Jyun-You Chiang

Degradation Tests Using Geometric Brownian Motion Process for Lumen Degradation Data

Running a traditional life test over an affordable time period with highly reliable products is inefficient to collect the lifetime information of products even if the products are subject to higher stress conditions. This fact makes it difficult to infer the reliability of highly reliable products. The accelerated degradation test (ADT) method has been suggested as an alternative to infer the reliability of highly reliable product based on its degradation measurements. The current study is motivated by the statistical modeling of the lumen degradation date set of transistor outline can packaged light emitting diodes (LEDs). All degradation measurements were collected from an ADT, which was conducted with two stress loadings, the ambient temperature and drive current. To study the reliability of the LEDs under the ADT, the geometric Brownian motion process and generalized Eyring model are applied to estimate the distribution parameters and percentiles of the LEDs. Planning strategies of the sample size and measurement times for the proposed ADT are established to minimize the asymptotic variance of maximum-likelihood estimator of the lower 100pth percentile of LED lifetimes under the given budget. An algorithm is provided to reach the planning strategy. The guidelines of this study can be extended to infer the reliability of other highly reliable product besides LEDs. Copyright

THE DESIGN OF ACCEPTANCE CONTROL CHART FOR NON-NORMAL DATA

ABSTRACT Control charts often are designed under the normality assumption. But in some manufacturing processes this assumption may not be valid. Tsai [12] developed a skew normal X control chart to monitor the process average for non-normal data. He showed that a considerable improvement over those of existing control charts can be achieved when the skew normal X control chart is used to monitor the process average. Based on the skew normal X control chart, the paper develops a skew normal acceptance control chart to monitor the process average and the fraction of nonconformities for non-normal data. The proposed acceptance control chart reduces to the conventional acceptance control chart as the underlying distribution of measurements is symmetric. Two examples are given for illustration. The presented examples show that the construction of the proposed acceptance control chart is easy, moreover, ignoring the non-normality effect will result in a higher type I or type II error probability.

An integrated approach for the optimization of tolerance design and quality cost

We use integrated approach method to establish an optimization strategy.The optimal tolerance limits and investment level of production are identified.The strategy is applicable for both the symmetric and skewed distributions.The new strategy helps to reduce the expected total cost of production. Different normality-based optimization strategy (NBOS) methods have been developed and used to perform quality improvement in the past few decays. Improving the quality of a production process using a NBOS method possibly incurs misleading results if the quality measurements follow a skewed distribution. An integrated model, with components of a tolerance cost model for the determinations of optimal tolerance limits and a quality investment model for the identification of optimal investment level, is applied to establish a new optimization strategy method for the skew normal distribution (SND), named SNDOS method. The SND generalizes the normal distribution to include skewed distributions as members, and hence the SNDOS method is applicable for quality improvement either the distribution of quality measurements follow a symmetric or skewed distribution. Two examples about car seat production process are used to illustrate the application of the SNDOS method. The sensitivity of the SNDOS method to the loss coefficient of the integrated model is evaluated for different inputs of the skewness parameter of the SND through a numerical study.

MEWMA Control Chart and Process Capability Indices for Simple Linear Profiles with Within‐profile Autocorrelation

A multivariate exponentially weighted moving average (MEWMA) control chart is proposed for detecting process shifts during the phase II monitoring of simple linear profiles (SLPs) in the presence of within-profile autocorrelation. The proposed control chart is called MEWMA-SLP. Furthermore, two process capability indices are proposed for evaluating the capability of in-control SLP processes, and their utilization is demonstrated through examples. Intensive simulations reveal that the MEWMA-SLP chart is more sensitive than existing control charts in detecting profile shifts. Copyright

Control charts for generalized exponential distribution percentiles

ABSTRACT The generalized exponential (GE) distribution, which was introduced by Mudholkar and Srivastava in 1993, has been studied for various applications of lifetime modelings. In this article, five control charts, that comprise the Shewhart-type chart and four parametric bootstrap charts based on maximum likelihood estimation method, the moment estimation method, probability plot method, and least-square error method for the GE percentiles, are investigated. An extensive Monte Carlo simulation study is conducted to compare the performance among all five control charts in terms of average run length. Finally, an example is given for illustration.

