数控机床可靠性试验设计及评估方法研究
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摘要
可靠性试验是获取故障信息、进行可靠性分析、评价、实施可靠性增长等可靠性研究的重要基础,可靠性试验方案合理与否必将影响后续可靠性工作的顺利进行。因此,进行数控机床可靠性试验和评价技术的研究对于快速、准确确定数控机床可靠性薄弱环节、评定其可靠性水平及选择合理措施实施可靠性增长具有重要的理论意义和实际意义。
本文在现有可靠性试验研究的基础上,结合数控机床的特点,分别从定时截尾试验、定数截尾试验、序贯试验和基于贝叶斯理论的试验四个方面,并综合考虑生产方风险、使用方风险、鉴别比、MTBF预计值等信息进行可靠性试验方案设计,对于不同试验方案提出相应的数据分析和可靠性评估方法。
论文首先针对数控机床服从威布尔分布的特点,将威布尔分布通过参数变换转化为指数分布模式,结合指数分布决策风险方程组,确定数控机床定时截尾试验方案和定数截尾试验并在厂家实施。考虑截尾时间对评估结果的影响,论文采用“故障总时间法”对故障数据进行处理;采用“取中逐步推移检验法”进行异常数据检验;采用“残存比率法”求解经验分布函数;根据故障数据的趋势,建立可靠性模型,根据可靠性模型中的形状参数与定时截尾、定数截尾试验方案设计时选取的形状参数进行对比,验证方案的设计是否合理,进而评价其可靠性水平。
其次根据数控机床故障发生个数的概率在威布尔分布下的描述,结合传统序贯试验方案设计方法,确定数控机床的序贯试验方案。由于序贯试验中故障点可能会处于继续试验区而迟迟不能做出判决,通过增加截尾故障数和截尾试验时间的方式,并调整接收线和拒收线以适应决策风险的约束,对数控机床设计出截尾序贯试验方案。由于序贯试验可能出现早早结束试验的情况,会导致故障信息不足而无法准确评估可靠性真值,因此本文基于序贯思想,采用动态截尾试验的方法,对故障数据进行实时的动态采集、动态评估,当可靠性评价指标值的变化处于允许误差的范围内,停止试验。
最后,根据数控机床故障率的先验信息,将贝叶斯理论引入到可靠性试验研究中,经贝叶斯的后验风险确定基于贝叶斯理论的定时截尾试验方案。将第2章定时截尾试验中采集到的故障数据应用于贝叶斯试验方案中,由于贝叶斯试验方案的试验时间较短使故障数据呈现小样本类型的特点,采用参数偏差修正方法对该故障数据建立的可靠性模型进行修正和验证,进而评价出可靠性水平。
定时或定数截尾试验不仅能做出判决,还能够在试验中得到足够的故障信息,从而可准确评估可靠性指标值。此外,定时截尾试验方案在试验前已确定试验时间及试验台数,便于控制试验的进程,以实现对试验费用和资源的预估;定数截尾试验方案在试验前能确定试验的最大故障数,从而得到足够的故障数据,为故障分析的工作提供基础信息。截尾序贯试验相对于定时和定数截尾试验的平均试验时间短,在只需判决数控机床的可靠性水平是否合格,并不需要评估其指标的情况下,选择截尾序贯试验更为适宜。在厂家急需做出判决,又不愿提高决策风险的情况下,若能够得到准确的故障率先验信息,可采用基于贝叶斯的定时截尾试验方案。
Reliability test is an important foundation for reliability study that includes obtaining fault information, conducting reliability analysis and evaluation, and implementing reliability improvement. Reliability experimental designs, whether reasonable or not, will greatly affect the smoothness of follow-up reliability work. Therefore, research on reliability tests and evaluation techniques of CNC machine tools has important theoretical and practical significance for promptly and accurately determining the weak links of CNC machine tools, assessing their reliability levels, and selecting reasonable measures to implement reliability improvement.
Based on the results available on reliability test research and the characteristics of CNC machine tools, this paper studies reliability test designs in the following four areas: fixed-time censoring scheme, fixed-number of failures censoring scheme, sequential progressive experiments, and Bayesian reliability tests. Considering manufacturer-side risks, user-side risks, identification ratio, MTBF expectation value, and other information, we conduct reliability experimental designs and propose data analysis and reliability assessment methods for different testing designs.
