Surajit Pal

An application of Gumbel's bivariate exponential distribution in estimation of warranty cost of motor cycles

In this article we present an application of Gumbels bivariate exponential distribution model in the context of estimating warranty costs of motor cycles under a new warranty policy. The problem in question is as follows: Under the present two‐dimensional warranty policy, repair costs (termed as warranty costs) of a motorcycle during the age of first six months or within the usage of 8,000 kilometers are borne by the company. To enhance customer satisfaction, the company wanted to bear the repair costs up to an age of one year or a usage of 12,000 kilometers. The problem is to estimate the expected hike in warranty costs if the warranty policy were revised as mentioned above. Using the past data, the problem is solved by studying the underlying renewal process. Gumbels bivariate exponential distribution function is found to be useful in approximating the renewal function. Some practical difficulties posed by the past data in the analysis are highlighted and tackled in an interesting way.

Evaluation of Nonnormal Process Capability Indices Using Generalized Lambda Distribution

Process capability indices (PCIs) are used to describe a manufacturing process expressing its ability to produce items within the specified limits. These indices are developed under the assumption that the underlying process distribution is normal. In industries, there are many manufacturing processes where process distribution can not be described by a normal distribution. In such cases, those PCIs will give misleading results about the process. The most commonly used approach for analysing a nonnormal process data is to fit a standard nonnormal distribution (e.g., weibull, gamma) or a family of distribution curves (e.g., Pearson, Johnson) to the process data and then to estimate the percentile points from the fitted distribution that can be used to compute generalized PCIs. In this article, we outline the procedure using the generalized lambda distribution (GLD) curve for modeling a set of process data and for estimating percentile points in order to compute generalized PCIs. The four-parameter GLD can assume a wide variety of curve shapes and hence it is very useful for the representation of data when the underlying model is unknown. Compared to the Pearson and Johnson family of distributions, the GLD is computationally simpler and more flexible. The article provides all necessary formulas for fitting a GLD curve, estimating its parameters, performing goodness-of-fit tests, and computing generalized PCIs. An example is used to illustrate the calculations that can be easily performed using spreadsheets.

A use-rate based failure model for two-dimensional warranty

We consider the problem of constructing probability model for product failure instances indexed by two scales, namely, age and usage. This is an important element in the analysis of two-dimensional warranty for automobiles. Specifically, we deal with models that apply to components or parts. The motivation for the same is stressed, and a model is proposed. The key feature of this model is: how use-rate affects life. Some existing models are then analyzed in the light of this feature, and the results are presented. Numerical examples are also provided to illustrate the application of this model in calculating warranty cost.

Multi-Response Optimization Using Multiple Regression–Based Weighted Signal-to-Noise Ratio (MRWSN)

ABSTRACT Several methods for optimization of multiple responses have been developed. Most of them have mathematical complexities and are not easily implemented by engineers. In this article, we propose a new method that integrates multiple regression technique and Taguchis signal-to-noise (SN) ratio concept and is also easily implemented. Two sets of experimental data are analyzed using the proposed method. The proposed method is found to be superior to other methods with respect to total SN ratio as well as closeness of individual responses to their respective target values, which are reflected in the expected mean square error (MSE) values for the individual responses.

Assessing effectiveness of the various performance metrics for multi-response optimization using multiple regression

Several methods for optimization of multiple response problems using planned experimental data have been proposed in the literature. Among them, an integrated approach of multiple regression-based optimization using an overall performance criteria has become quite popular. In this article, we examine the effectiveness of five performance metrics that are used for optimization of multiple response problems. The usefulness of these performance metrics are compared with respect to a utility measure, namely, the expected total non-conformance (NC), for three experimental datasets taken from the literature. It is observed that multiple regression-based weighted signal-to-noise ratio as a performance metric is the most effective in finding an optimal solution for multiple response problems.

ESTIMATION OF PROCESS CAPABILITY INDEX FOR CONCENTRICITY

Concentricity of any hollow circular or cylindrical job is a critical quality characteristic whose variation pattern can be explained by an extreme value distribution. Estimation of the process capability index is a prerequisite for control and improvem..

A note on calculating cost of two-dimensional warranty policy

We study the derivation of warranty cost under rectangular two-dimensional policy for both repairable as well as non-repairable product. Typically, two approaches are adopted, namely, one-dimensional (1D) and two-dimensional (2D). We show the difference in results obtained from the formulae under the two approaches through several examples. Merits of the formulae are then analyzed to identify the correct ones.

Warranty cost estimation of a multi‐module product

This article deals with the problem of cost estimation for increased warranty time of a multi‐module product. The warranty policy of interest is two‐dimensional involving warranty limits on both age and usage of the product. Failure of the product is caused due to malfunctioning of its module(s). Warranty service is rendered through repair or replacement of the respective module(s). From the past data, it is observed that age and usage are highly correlated. Based on life (age) data, the joint life distribution of the modules is well described by multivariate exponential distribution of Marshall and Olkin. The same is utilized to estimate cost for desired warranty times by the method of simulation.

Process Control and Evaluation in the Presence of Systematic Assignable Cause

A process is assumed to be free from assignable causes of variation while evaluating its capability. There are processes where variation occurs due to assignable causes which have to be tolerated. Traditional methods for process control and process capa..

Effect of use‐rate on system life and failure models for 2D warranty

Purpose – The purpose of this paper is to characterise the failure model of a system that is covered by a two‐dimensional warranty, one dimension depicting time and the other usage. Specifically, the authors study the effect of use‐rate on system life when each constituent component life is described by an accelerated‐failure‐time (AFT) type model.Design/methodology/approach – The paper evaluates the effect of use‐rate on the expected failure time of a system having different internal configurations involving components. Firstly, the coherent structure as well as modules with redundant structures (standby and load‐sharing) are analysed, whereby component failures are assumed to be conditionally independent. Study systems of some basic configurations with a general dependence structure among component failure instances are also studied.Findings – The results strongly indicate that, irrespective of the internal component‐configuration of the system, the models should posses the property that the expected fa...