Estimation on the lower confidence limit of the breaking strength percentiles under progressive type-II censoring

The breaking strength information of structure components is highly correlated with the safety manufacturing and much concerned by engineers. Components with deficient safety quality will be rejected to rework or discard due to an unsatisfactory level of the lower critical breaking strength percentile. When the breaking strength of components is assumed to have a Burr type-XII distribution, five parametric bootstrap methods are suggested to adjust the bias of the lower confidence limit estimate of the lower percentile with progressive type-II censored samples. The performance of the proposed bootstrap methods is evaluated through an intensive simulation study. Numerical results show that the hybrid bootstrap method and the bias-corrected and accelerated bias-corrected methods perform better with coverage probabilities near the nominal confidence level for almost all the cases considered. An example of the breaking strength data set of aluminum sheets is used for illustration.

Adaptive control charts for skew-normal distribution

The standard Shewhart-type X̄ chart, named FSS-X̄ chart, has been widely used to detect the mean shift of process by implementing fixed sample and sampling frequency schemes. The FSS-X̄ chart could be sensitive to the normality assumption and is inefficient to catch small or moderate shifts in the process mean. To monitor non-normally distributed variables, there are papers concerning skew-normal FSS-X̄ (SN FSS-X̄) chart with exact control limits for the SN distribution. To enhance the sensitivity of the SN FSS-X̄ chart on detecting small or moderate mean shifts in the process, adaptive X̄ charts with variable sampling interval (VSI), variable sample size (VSS), and variable sample size and sampling interval (VSSI) are introduced for the SN distribution in this study. The proposed adaptive control charts include the normality adaptive charts as special cases. Simulation results show that all the proposed SN VSI-X̄ , SN VSS-X̄ and SN VSSI-X̄ charts outperform the SN FSS-X̄ chart on detecting small or moderate shifts in the process mean. The impact of model misspecification on using the proposed adaptive charts and the sample size impact for using the FSS-X̄ chart to monitor the mean of SN data are also discussed. An example about single hue value in polarizer manufacturing process is used to illustrate the applications of the proposed adaptive charts.

Empirical Bayesian Strategy for Sampling Plans with Warranty Under Truncated Censoring

To reach an optimal acceptance sampling decision for products, whose lifetimes are Burr type XII distribution, sampling plans are developed with a rebate warranty policy based on truncated censored data. The smallest sample size and acceptance number are determined to minimize the expected total cost, which consists of the test cost, experimental time cost, the cost of lot acceptance or rejection, and the warranty cost. A new method, which combines a simple empirical Bayesian method and the genetic algorithm (GA) method, named the EB-GA method, is proposed to estimate the unknown distribution parameter and hyper-parameters. The parameters of the GA are determined through using an optimal Taguchi design procedure to reduce the subjectivity of parameter determination. An algorithm is presented to implement the EB-GA method. The application of the proposed method is illustrated by an example. Monte Carlo simulation results show that the EB-GA method works well for parameter estimation in terms of small bias ...

Model Selection Approaches for Predicting Future Order Statistics from Type II Censored Data

This paper studies a discriminant problem of location-scale family in case of prediction from type II censored samples. Three model selection approaches and two types of predictors are, respectively, proposed to predict the future order statistics from censored data when the best underlying distribution is not clear with several candidates. Two members in the location-scale family, the normal distribution and smallest extreme value distribution, are used as candidates to illustrate the best model competition for the underlying distribution via using the proposed prediction methods. The performance of correct and incorrect selections under correct specification and misspecification is evaluated via using Monte Carlo simulations. Simulation results show that model misspecification has impact on the prediction precision and the proposed three model selection approaches perform well when more than one candidate distributions are competing for the best underlying distribution. Finally, the proposed approaches are applied to three data sets.

Robust bootstrap control charts for percentiles based on model selection approaches

Abstract This paper presents two model selection approaches, namely the random data-driven approach and the weighted modeling approach, to construct robust bootstrap control charts for process monitoring of percentiles of the shape-scale class of distributions under model uncertainty. The generalized exponential, lognormal and Weibull distributions are considered as candidate distributions to establish the proposed process control procedures. Monte Carlo simulations are conducted with various combinations of the percentiles, false-alarm rates and sample sizes to evaluate the performance of the proposed robust bootstrap control charts in terms of the average run lengths. Simulation results exhibit that the two proposed robust model selection approaches perform well when the underlying distribution of the quality characteristic is unknown. Finally, the proposed process monitoring procedures are applied to two data sets for illustration.