Tzong-Ru Tsai

Acceptance Sampling Plans from Truncated Life Tests Based on the Birnbaum–Saunders Distribution for Percentiles

Time to failure due to fatigue is one of the common quality characteristics in material engineering applications. In this article, acceptance sampling plans are developed for the Birnbaum–Saunders distribution percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customers risk. The operating characteristic values (and curves) of the sampling plans as well as the producers risk are presented. The R package named spbsq is developed to implement the developed sampling plans. Two examples with real data sets are also given as illustration.

Acceptance sampling plans from truncated life tests based on the Burr type XII percentiles

In this article, acceptance sampling plans are developed for the Burr type XII distribution percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customers risk. The operating characteristic values (tables) of the sampling plans as well as producers risk are presented. The R package named spBurr is developed to implement the sampling plans. Two real datasets regarding the oil breakdown of an insulating fluid under high test voltage and the first failure times of small electric carts used for internal transportation and delivery are given as illustration.

Reliability sampling plans for Weibull distribution with limited capacity of test facility

This paper establishes reliability sampling plans for the Weibull lifetime distribution based on type II censored data with limited capacity of test facility. The products are sold under a general rebate warranty policy. It is also assumed that the shape parameter of the lifetime distribution is known, and the scale parameter is a random variable varying from lot to lot. A cost model is established which contains the cost per unit on test, the cost per unit time for life test, and the costs of rejecting and accepting a unit. An algorithm for determining the optimal reliability sampling plans which minimize the expected average cost per lot is provided. Some numerical results to illustrate the use of the proposed method are studied.

Inference From Lumen Degradation Data Under Wiener Diffusion Process

The lumen degradation of light emitting diodes subject to increasing stress loading is investigated by using a cumulative damage model. The cumulative damage process is taken as a Wiener diffusion process with a drift which depends on two stress loadings. General statistical inferences on the parameters and percentiles of the light emitting diode lifetime distribution are presented based on the cumulative damage measurements, collected from a two-variable constant-stress loading accelerated degradation test. Approximate lower s-confidence bounds of the light emitting diode lighting lifetime percentiles are given using the Fisher information of the maximum-likelihood estimators, and Bonferronis inequality. The application of the proposed method is illustrated by a lumen cumulative damage data set of high power light emitting diodes.

ESTIMATION OF TIME-TO-FAILURE DISTRIBUTION DERIVED FROM A DEGRADATION MODEL USING FUZZY CLUSTERING

SUMMARY Some life tests are terminated with few or no failures. In such cases, a recent approach is to obtain degradation measurements of product performance that may contain some useful information about product reliability. Generally degradation paths of products are modeled by a nonlinear regression model with random coefficients. If we can obtain the estimates of parameters under the model, then the time-to-failure distribution can be estimated. In some cases, the patterns of a few degradation paths are different from those of most degradation paths in a test. Therefore, this study develops a weighted method based on fuzzy clustering procedure to robust estimation of the underlying parameters and time-to-failure distribution. The method will be studied on a real data set. Copyright

Optimal Decisions on the Accelerated Degradation Test Plan Under the Wiener Process

Abstract The cumulative damage of highly reliable products that subject to multiple loading stresses is investigated under Wiener process. Optimal strategies on the constant-stress accelerated degradation test plan are established to reach a compromised decision between the experiment budget and the estimation precision on the reliability inference. An algorithm is provided to search an optimal strategy for the accelerated degradation test. An example of light emitting diodes is used for illustrating the application of the proposed method.

Optimal Two-Variable Accelerated Degradation Test Plan for Gamma Degradation Processes

An accelerated degradation test (ADT) can be used to assess the reliability of highly reliable products by using degradation information. In this study, to exhibit a monotone increasing pattern, the gamma process is used to model the degradation of a product subject to a constant-stress ADT of two loadings. Maximum likelihood estimates (MLEs) of the parameters of the ADT model were obtained. Given a budget for the total cost, an optimal ADT procedure was established to minimize the asymptotic variance of the MLE of the mean time to failure of a product, and the sample size and termination time of each run of the ADT at a constant measurement frequency were determined. An algorithm is provided to achieve an optimal ADT plan. An extensive Monte Carlo simulation was implemented to evaluate the sensitivity of the MLE variations to the sample size. A lumen degradation data set of light emitting diodes is presented to illustrate the proposed method.

On monitoring of multiple non-linear profiles

Most state-of-the-art profile monitoring methods involve studies of one profile. However, a process may contain several sensors or probes that generate multiple profiles over time. Quality characteristics presented in multiple profiles may be related multiple aspects of product or process quality. Existing charting methods for simultaneous monitoring of each multiple profile may result in high false alarm rates. Or worse, they cannot correctly detect potential relationship changes among profiles. In this study, we propose two approaches to detect process shifts in multiple non-linear profiles. A simulation study was conducted to evaluate the performance of the proposed approaches in terms of average run length under different process shift scenarios. Pros and cons of the proposed methods are discussed. A guideline for choosing the proposed methods is introduced. In addition, a hybrid method combining the salient points of both approaches is explored. Finally, a real-world data-set from a vulcanisation process is used to demonstrate the implementation of the proposed methods.

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

Control Charts for Monitoring Burr Type-X Percentiles

When the sampling distribution of a parameter estimator is unknown, using normality asymptotically, the Shewhart-type chart may provide improper control limits. To monitor Burr type-X percentiles, two parametric bootstrap charts (PBCs) are proposed and compared with the Shewhart-type chart via a Monte Carlo simulation. Simulation results exhibit that the proposed PBCs perform well with a short average run length to signal out-of-control when the process is out-of-control, and have more adequate control limits than the Shewhart-type chart in view of in-control false alarm rate. An example regarding single fiber strength is presented for illustrating the proposed PBCs.