R. Jiang

Health state evaluation of an item: A general framework and graphical representation

This paper presents a general theoretical framework to evaluate the health state of an item based on condition monitoring information. The items health state is defined in terms of its relative health level and overall health level. The former is evaluated based on the relative magnitude of the composite covariate and the latter is evaluated using a fractile life of the residual life distribution at the decision instant. In addition, a method is developed to graphically represent the degradation model, failure threshold model, and the observation history of the composite covariate. As a result, the health state of the monitored item can be intuitively presented and the evaluated result can be subsequently used in a condition-based maintenance optimization decision model, which is amenable to computer modeling. A numerical example is included to illustrate the proposed approach and its appropriateness.

Impact of quality variations on product reliability

The reliability of manufactured products can differ from the desired design reliability due to variations in manufacturing quality. Failure data from field provide useful information to assess if the changes in product reliability variations are significant or not and to identify the cause for the variation. In order to devise statistical methods to detect this, one needs to model the effect of quality variations in manufacturing on product reliability. This paper looks at this issue and examines the Weibull case in detail.

Optimization of alarm threshold and sequential inspection scheme

An item is subject to gradual degradation. The degradation can be represented by a measurable, non-negative and non-decreasing quantity. The item can be in one of three different states: normal (when the degradation quantity is smaller than a threshold of alarm or potential failure), functional failure (when the degradation quantity is larger than a functional failure threshold) and in-between or potential failure (when the degradation quantity is larger than the alarm threshold and smaller than the functional failure threshold). A sequential inspection scheme is implemented to determine the state of the item so as to prevent a functional failure. The paper presents a flexible degradation model and two cost models to optimize the alarm threshold and the sequential inspection scheme. The usefulness and appropriateness of the proposed models are illustrated by examples.

An optimal burn-in preventive-replacement model associated with a mixture distribution

A mixture arises in a number of situations. A typical situation is that a population is heterogeneous and consists of several sub-populations, which represent mutually exclusive failure modes (usually early failures where the mean time to failure (MTTF) is ‘short’ and wear-out failures where the MTTF is ‘long’ and the hazard rate is increasing). When the time to failure of an item follows a mixture distribution, it is difficult to determine an appropriate operational or/and maintenance policy to reduce the early-phase failures and field operational cost. This paper examines the effectiveness of jointly applying a burn-in procedure and preventive replacement policy to such items, and discusses implementation-related issues associated with the combined policy. A numerical example is also included. Copyright

Discrete competing risk model with application to modeling bus-motor failure data

Failure data are often modeled using continuous distributions. However, a discrete distribution can be appropriate for modeling interval or grouped data. When failure data come from a complex system, a simple discrete model can be inappropriate for modeling such data. This paper presents two types of discrete distributions. One is formed by exponentiating an underlying distribution, and the other is a two-fold competing risk model. The paper focuses on two special distributions: (a) exponentiated Poisson distribution and (b) competing risk model involving a geometric distribution and an exponentiated Poisson distribution. The competing risk model has a decreasing-followed-by-unimodal mass function and a bathtub-shaped failure rate. Five classical data sets on bus-motor failures can be simultaneously and appropriately fitted by a general 5-parameter competing risk model with the parameters being functions of the number of successive failures. The lifetime and aging characteristics of the fitted distribution are analyzed.

A study of Weibull shape parameter: Properties and significance

The two-parameter Weibull distribution has been widely used for modelling the lifetime of products and components. In this paper we study the effect of the shape parameter on the failure rate and three variables of importance in the context of maintenance and reliability improvement. These variables are (i) time to failure, (ii) age at replacement based on risk and (iii) residual life. We propose a classification scheme for the distribution based on the shape parameter and discuss the application of the results.

A Gamma-normal series truncation approximation for computing the Weibull renewal function

Abstract This paper presents a series truncation approximation for computing the Weibull renewal function. In the proposed model, the n-fold convolution of the Weibull Cdf is approximated by a mixture of the n-fold convolutions of Gamma and normal Cdfs. The mixture weight can be optimally determined and fitted into a very accurate linear function of Weibull shape parameter β . Major advantages of the proposed model include: (a) The proposed model and its parameters can be directly written out. Using the proposed model, the renewal density and variance functions can be easily evaluated. (b) The proposed model includes Gamma and normal series truncation models as its special cases. It is easy to be implemented in Excel. The series converges fairly fast. (c) Over the range of β ∈ ( 0.87 , 8.0 ) , the maximum absolute error is smaller than 0.01; and over β ∈ ( 3.0 , 8.0 ) , the maximum absolute error is smaller than 0.0037. (d) The model can be easily extended to non-Weibull case with some additional work.

A new bathtub curve model with a finite support

The failure rate with a bathtub shape usually increases very fast in the wear-out phase. In this case, the bathtub curve model with a finite support can better adapt the sharp change in failure rate. There are few models with the finite support. This paper presents such a model. However, the maximum likelihood estimator of the location parameter of such models sometimes converges to the largest observation of a dataset. An extended maximum spacing method is developed to estimate the parameters for the case where the maximum likelihood method fails. Three examples are included to illustrate the appropriateness of the proposed model and estimation method.

Composite scale modeling in the presence of censored data

A composite scale modeling approach can be used to combine several scales or variables into a single scale or variable. A typical application is to combine age and usage together to form a composite timescale model. The combined scale is expected to have better failure prediction capability than individual scales. Two typical models are the linear and multiplicative models. Their parameters are determined by minimizing the sample coefficient of variation of the composite scale. The minimum coefficient of variation is hard to apply in the presence of censored data. Another open issue is how to identify key variables when a number of variables are combined. This paper develops methods to handle these two issues. A numerical example is also included to illustrate the proposed methods.

An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon

It is difficult to find the optimal solution of the sequential age replacement policy for a finite-time horizon. This paper presents an accurate approximation to find an approximate optimal solution of the sequential replacement policy. The proposed approximation is computationally simple and suitable for any failure distribution. Their accuracy is illustrated by two examples. Based on the approximate solution, an approximate estimate for the total cost is derived.