The Constant Shape Parameter Assumption in Weibull Regression

ABSTRACT

The usual assumption in Weibull regression is that the scale parameter is a function of the predictor variables, and the shape parameter is constant. We consider the problem of estimating parameters in the presence of a nonconstant shape parameter and the effect of assuming a constant shape parameter when it really is not constant. We consider both classical and Bayesian methods of estimation. The misspecification of a constant shape parameter can lead to a loss of power for tests regarding the slope parameters. We find that prediction intervals can be inaccurate when the shape parameter is incorrectly assumed to be constant.     

Mechanical fatigue of an electronic component under random vibration

Electronic equipment, which is widely used in military applications, must be able to survive harsh environments. The endurance of such equipment is defined by the durability of their internal sensitive components. In this study, vibration induced fatigue life analysis of an axial leaded aluminium capacitor is performed. Three point bending tests are performed for the composite FR‐4 printed circuit boards (PCBs) material in order to determine bending modulus. Experimental modal analysis is used to validate a simulation model of the PCB. Step stress tests (SSTs) of reinforced and unreinforced capacitors which are mounted on the test PCBs are performed. It is found that the failure locations on the test PCBs are compatible among themselves and all the failures are due to flexure stress developed at the lead wires and solder joints. Numerical fatigue analyses are performed to define failure in terms of damage index. In addition, the Weibull model is used to define mean time to failure (MTTF) values. The comparison between MTTF values shows that the fatigue lives are strongly increased by the eccobond reinforcement. The last stage in this work is to focus on the influence of some design parameters on the fatigue life. An exponential equation is proposed to find the relation between lead‐wire diameter and the fatigue damage. It is shown that fatigue damage becomes a maximum for a square shaped PCB and it appears that component body diameter is more effective than the body length in increasing fatigue life.     

高分子电容湿敏传感器加速寿命试验统计模型的验证

针对目前普遍存在的加速寿命试验可靠性统计模型的准确性问题,结合加速寿命试验的几个基本假设条件,利用某高分子电容湿敏传感器恒定双应力加速寿命试验数据对加速模型准确性进行了验证。结果表明该产品加速寿命试验满足基本假设条件,所做的加速寿命试验合理,为后续加速寿命试验的分析和评估奠定了基础。     

Testing for Reliability

This tutorial article describes the role of testing in the creation of reliable products. It is based upon parts of the author's book ‘Test Engineering’.Reproduced by permission of John Wiley & Sons, Ltd. The book has a web page (www.pat‐oconnor.co.uk/testengineering.htm), which provides information on and links to test organizations, standards, suppliers of equipment and facilities, etc. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluation of materials for artificial heart valves

The heart of a normal human being beats about 38 million cycles every year. An artificial heart valve, to perform at this rate in the adverse conditions inside the heart for 20 years or more, should be highly wear-resistant with excellent fatigue strength. Thus, the study of mechanical and physical properties of the materials intended for use in artificial valves becomes an inseparable part of the valve development process itself. The physical and mechanical requirements of the materials used in the Chitra heart valve have been evaluated by studying their water absorption, adhesive wear and abrasive properties. The mechanical durability of the device has been assessed by accelerated life cycle testing. The test systems developed for the above are described here. The results show UHMW-PE to be a highly wear-resistant material suitable for the occluder. The accelerated wear tests show that the valve with Haynes-25 alloy cage and UHMW-PE disc has durability in excess of 50 years.     

威布尔分布的环保型电子节能灯寿命的极大似然估计

提出了一种利用改进的极大似然估计法对基于威布尔分布的环保型电子节能灯寿命数据进行分析的方法.该方法利用加速寿命实验获取环保型电子节能灯使用寿命的数据,利用统计学的方法和威布尔分布模型,实现高应力下的实验时间的等效折算.采用改进的极大似然估计,有益于对环保型电子节能灯的寿命数据进行分析.     

Optimum life test plan for Type-I hybrid censored Weibull distributed products sold under general rebate warranty

The selection of an appropriate life test plan is extremely important for any product as it not just improves the quality of the product but also reduces testing costs. In this approach, however, the choice of suitable costs play an important role. In this paper, a decision model is developed to determine the optimal life testing plan (LTP) by minimising the relevant costs involved for non-repairable products sold under the general rebate warranty. LTP are developed in the presence of Type-I hybrid censoring for products having Weibull distributed lifetimes. A constrained optimisation approach is followed considering both producer's and consumer's risk and suitable analysis techniques are employed in obtaining the optimal solution. Monte Carlo simulation is conducted for numerical illustration. In order to study the sensitivity of the optimal solution due to mis-specification of parameter values and cost components, a well-designed sensitivity analysis is incorporated using a real-life Type-I hybrid censored data set.     

SAS Software Roadmaps

In this article we compute the expected Fisher information and the asymptotic variance–covariance matrix of the maximum likelihood estimates based on a progressively type II censored sample from a Weibull distribution by direct calculation as well as the missing-information principle. We then use these values to determine the optimal progressive censoring plans. Three optimality criteria are considered, and some selected optimal progressive censoring plans are presented according to these optimality criteria. We also discuss the construction of progressively censored reliability sampling plans for the Weibull distribution. Three illustrative examples are provided with discussion.