In this paper, based on the characteristics of CNC machine tools’life following the Weibull distribution, we first transfer the Weibull distribution to the exponential distribution through a parameter transformation, combine with the exponential distribution decision-making risk equations, determine the fixed-time censoringand fixed-number test designs for CNC machine tools, and implement the designs in the manufacturers. By considering the impact of truncated time on assessment results, the paper analyzes the fault data using the total failure time method, conducts abnormal data testing using the "average and gradually take over test method" , solves empirical distribution functions based on the "residual ratio method", builds reliability models according to the trend in the fault data, verifies whether the proposed designs are reasonable or not and assesses their reliability levels by comparing the estimated shape parameter in the reliability models with the shape parameters selected initially in the fixed-time design and in the fixed-number design.
Second, based on the probability of number for CNC machine tool failures under the Weibull distribution and combining with the traditional sequential experimental design approach, we determine sequential experimental designs for the CNC machine tools. As a decisionin a sequential experimental design may be delayed for long time because the failure points may still be in the testing period, we design truncated sequential experiments for CNC machine tools by increasing truncated failure number and truncated testing time, and modify the acceptation line and rejection line to meet the constraints of decision-making risks. Since a sequential test may be ended too early and result in insufficient failure information for assessing the true reliability value accurately, in this paper, we use the dynamic censoring method for reliability assessment of CNC machine tools based on the idea of sequential experiments, dynamically collect and assess fault data, and stop the experiment when the change of the reliability assessment index is within the tolerable error range.
Third, based on the prior information for the CNC machine tool failure rate, we introduce the Bayesian theory into the reliability test research and determine Bayesian fixed-time censoring experimental designs by calculating the Bayesian posterior risks. The fault data collected in the fixed-time censoring experiment in chapter 2 will be applied to the Bayesian experimental design. Since the testing time of a Bayesian experimental design is relatively shorter and results in smaller number of fault data points, we adopt the parameters bias correction method to modify and verify the reliability model built based on the fault data, and further evaluate the reliability level.
Fixed-time censoring and fixed-number censoring experiments are able to make the right decision, obtain enough fault data information in the experiment, and accurately assess the reliability index. In addition, fixed-time censoring scheme determines the total test time and number of machine tools before the experiment, which is easy to control the trial process and estimate the cost and resources of the experiment; fixed-number censoring experiment determines the maximum number of failures before the experiment, which gathers enough failure information and provides a reasonable basis for the failure analysis. The average test time of a truncated sequential test is shorter than that of fixed-time censoring and fixed-number censoring experiments. When we only need to decide whether the reliability level of CNC machine tools is satisfied or not and do not need to assess the reliability index, selecting the truncated sequential experimental design is more appropriate. If the manufacturers need to make judgments urgently and do not want to increase the decision risks, fixed-time censoring experimental designs based on the Bayesian method should be selected if prior information of the failure rate could be obtained accurately.
本文在现有可靠性试验研究的基础上,结合数控机床的特点,分别从定时截尾试验、定数截尾试验、序贯试验和基于贝叶斯理论的试验四个方面,并综合考虑生产方风险、使用方风险、鉴别比、MTBF预计值等信息进行可靠性试验方案设计,对于不同试验方案提出相应的数据分析和可靠性评估方法。
论文首先针对数控机床服从威布尔分布的特点,将威布尔分布通过参数变换转化为指数分布模式,结合指数分布决策风险方程组,确定数控机床定时截尾试验方案和定数截尾试验并在厂家实施。考虑截尾时间对评估结果的影响,论文采用“故障总时间法”对故障数据进行处理;采用“取中逐步推移检验法”进行异常数据检验;采用“残存比率法”求解经验分布函数;根据故障数据的趋势,建立可靠性模型,根据可靠性模型中的形状参数与定时截尾、定数截尾试验方案设计时选取的形状参数进行对比,验证方案的设计是否合理,进而评价其可靠性水平。
其次根据数控机床故障发生个数的概率在威布尔分布下的描述,结合传统序贯试验方案设计方法,确定数控机床的序贯试验方案。由于序贯试验中故障点可能会处于继续试验区而迟迟不能做出判决,通过增加截尾故障数和截尾试验时间的方式,并调整接收线和拒收线以适应决策风险的约束,对数控机床设计出截尾序贯试验方案。由于序贯试验可能出现早早结束试验的情况,会导致故障信息不足而无法准确评估可靠性真值,因此本文基于序贯思想,采用动态截尾试验的方法,对故障数据进行实时的动态采集、动态评估,当可靠性评价指标值的变化处于允许误差的范围内,停止试验。
最后,根据数控机床故障率的先验信息,将贝叶斯理论引入到可靠性试验研究中,经贝叶斯的后验风险确定基于贝叶斯理论的定时截尾试验方案。将第2章定时截尾试验中采集到的故障数据应用于贝叶斯试验方案中,由于贝叶斯试验方案的试验时间较短使故障数据呈现小样本类型的特点,采用参数偏差修正方法对该故障数据建立的可靠性模型进行修正和验证,进而评价出可靠性水平。
定时或定数截尾试验不仅能做出判决,还能够在试验中得到足够的故障信息,从而可准确评估可靠性指标值。此外,定时截尾试验方案在试验前已确定试验时间及试验台数,便于控制试验的进程,以实现对试验费用和资源的预估;定数截尾试验方案在试验前能确定试验的最大故障数,从而得到足够的故障数据,为故障分析的工作提供基础信息。截尾序贯试验相对于定时和定数截尾试验的平均试验时间短,在只需判决数控机床的可靠性水平是否合格,并不需要评估其指标的情况下,选择截尾序贯试验更为适宜。在厂家急需做出判决,又不愿提高决策风险的情况下,若能够得到准确的故障率先验信息,可采用基于贝叶斯的定时截尾试验方案。
Reliability test is an important foundation for reliability study that includes obtaining fault information, conducting reliability analysis and evaluation, and implementing reliability improvement. Reliability experimental designs, whether reasonable or not, will greatly affect the smoothness of follow-up reliability work. Therefore, research on reliability tests and evaluation techniques of CNC machine tools has important theoretical and practical significance for promptly and accurately determining the weak links of CNC machine tools, assessing their reliability levels, and selecting reasonable measures to implement reliability improvement.
