Huairui Guo

Reliability estimation for one-shot systems with zero component test failures

Te for one-shot systems such as missiles and rockets are very expensive. In order to design an efficient test plan to demonstrate the required reliability in the final system test, system reliability should be studied in advance. Before the final system tests, many subsystem level tests usually have already been conducted by customers and manufacturers. Therefore, the system reliability can be estimated using the information obtained from these tests before the final system test. Due to the highly reliable nature of one-shot systems, it is very unlikely to observe many failures, even at the subsystem level tests. To accurately estimate the system reliability with few failures or even without failures is very challenging. A lot of research has been done on how to estimate the system reliability and its confidence intervals from its subsystem test data. However, most of them require failures at the sub-level tests. When there are no failures, these methods do not work. In this paper, a flexible and practical method is designed to estimate the system reliability and its confidence bounds when there are few or no failures during the subsystem tests. This method can be applied to series, parallel and complex systems. The estimated system reliability information is then used to design an efficient test plan for the final system reliability demonstration test. A case study shows that the proposed method is very efficient and accurate when compared with existing methods and simulation results.

Designing Reliability Demonstration Tests for One-Shot Systems Under Zero Component Failures

It is difficult to estimate the confidence interval of a systems reliability with zero failures experienced. We approach this problem by proposing a hybrid model that integrates the Bayesian model with the variance propagation technique. The Bayesian model will compute the moments of component reliability estimates, and the variance propagation technique is used to estimate the system reliability variance. The confidence interval for the system reliability is then derived by matching the moments with a beta distribution. As a major contribution, the distribution for reliability estimates with zero failures is explicitly derived. The performance of the new model is compared with existing methods, and further validated by simulation data. The results show that the hybrid model generally outperforms existing methods in terms of estimation accuracy. Because the new model does not require multiple integral calculations, it can be applied to design complex systems configured in mixed series-parallel or networked components.

Modeling and analysis for degradation with an initiation time

For failure modes that are caused by a degradation mechanism, almost all of the existing models assume that degradation starts once a product begins operation. However, under some situations, there is a degradation free period where degradation starts only after an initiation time. Both the initiation period and the degradation growth period affect the product reliability. The lengths of these two periods are usually governed by different failure mechanisms. In this paper, a two-step strategy for modeling degradation with an initiation period is proposed. Individual models are first built for the degradation free and the degradation growth periods. These two models are then integrated to obtain the final reliability model of the system. The relative importance values of the degradation free period and the degradation growth period with respect to product reliability are also studied. The importance values can help engineers allocate resources to improve the reliability of a product more effectively.

Piecewise NHPP models with maximum likelihood estimation for repairable systems

Non-homogeneous Poisson process (NHPP) models are widely used for repairable system analysis. Different NHPP models have been developed for different applications. It has been noticed that almost all the existing models apply only a single model for the entire system development or operation period. However, in some circumstances, such as when the system design or the system operation environment experiences major changes, a single model will not be appropriate to describe the failure behavior for the entire timeline. In this paper, we proposed a piecewise NHPP model for repairable systems with multiple stages. The maximum likelihood estimation (MLE) for the model parameters is also provided.

Warranty prediction for products with random stresses and usages

Making accurate warranty predictions is challenging. It becomes even more challenging when products are operated under random stresses and random usages. Traditional method only uses the average values of these random variables for warranty prediction. The randomness of the variables is ignored, which may result in inaccurate results. This paper presents methods to solve this issue. Solutions for two different situations are discussed. In the first situation, only random stresses are the major concern. In the second situation, both random stresses and random customer usages are considered. Two analytical solutions, the exact and the approximated solution, are provided for each case. The comparison shows that, although they are simple to use, approximated solutions can be very different from the exact results. In this paper, not only the mean value of the warranty prediction, but also the variances and intervals of the prediction are calculated. This is much better because interval estimate provides more information than a simple point estimate. The proposed methods can be applied to many industries such as electronic, automobile and home appliance companies.

Improved Reliability Using Accelerated Degradation & Design of Experiments

For many products, an underlying degradation process is the root cause of failures. Often, such degradation processes are not directly observable and all that can be learned from the test is the time of failure. In order to get useful information in a short time, accelerated degradation testing is frequently used. Most of the existing degradation analysis methods assume that the degradation process can be regularly inspected and the degradation amount can be easily and accurately measured. Unfortunately, for many products and many testing processes, this is not an easy task. In this paper, a design of experiment (DOE) method of using the degradation process together with the observed failure data to improve reliability is proposed. Unlike other degradation analysis methods, the proposed method does not require regular degradation measurements. In the use of DOE, all the factors that affect the degradation process are classified into two types. The Type I factor is called the amplification factor. Its effect on degradations is well known based on the engineering knowledge of the physical process of the degradation. This factor is used to amplify (accelerate) the degradation process. The type II factors are called control factors. Their effects are unknown and need to be studied by experiments. By combing the engineering knowledge and the observed failures, the effects of control factors are analyzed using a linear regression method. Important effects and the optimum settings of control factors are identified. The product reliability can be improved by operating under the optimum settings.

