摘要
试验样本容量的选择在科学研究及产品开发中占有十分重要的地位。随着机械设备系统越来越复杂,功能要求越来越多样,人们对产品的可靠性要求也不断提高。验证高可靠性产品往往需要试验大量样品,这既耗费大量时间又增加研制成本。为解决这个问题,本文开展了汽车零部件可靠性评估的小样本方法研究,主要工作及结论如下:
(1)引入继承因子来利用验前信息,推导了带继承因子的二项分布、指数分布可靠度置信下限。研究结果表明:可靠度随继承因子增大而增大,但评估结果介于历史可靠度和现场试验可靠度之间。二项分布验后分布密度对验前分布超参数较敏感,特别当代表验前失效次数的b值较大时会出现验后密度为负值的不合理现象,建议当b≤3时使用Beta验前分布。
(2)以试验时间为纽带建立可靠度与试验应力之间的关系。根据这个关系可以通过改变试验应力来改变设计可靠度。结果表明:对于有替换定时截尾情形,当截尾时间延长至原来的k倍后,如果保持可靠度和置信度不变,指数分布所需样本数减至原来的1 /k,Weibull分布所需样本数减至原来的1 /km(m为Weibull分布形状参数);延长的时间可以通过加速寿命技术来缩短。算例表明,指数分布平均寿命延长至原来的1.784倍后,可靠度从0.9增至0.9427,相当于保持可靠度为0.9时试验样本从6减至1,减幅达83%;Weibull分布特征寿命延长至原来的1.72倍后,可靠度从0.9增至0.99,相当于保持可靠度为0.9861时试验样本从6减至1。对于高可靠度产品,样品数减幅将更大。
(3)通过对可靠性影响因素研究,建立了生产过程中关键特征的联合分布密度函数来推导产品寿命与关键特征的函数关系。根据关键特征分布密度函数及其与产品寿命的关系推导寿命的分布密度函数,并由寿命分布密度函数建立可靠度函数。最后通过调查一个工厂某种产品的历史质量状况(过程能力指数)来初步确定该类产品的历史可靠性。根据历史可靠度Rd,实际测试样本量可减少为为原来的100(1-Rd)%。
Determination of testing sample size is occupied a critical position in the scientific study and product development. With the mechanical system and function getting more and more complicated, the reliability requirement of product is also getting strict. It needs lots of samples to verify the reliability requirement, which may consume much time and raise product cost. To solve this problem, the reliability assessment methods with small sample size have been studied in this paper. Main contents are as following.
(1) By introducing inherited factor, the lower limit formula of reliability is derived on binominal distribution and exponential distribution. Reliability grows with the growing of inherited factor, and last results of reliability evaluation are between prior-test reliability and testing reliability. The density of the binomial distribution is sensitive to parameters of prior-test distribution. Especially, when parameterb which represents failure times is too large, the post-test density is sometimes negative or larger than 1, which is obviously unreasonable. So, b≤3 is suggested when using prior-test Beta distribution.
(2) In order to building a relationship between testing stress level and reliability, duty time is used as an intermediate variable which is like a belt. For time-fixed replaceable cesser test, if the the cesser-time is extended tok times of original one, the required sample size of exponential distribution will become 1 /kof it, and Weibull distribution will be 1 /km. The calculation shows that when average life is extended to 1.784 times of requirement, the reliability of exponential distribution will increase from 0.9 to 0.9427, which means the testing sample size decreases from 6 to 1, and the decrease rate is 83%. For Weibull distribution, when character lifeηis extended to 1.72 times, the reliability will grow from 0.9 to 0.99, which means the sample size decrease from 6 to 1 still with reliability 0.9861. Especially for products with high reliability, the decrease of sample size will be larger.
(3) The influencing factors of reliability are researched in this paper. The jointed probability density function of critical characteristics and the life function of critical characteristics are built for deriving the probability density function of life. According to the life probability density function, the reliability function is built to calculate the historical reliability of the products with the same category. By investigating the quality history (process capability index), the historical reliability Rd can be calculated for reducing the testing sample size, and the testing sample size can decrease by 100Rd%.
引文
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