Papers by Muralidharan Kunnummal
We use the q-Weibull distribution and define a new counting process using the fractional order. A... more We use the q-Weibull distribution and define a new counting process using the fractional order. As a consequence, we introduce a q-process with q-Weibull interarrival times. Some interesting special cases are also discussed which leads to a Mittag-Leffler form.
In reliability and life data analysis, the Weibull distribution is widely used to accommodate mor... more In reliability and life data analysis, the Weibull distribution is widely used to accommodate more data characteristics by changing the values of the parameters. We frequently observe many zeros or close to zero data points in reliability and life testing experiments. We call this phenomenon a nearly instantaneous failure. Many researchers modified the commonly used univariate parametric models such as exponential, gamma, Weibull, and log-normal distri
Journal of Modern Mathematics and Statistics, 2011
A conditional test based on quadratic form using type-2 censored sample for testing exponentialit... more A conditional test based on quadratic form using type-2 censored sample for testing exponentiality against Weibull alternative is proposed. The simulated percentage points and powers are given. The proposed test performs well for identifying Weibull DFR alternative e v en for small sample. An example is also given.
MATHEMATICAL JOURNAL OF INTERDISCIPLINARY SCIENCES, 2014
One of the questions most frequently asked of a statistician is: how big should the sample be? Ma... more One of the questions most frequently asked of a statistician is: how big should the sample be? Managers are anxious to obtain an answer to this fundamental question during the planning phase of the survey since it impacts directly on operational considerations such as the number of interviewers required. There is no magical solution and no perfect recipe for determining sample size. It is rather a process of compromise in which the precision requirements of the estimates are weighed against various operational constraints such as available budget, resources and time. In this article we revisit to the estimate of sample size for various project characteristics. Examples for each are supported numerically.
Inliers in a data set are subset of observations not necessarily all zeroes, which appears to be ... more Inliers in a data set are subset of observations not necessarily all zeroes, which appears to be inconsistent with the remaining data set. They are either the resultant of instantaneous or early failures usually encountered in life testing, financial, clinical trial and many other studies. We study the estimation of inliers in Normal distribution. The masking effect problem for correctly identifying the inliers is also discussed. An illustration and a real life example is presented with detailed discussions.
Journal of Statistical Theory and Practice, 2017
Inliers (instantaneous or early failures) are natural occurrences of a life test, where some of t... more Inliers (instantaneous or early failures) are natural occurrences of a life test, where some of the items fail immediately or within a short time of the life test due to mechanical failure, inferior quality or faulty construction of items and components. A similar situation is observed in mortality studies, where the life pattern of new born babies include still births (no life), neo-natal births (life less than 28 days may be recorded as 1) and babies surviving more than a month and longer. The inconsistency of such life data is modeled using a nonstandard mixture of distributions; with degeneracy occurring at zero and one, and a probability distribution for positive observations. Keeping the underlying distribution as exponential distribution, we model the inliers situation and propose various estimators and characteristics of the model. The model is implemented on a mortality data obtained through the NFHS-3 studies.
Inliers in a data set are observations which appear to be too small compared to the remaining obs... more Inliers in a data set are observations which appear to be too small compared to the remaining observations in the usual life testing experiments with failure time distribution (FTD),F(x,�), x ≥ 0, � ∈ . These inconsistent observations may be the resultant of the occurrences of instantaneous failures or early failures in life testing experiments. To accommodate such instances the failure time distributions (FTD) are modified by defining early failures as those observations which are very small compared to the other positive observations and are called inliers. We propose various inlier prone models and their statistical significances. The maximum likelihood estimates (MLE) are obtained for parameterof the target distribution F and alsoof the contaminating population G. Assuming that there are k inliers, we obtained the MLE of k and proposed tests of hypothesis for k = 0 (no inliers) when target population is exponential with mean life�. We present different methods of detecting inlie...
Education Sciences
The democratic welfare government is not only interested in creating educational institutions as ... more The democratic welfare government is not only interested in creating educational institutions as infrastructure for education for all, but is also equally keen on quality-oriented, even-handed, and equitable education. In fact, the focus of the Global Agenda SDG 4 is to raise the standard of living and quality of life by ensuring quality and lifelong education irrespective of region, race, religion, color, and caste, etc. Thus, there is a strong focus in India to reach global targets and more importantly, this is due to the necessity of fulfilling the government’s goals on overhauling India’s education system in the context of far-reaching changes that have taken place in terms of economic, social, and scientific areas over a period of last twenty years. The outcome of all these complex issues and critical thinking across stakeholders in social development manifested into policy action called the New Education Policy 2020 (NEP 2020). Therefore, it is critically important to analyze ...