On determining optimal inspection interval for minimizing maintenance cost

The majority of system failures do not occur without any warning signs. This is especially true for failures caused by degradation. By examining the failure-critical indexes during scheduled inspections, actions can be taken to address degraded components and prevent big losses due to failures. In this paper, we assume that an imminent failure can be noticed when an inspection is conducted during a short time period right before the failure. Clearly, by conducting frequent inspections, failures can always be detected and prevented. However, the total inspection cost will be very high if the inspection interval is too short. On the other hand, if the inspection interval is too long, a coming failure may not be effectively detected and the total cost due to failures will be high. Therefore, an optimal inspection interval balancing these two costs needs to be identified. A model for determining the optimal inspection interval to minimize the maintenance cost is proposed in this paper. The analytical solution of the model is provided and compared with simulation results. The proposed method is especially useful for process industries such as oil and gas refineries, food processing and pharmaceutical manufacturing. By conducting optimal inspections for components with degradation characteristics, failures will be prevented, maintenance cost will be reduced and the process throughput can be improved.

Improving the 1-parameter Weibull: A Bayesian approach

Using maximum likelihood estimation (MLE) to estimate the parameters in a Weibull distribution will lead to a biased estimation of the shape parameter when the sample size is small or too few failures are observed. This bias may lead to inaccurate reliability point estimates. In addition, with few data points available in the calculation, the uncertainty of the estimated parameters is high, which again leads to high uncertainty in the predicted reliability (i.e. wide confidence bounds). To overcome these two issues, the 1-parameter Weibull distribution has been widely used, provided that the shape parameter is known beforehand. This approach, however, does not account for any uncertainty in the assumed value of the shape parameter and can therefore yield optimistic results in the form of tight confidence bounds. It can be improved with better information about the variability of the shaper parameter. In this paper, a Bayesian model, which is an improved approach for the 1-parameter Weibull, is discussed. Recommendations for establishing variability models for the Weibull shape parameter are presented.

On planning accelerated life tests for comparing two product designs

Accelerated life test (ALT) planning is one of the most important and challenging tasks for reliability engineers. Since the late 1970s, methods for efficient ALT planning have been studied extensively and over 150 research papers have been published [1]. Most of the existing methods focus on designing tests to minimize the estimation precision of model parameters or their functions. Popularly used test designs such as the 2-level statistically optimum plan, 3-level best compromise plan and 3-level best standard plan are all based on this theory. However, although these designs are very useful for estimating distribution parameters or given reliability metrics, they are not efficient for planning tests that compare different products. In this paper, we will present two methods for designing ALT to compare two different designs in terms of their B10 life. The probability of detecting a given amount of difference of the B10 lives is the focus of the proposed methods. This probability usually is called detection power. Comparing the estimated lives of two designs is the same as comparing two random variables since each life estimated through the ALT data is a random variable. According to the required detection probability, the sample size of a comparison test can be determined by either the analytical or the simulation method given in this paper. An example is used in the paper to illustrate the theory and the applications of the proposed methods. The presented methods are general methods and can be extended to other situations and applied beyond the example used in this paper.

Field repairable system modeling with missing failure information

Many systems, ranging from military vehicles to drink dispensers used in restaurants, are repairable. Operation and failure data from this type of system are often collected by manufacturers and customers. The data are used to monitor system performance as well as for reliability prediction and system improvement. However, due to errors in collecting the data, including human errors, raw field data are rarely suitable for reliability modeling. Data cleanup and certain assumptions have to be made in order to use existing statistical modeling technologies. This is the main challenge the authors have encountered when they tried to model a fleet of fielded repairable systems. An example is a situation where multiple machines are located at the same site, and data on the sites location, instead of the failed machines ID, are collected. Without knowing which particular machine had the failure, the existing non-homogeneous Poisson process (NHPP) modeling method cannot be applied [1-3]. This type of missing data is called masked data for repairable systems. In this paper, a method for modeling masked failure data is proposed and its application is illustrated using a case study. The proposed method can be used to predict the number of failures and the confidence bounds at a given operation time.