A modified approximate method for analysis of degradation data

Estimation of the lifetime distribution of industrial components and systems yields very important information for manufacturers and consumers. However, obtaining reliability data is time consuming and costly. In this context, degradation tests are a useful alternative approach to lifetime and accelerated life tests in reliability studies. The approximate method is one of the most used techniques for degradation data analysis. It is very simple to understand and easy to implement numerically in any statistical software package. This paper uses time series techniques in order to propose a modified approximate method (MAM). The MAM improves the standard one in two aspects: (1) it uses previous observations in the degradation path as a Markov process for future prediction and (2) it is not necessary to specify a parametric form for the degradation path. Characteristics of interest such as mean or median time to failure and percentiles, among others, are obtained by using the modified method. A simulation study is performed in order to show the improved properties of the modified method over the standard one. Both methods are also used to estimate the failure time distribution of the fatigue-crack-growth data set.     

Direct products: a powerful tool for the analysis of balanced data

This paper focuses attention on the use of direct (Kronecker) product techniques in the study of general balanced models. Direct products provide a powerful tool which facilitates the derivation of certain properties of these models. This is clearly demonstrated in determining the distribution of sums of squares in a balanced mixed-effects model under normality assumptions. Further evidence of its usefulness is also indicated.     

A competing risks derivation of a mixture model for the analysis of survival data

Boag (1949) and Berkson and Gage (1952) proposed a mixture model for the analysis of survival time data when aproportion of treated patients are cured. This paper presents a derivation of the Boag/Berkson-Gage mixture model as well as a eneralization of the model based on the theory of competing risks. The assumptions underlying the model are stated and discussed and a general likelihood function is obtained. Use of the model is illustrated ith data from the Stanford Heart Transplant Program.     

Reliability analysis for stress-strength model from a general family of truncated distributions under censored data

Abstract

Under progressive Type-II censoring, inference of stress-strength reliability (SSR) is studied for a general family of lower truncated distributions. When the lifetime models of the strength and stress variables have arbitrary and common parameters, maximum likelihood and pivotal quantities based generalized estimators of SSR are established, respectively. Confidence intervals are constructed based on generalized pivotal quantities and bootstrap technique under different parameter cases as well. In addition, to compare the equivalence of the strength and stress parameters, likelihood ratio testing of interested parameters is provided as a complementary. Simulation studies and two real-life data examples are provided to investigate the performance of proposed methods.     

The use of restricted cubic splines to approximate complex hazard functions in the analysis of time-to-event data: a simulation study

If interest lies in reporting absolute measures of risk from time-to-event data then obtaining an appropriate approximation to the shape of the underlying hazard function is vital. It has previously been shown that restricted cubic splines can be used to approximate complex hazard functions in the context of time-to-event data. The degree of complexity for the spline functions is dictated by the number of knots that are defined. We highlight through the use of a motivating example that complex hazard function shapes are often required when analysing time-to-event data. Through the use of simulation, we show that provided a sufficient number of knots are used, the approximated hazard functions given by restricted cubic splines fit closely to the true function for a range of complex hazard shapes. The simulation results also highlight the insensitivity of the estimated relative effects (hazard ratios) to the correct specification of the baseline hazard.     

Correspondence analysis of repair data: a case study for electric cable shovels

In mining operation, effective maintenance scheduling is very important because of its effect on the performance of equipment and production costs. Classifying equipment on the basis of repair durations is considered one of the essential works to schedule maintenance activities effectively. In this study, repair data of electric cable shovels used in the Western Coal Company, Turkey, has been analyzed using correspondence analysis to classify shovels in terms of repair durations. Correspondence analysis, particularly helpful in analysing cross-tabular data in the form of numerical frequencies, has provided a graphical display that permitted more rapid interpretation and understanding of the repair data. The results indicated that there are five groups of shovels according to their repair duration. Especially, shovels numbered 2, 3, 7, 10 and 11 required a repair duration of<1 h and maintained relatively good service condition when compared with others. Thus, priority might be given to repair them in maintenance job scheduling even if there is another failed shovel waiting to be serviced. This type of information will help mine managers to increase the number of available shovels in operation.