International Journal for Quality Research
Lean Six Sigma (LSS) modifies the DMAIC approach by emphasizing speed. Lean focuses on streamlini... more Lean Six Sigma (LSS) modifies the DMAIC approach by emphasizing speed. Lean focuses on streamlining a process by identifying and removing non-value added steps. A leaned production process eliminates waste. The target metrics, which affect any business include zero wait time, zero inventory, scheduling using customer pull, cutting batch sizes to improve flow, line balancing, and reducing overall process time. Lean Six Sigma's goal is to produce quality products that meet customer requirements as efficiently and effectively as possible. In this article, we present various Lean performance characteristics that can be effectively used for improving a sustainable business process through a case study.
Journal of the Indian Society for Probability and Statistics
AbstractInliers (instantaneous or early failures) are natural occurrences of a life test, where s... more AbstractInliers (instantaneous or early failures) are natural occurrences of a life test, where some of the items fail immediately or within a short time of the life test due to mechanical failure, inferior quality or faulty construction of items and components. The inconsistency of such life data is modeled using a nonstandard mixture of distributions; with degeneracy occurring at zero and one, and a probability distribution for positive observations. In this paper, the estimation of parameters based on type-II censored sample from a Weibull distribution with discrete mass at zero and one is studied. The maximum likelihood estimators (MLE) are developed for estimating the unknown parameters. The Fisher information matrix, as well as the asymptotic variance–covariance matrix of the MLEs are derived. Uniformly minimum variance unbiased estimate (UMVUE) of model parameters as well as UMVUE of density function, reliability function and some parametric function is obtained along with UMVUE of the different estimators. The model is implemented on a real data of tumor size in invasive ductal breast carcinoma of female patients.
Mathematical Journal of Interdisciplinary Sciences
International Journal of Reliability, Quality and Safety Engineering
Understanding variation is critical to quality (CTQ) of product or service delivery, which is the... more Understanding variation is critical to quality (CTQ) of product or service delivery, which is the key to success. Six Sigma is the business process improvement strategy that extensively focuses on variation reduction thereby reducing number of defects. One of the major constituents of Six Sigma definitions is 1.5 sigma shift, which is attributable to random error. It is not possible to understand Six Sigma thoroughly by overlooking the concept of 1.5 sigma shift. A conventional 3.4 defect per million opportunity (DPMO) capability of Six Sigma process is based on 1.5 sigma shift. This paper aimed at explaining ancestry of 1.5 sigma shift in connection with quality engineering methods. Origin of 1.5 sigma shift factor with reference to producibility analysis, worst-case sampling error and other quality engineering methods has been discussed in this paper.
The power law model is the most commonly used model in the class of nonhomogeneous Poisson proces... more The power law model is the most commonly used model in the class of nonhomogeneous Poisson process (NHPP), for the repairable systems. If the power law model is rejected by a goodness-of-fit test, other NHPP models can be fitted and tested. One such model was proposed by Cox and Lewis (1966) with intensity function () t e t β α λ + =. In this paper, we study some inferences and propose a conditional test by exploiting the property of sufficient statistics for testing the shape parameter β, treating the other parameter ρ as nuisance parameter. We have performed a simulation study to compute the powers of the proposed test.
Six Sigma is considered to be one of the best quality improvement methodology applied successfull... more Six Sigma is considered to be one of the best quality improvement methodology applied successfully to organizational areas like manufacturing, production, accounting and finance, sales and marketing, information systems, human resource management etc. In this era of economic slowdown organizations expect high return on investment (ROI) form every business function. Productivity of sales and marketing processes has always remains questionable. In order to justify significance of sales and marketing process compared to other business process to generate significant ROI structured approach is required that alter the way of looking towards sales and marketing from merely creative field to the structured process based approach. Application of Six Sigma to sales and marketing offers provides channel to the creativity that result in high ROI. Different tools and techniques based on application of Six Sigma in marketing process have been discussed in this article with their Key Performance ...
IOSR Journal of Business and Management, 2013
The financial sector in India has undergone radical reforms, particularly in the stock market seg... more The financial sector in India has undergone radical reforms, particularly in the stock market segment, since early 1990s. Testing duration in stock markets concerns the ability to predict the turning points of bull and bear cycles. This article study some point process models to fit the data from Indian stock market cycles. We have considered the BSE 30 (SENSEX) data from January, 1991 to August, 2012 for bull and bear markets. The duration dependence of stock market cycles can help to pinpoint the peaks and troughs in these cycles. Upon carrying out various statistical procedures and goodness of fit tests, we found that the Nonhomogeneous Poisson Process models like Power Law Process, Modulated Power Law Process, Log-linear process and other models are some of the possible alternative models to describe the data. We provide estimates, confidence interval estimates and tests of hypothesis for the parameters involved in a particular model.
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Papers by Muralidharan Kunnummal