Based on the results available on reliability test research and the characteristics of CNC machine tools, this paper studies reliability test designs in the following four areas: fixed-time censoring scheme, fixed-number of failures censoring scheme, sequential progressive experiments, and Bayesian reliability tests. Considering manufacturer-side risks, user-side risks, identification ratio, MTBF expectation value, and other information, we conduct reliability experimental designs and propose data analysis and reliability assessment methods for different testing designs.
In this paper, based on the characteristics of CNC machine tools’life following the Weibull distribution, we first transfer the Weibull distribution to the exponential distribution through a parameter transformation, combine with the exponential distribution decision-making risk equations, determine the fixed-time censoringand fixed-number test designs for CNC machine tools, and implement the designs in the manufacturers. By considering the impact of truncated time on assessment results, the paper analyzes the fault data using the total failure time method, conducts abnormal data testing using the "average and gradually take over test method" , solves empirical distribution functions based on the "residual ratio method", builds reliability models according to the trend in the fault data, verifies whether the proposed designs are reasonable or not and assesses their reliability levels by comparing the estimated shape parameter in the reliability models with the shape parameters selected initially in the fixed-time design and in the fixed-number design.
Second, based on the probability of number for CNC machine tool failures under the Weibull distribution and combining with the traditional sequential experimental design approach, we determine sequential experimental designs for the CNC machine tools. As a decisionin a sequential experimental design may be delayed for long time because the failure points may still be in the testing period, we design truncated sequential experiments for CNC machine tools by increasing truncated failure number and truncated testing time, and modify the acceptation line and rejection line to meet the constraints of decision-making risks. Since a sequential test may be ended too early and result in insufficient failure information for assessing the true reliability value accurately, in this paper, we use the dynamic censoring method for reliability assessment of CNC machine tools based on the idea of sequential experiments, dynamically collect and assess fault data, and stop the experiment when the change of the reliability assessment index is within the tolerable error range.
Third, based on the prior information for the CNC machine tool failure rate, we introduce the Bayesian theory into the reliability test research and determine Bayesian fixed-time censoring experimental designs by calculating the Bayesian posterior risks. The fault data collected in the fixed-time censoring experiment in chapter 2 will be applied to the Bayesian experimental design. Since the testing time of a Bayesian experimental design is relatively shorter and results in smaller number of fault data points, we adopt the parameters bias correction method to modify and verify the reliability model built based on the fault data, and further evaluate the reliability level.
Fixed-time censoring and fixed-number censoring experiments are able to make the right decision, obtain enough fault data information in the experiment, and accurately assess the reliability index. In addition, fixed-time censoring scheme determines the total test time and number of machine tools before the experiment, which is easy to control the trial process and estimate the cost and resources of the experiment; fixed-number censoring experiment determines the maximum number of failures before the experiment, which gathers enough failure information and provides a reasonable basis for the failure analysis. The average test time of a truncated sequential test is shorter than that of fixed-time censoring and fixed-number censoring experiments. When we only need to decide whether the reliability level of CNC machine tools is satisfied or not and do not need to assess the reliability index, selecting the truncated sequential experimental design is more appropriate. If the manufacturers need to make judgments urgently and do not want to increase the decision risks, fixed-time censoring experimental designs based on the Bayesian method should be selected if prior information of the failure rate could be obtained accurately.
引文
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