifically. By testing the hypothesis, it is determined whether the sample distribution function is acceptable in reliability. If acceptable, the sample distribution function can be considered to replace the overall partial function; otherwise, the sample distribution function hypothesis should be re-performed. Probability paper method is used to determine the distribution function. Although it is intuitive and practical, the straight line varies from person to person. Therefore, in engineering applications, hypothesis testing should be used as much as possible. anping yaqi wire mesh co.,ltd , https://www.yaqisteelwire.com
February 13, 2024