各数学分布在可靠性中的应用.
数学分布及分析计算表 以前从338B标准整理出来的,再摘录如下,供大家参考,详细的可见原贴附件:
5.3.1 正态分布(高斯分布)
Normal (or Gaussian) Distribution MIL-HDBK-338B PAGE 90
对可靠性来说,正态分布有两种用途:
1)用于分析由于磨损(如机械装置)而发生的帮障产品.(磨损故障往往最接近正态分布) 2)对制造的产品及性能是否符合规范进行分析.
5.3.3 Lognormal Distribution 对数正态分布The lognormal distribution is the distribution of a random variable whose natural logarithm is distributed normally; in other words, it is the normal distribution with ln t as the variate. The density function is
对数正态分布是其随机变量的自然对数按正态分布的一种分布,也就是说,它是正态分布,其变量为Ln t
The lognormal distribution is used in reliability analysis of semiconductors and fatigue life of certain types of mechanical components. This distribution is also commonly used in maintainability analysis and will be further discussed in Section 5.6.2.1.
对数正态分布用于半导体器件的可靠性分析和某些种类的机械零件疲劳寿命.其主要用途是在维修性分析中对修理时间数据进行
确切地分析.这一点将在5.6.2.1节进一步讨论.
5.3.4 Exponential Distribution 指数分布 MIL-HDBK-338B PAGE 100
This is probably the most important distribution in reliability work and is used almost exclusively for reliability rediction of electronic equipment (Ref. MIL-HDBK-217). It describes the situation wherein the hazard rate is constant which can be hown to be generated by a Poisson process. This distribution is valuable if properly used. It has the advantages of
这种分布是可靠性工作中最重要的一种分布,并且几乎是专门用于电子设备可靠性预计的一种分布.它描述瞬时故障率是常数的情况.
它可以表示为由泊松过程形成的分布.
Some particular applications of this model include
(1) Items whose failure rate does not change significantly with age
(2) Complex and repairable equipment without excessive amounts of redundancy
(3) Equipment for which the early failures or "infant mortalities" have been eliminated byburning in the equipment for some reasonable time period
这种模型的一些具体应用有:
1)其故障率随着工作时间的增长没有很大变化的产品;
2)没有过多余度的复杂的可修复设备;
3)在某一合理的时间内经过进行老化面消除早期故障或固有故障的设备.
The failure density function is
故障密度函数是f(t)=λe-λt
5.3.5 Gamma Distribution 伽马分布 page 101
The gamma distribution is used in reliability analysis for cases where partial failures can exist,i.e., when a given umber of partial failures must occur before an item fails (e.g., redundant systems) or the time to second failure when the time to failure is exponentially distributed. The failure density function is
当存在局部故障,即在某个产品发生故障(如余度系统)之前或到第二次故障发生的时间(当故障前工作时间为指数分布)之前必定发生一定数量的局部故障的情况下,用伽马分布分布进行可靠性分析.故障密度函数是:
伽马分布还可以用于描述一升或下降的瞬时故障率 α>1,h(t)上升, α<1时h(t)下降
5.3.6 Weibull Distribution 威布尔分布 page 104 (注:这个最强大,因为参数的改变,可以转换成其它几个分布类型,所以可靠性里常用这个来,有些可靠性商业软件也有此模块.)
The Weibull distribution is particularly useful in reliability work since it is a general distribution which, by adjustment of the distribution parameters, can be made to model a wide range of life distribution characteristics of different classes of engineered items.
One of the versions of the failure density function is
在可靠性工作中威布尔分布非常有用,因为它是通用分布,通过调整分布参数就可以构成这种分布,以便为不同类别的工程项目的各种寿命分布特性建立模型.故障密度函数的一种形式是:
5.3.7.1 Binomial Distribution 二项分布 PAGE 106
The binomial distribution is used for those situations in which there are only two outcomes, such as success or failure, and the probability remains the same for all trials. It is very useful in reliability and quality assurance work. The probability density function (pdf) of the binomial distribution is
二项分布(属离散型分布)一般用于下述情况,即当只有两种结果时,如成功或失败,并且对所有试验来说,概率都相同,这种分布对可靠性和质量保证工作都很有用.二项分布的概率密度函数是:
f(x) is the probability of obtaining exactly x good items and (n-x) bad items in a sample of n items where p is the probability of obtaining a good item (success) and q (or 1-p) is the probability of obtaining a bad item (failure).
f(x)是在含有N个产品的样本中,确切获得X个好产品和(N-X)个坏产品的概率,式中P是获得好产品(成功)的概率,
Q(或1-P)是获得坏产品(失效)的概率
可靠性示例:
The binomial is useful for computing the probability of system success when the system employs partial redundancy. Assume a five channel VHF receiver as shown in Figure 5.3-3.
As long as three channels are operational, the system is classified as satisfactory. Thus, two channel failures are allowed. Each channel has a probability of 0.9 of surviving a 24 hour operation period without failure. What is the probability that the receiver will survive a 24 hour mission without loss of more than two channels?
当系统使用部分余度时,二项分布可用于计算系统的成功概率.假设有1台5频道的接收机,如图.只要有3个频道工作,即为正常
每个频道在24小时工作期间无故障工作的概率为0.9.因此,允许有2个频道发生故障,接收机正常工作24小时,而发生故障的频道
数不多于2个的概率是多少?
质量控制示例:
In a large lot of component parts, past experience has shown that the probability of a defective part is 0.05. The acceptance sampling plan for lots of these parts is to randomly select 30 parts for inspection and accept the lot if 2 or less defectives are found. What is the probability, P(a), of accepting the lot?
过去的经验表明,在一大批元器件中,有缺陷的元器件的概率为0.05,大量生产这些元器件的接收抽样方案是随机抽取30个元器件进行检验,如果发现一批有2个或少于2个缺陷,该批就被接收.求该批被接收的概率是多少.
5.3.8 Poisson Distribution 泊松分布 PAGE108
This distribution is used quite frequently in reliability analysis. It can be considered an extension of the binomial distribution when n is infinite. In fact, it is used to approximate the binomial distribution when n≥ 20 and p≤ 0.05.
If events are Poisson distributed, they occur at a constant average rate and the number of events occurring in any time interval are independent of the number of events occurring in any other time interval. For example, the number of failures in a given time would be given by
这种分布是可靠性分析中很常用的一种分布形式,右以把这种分布认为是当N为无限大时的二项分布的扩展.
事实上,当N大于等于20,P大于等于0.05,这种分布用来近似表示二项分布.
如果事件是泊松分布的,它们以恒定的平均变化率出现,并且在任一时间间隔中,事件出现的次数与在任一其它时间间隔出现的事件次数无关.如,在某一给定时间的故障数将由下式给出:
具体都可参考MIL-HDBK-338B, 论坛中中英文都可以下载到
