عدم قطعیت و تجزیه و تحلیل حساسیت از مدل ارزیابی ریسک عملیاتی پویا: یک مطالعه موردی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|26328||2010||8 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Loss Prevention in the Process Industries, Volume 23, Issue 2, March 2010, Pages 300–307
In Dynamic Operational Risk Assessment (DORA) models, component repair time is an important parameter to characterize component state and the subsequent system-state trajectory. Specific distributions are fit to the industrial component repair time to be used as the input of Monte Carlo simulation of system-state trajectory. The objective of this study is to propose and apply statistical techniques to characterize the uncertainty and sensitivity on the distribution model selection and the associated parameters determination, in order to study how the DORA output that is the probability of operation out-of-control, can be apportioned by the distribution model selection. In this study, eight distribution fittings for each component are performed. Chi-square test, Kolmogorov–Smirnov test, and Anderson-Darling test are proposed to measure the goodness-of-fit to rank the distribution models for characterizing the component repair time distribution. Sensitivity analysis results show that the selection of distribution model among exponential distribution, gamma distribution, lognormal distribution and Weibull distribution to fit the industrial data has no significant impact on DORA results in the case study.
For Dynamic Operational Risk Assessment (DORA) models (Fig. 1), component state sojourn time distributions are the inputs for system-state trajectory simulation. Among the three component states (Fig. 2), the third state (abnormal detected and under repair) sojourn time distribution is obtained by fitting distribution to industry component repair time data. In the case that the collected data is sufficient enough, distribution fitting is statistically satisfied with accepted uncertainty. However, it is not always possible to find enough data. In a highly reliable system, a single failure may occur at a frequency in order of 10−6 or 10−7and repair happens at a corresponding low frequency so that the repair data is usually not enough for a good distribution fitting. Given the limited repair time data points, the major concern on uncertainty includes: 1) what distribution type should be selected; 2) whether the distribution type is a sensitive factor for DORA results. Full-size image (46 K) Fig. 1. Scheme of DORA model. Figure options Full-size image (28 K) Fig. 2. Component state flow diagram. Figure options Therefore the problem first becomes to select a distribution model and the associated distribution parameters for characterizing component state sojourn time that have the best representation among a class of distributions. There are several techniques to examine how well a sample of data agrees with a given distribution as its population. In those goodness-of-fit techniques, hypothesis test is based on measuring the discrepancy or consistency of the sample data to the hypothesized distribution. Chi-square test is used to measure how well the fit matches the data if the data are represented by discrete points with Gaussian uncertainties (Bock & Krischer, 1998). However, the value of the chi-square test statistic depends on how the data is binned. Another disadvantage of the chi-square is that it requires an adequate sample size for the approximations to be valid. Pearson's Chi-square test is distinguished from the case with Gaussian errors, and is applied if the data are represented by integer numbers of events in discrete bins, following Poisson statistics rule (Cowan, 1998). Kolmogorov–Smirnov (K–S) test is a goodness-of-fit measurement technique for one-dimensional data samples. It is used to test whether the data sample comes from a population with a specific distribution (Chakravarti, Laha, & Roy, 1967). Anderson-Darling test (Stephens, 1974) is a modification of K–S test and gives more weight to the tails than does the K–S test. There are several others, such as the Shapiro–Wilk test (Shapiro & Wilk, 1965) and the probability plot (Chambers, Cleveland, Kleiner, & Tukey, 1983) for goodness-of-fit measurement. When a failure occurs to a component, the component must be repaired and it is then unavailable for processing during a certain amount of time called the repair time (Dallery & Gershwin, 1992). In reliability engineering, random variables from exponential distribution, gamma distribution, lognormal distribution or Weibull distribution are usually assumed to characterize the time-to-repair distribution in most of the models. By selecting candidates from those distribution families, epistemic uncertainty is reduced using engineer expert judgment. The uncertainty is further reduced by selecting the distribution model according to the rank of goodness-of-fit. In Section 2 of this paper, eight distributions are fitted into the component repair time data. In Section 3 the goodness-of-fit is measured using Chi-square test, K–S test and A-D test. A sensitivity analysis is performed in Section 4 to study the impact of distribution type selection to the dynamic operational risk assessment results. A summary of this research study is presented in Section 5.
نتیجه گیری انگلیسی
In this study, the component State 3 sojourn time was characterized by fitting distributions to the limited industrial data. Four time-to-repair distribution types widely applied in reliability engineering and used in this study are exponential distribution, gamma distribution, lognormal distribution, and weibull distribution. Two distributions with different number of parameters from each distribution type were selected as the fitting candidates. Goodness-of-fit measurement results show that pump and LT repair time data fit to lognormal distribution with three parameters the best and CV repair time data fit to lognormal distribution the best. Uncertainty associated with the component State 3 sojourn time distribution type was reduced by ranking the fitting hypothesis using Chi-square test, K–S test, and A-D test. The significance of this study is that statistical approaches are recommended and applied to analyze data before DORA study, and sensitivity analysis is recommended to study the response of DORA results to the initial data inputs. Sensitivity analysis results show that the probability of operation out-of-control has no significant response to the component repair time distribution model chosen as the DORA input in this level control system in the oil/gas separator case study. This conclusion does not mean that any distribution type could be selected as DORA input. On the contrary, the uncertainty and sensitivity analysis proposed in this paper should be performed for any other DORA study to achieve desirable quality of a risk assessment.