Sanku Dey

St. Anthony's College · Department of Statistics

The process capability index (PCI), C pk , one of the widely-used tools for assessing the capability of a manufacturing process, expresses the deviation of the process mean from the midpoint of the specification limits. The C pk is known to perform well under the general assumption that the experimental data are normally distributed without contami...

We consider the process capability index, a widely-used quality-related statistic used to assess the quality of products and performance of monitored processes in various industries. It is widely known that the conventional process capability indices perform well when the quality process being monitored has a normal distribution. Unfortunately, usi...

In this article, we propose a new process capability index called C pmc which is based on asymmetric loss function (linear exponential) and tolerance cost function for a normal process which provides a tailored way of incorporating the loss and tolerance cost in capability analysis. Next, we estimate the proposed PCI C pmc when the process follows...

A new two-parameter weighted-exponential (WE) distribution, as a beneficial competitor model to other lifetime distributions, namely: generalized exponential, gamma, and Weibull distributions, is studied in the presence of adaptive progressive Type-II hybrid data. Thus, based on different frequentist and Bayesian estimation methods, we study the in...

Mixture models are more appealing and appropriate for studying the heterogeneous nature of lifetimes of certain mechanical, biological, social, economic and several other processes as compared to simple models. This paper considers a mixture of generalized Rayleigh distributions under classical and Bayesian perspectives based on type I censored sam...

To reduce total test time and increase the efficiency of statistical analysis of a life-testing experiment adaptive progressive Type-II censoring scheme has been proposed. This paper addresses the statistical inference of the unknown parameters, reliability, and hazard rate functions of logistic exponential distribution under adaptive progressive T...

The process capability indices (PCIs) are frequently adopted to measure the performance of a process within the specifications. Although higher PCIs indicate higher process “quality”, yet it does not ascertain fewer rates of rejection. Thus, it is more appropriate to adopt a loss-based PCI for measuring the process capability. In this paper, our fi...

In this paper, studies of competing risks model are considered when the observations are left-truncated and right-censored data. When the failure times of the competing risks are distributed by a generalized inverted exponential model with same scale but different shape parameters with partially observed failure causes, statistical inference for th...

This paper explores estimation of stress-strength reliability based on upper record values. When the strength and stress variables follow unit-Burr Ⅲ distributions, a generalized inferential approach is proposed for estimating stress-strength reliability (SSR). Under the common strength and stress parameter case, two types of pivotal quantities are...

Order statistic plays an important role in statistical theoretical and practical problems. In this paper, we derive algebraic expressions for both single and product moments of order statistics from generalized Topp-Leone (GTL) distribution. These expressions will be useful for computational purposes. Further, based on order statistics, we have obt...

This article suggests a novel process capability index (PCI) termed as S pk , which is based on an asymmetric loss function (linear exponential) for a normal process and offers a specific method of incorporating the loss in capability analysis. Next, we estimate the suggested PCI using the moment estimation approach when the process follows a norma...

In this study, we propose a new three-parameter lifetime model based on the type-I half-logistic G family and the unit-Gompertz model, which we named the half-logistic unit Gompertz type-I distribution. The key feature of such a novel model is that it adds a new tuning parameter to the unit-Gompertz model using the type-I half-logistic family in or...

The process capability index (PCI) has been one of the most useful indicators for evaluating the capability of a manufacturing process. Since PCI is based on sample observations, it is essentially an estimated value. Hence, it is natural to think of a confidence interval (CI) of the PCI. In this paper, bootstrap confidence intervals and highest pos...

In this article, we first define a new two-sided distribution called the two-sided Kumaraswamy distribution and then we propose a generalized class of lifetime distributions via compounding two-sided Kumaraswamy and a baseline distribution. One of the advantages of this class of new distributions is that they can be unimodal or bimodal. The general...

Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) with common scale parameters, maximum likelihood estimate of MSS reliability is established along with associated existence and uniqueness, and approximate...

In this paper a modified group acceptance sampling plan using chaining the past lot(s) results is developed called modified chain group acceptance sampling inspection plan (MChGSP). This sampling plan is based on time truncated lifetimes when the lifetime of an item follows the generalized exponential distribution with known shape parameter. The pr...

Process capability indices (PCIs) are most effective devices/techniques used in industries for determining the quality of products and performance of manufacturing processes. In this article, we consider the process capability index S' pmk which is based on an asymmetric loss function (linear exponential) and is applicable to normally as well as no...

Ranked set sampling (RSS) provides an efficient and flexible approach to collect failure information from perspectives of saving time and cost. In this paper, inference of a competing risks model is proposed based on a popular RSS named minimum ranked set sampling with unequal samples setting. When the lifetimes of competing risks follow exponentia...

This article aims to describe some statistical properties of the power generalized Weibull distribution along with some parametric estimation methods. An extensive simulation study is carried out to assess the effectiveness of the estimation of model parameters using numerous well known classical methods of estimation. Next, the Bayes estimators of...

In this paper, the estimation of the unknown parameters of inverted modified Lindley distribution using the concept of dual generalized order statistics (dgos) is investigated from both classical and Bayesian viewpoints. Based on this considered distribution, first, the maximum likelihood estimator (MLE) and approximate confidence interval of the m...

The first objective of the paper is to modify the existing process capability index (PCI) I using Gini's mean difference (GMD) for a Weibull distribution (WD). Next, in order to estimate the proposed PCI when the process follows WD, we have used five classical methods of estimation, and the performance of the proposed PCI based on considered classi...

The process capability index has been introduced as an effective tool used in industries to aid in the assessment of process performance as well as to measure how much the product meets the costumer expectations. We are aware that classical process capability indices provide better results when the quality characteristic of the processes follows no...

Accelerated life testing has been used frequently in several fields as it provides an economical way for obtaining failure time data rapidly or in a shorter time as compared to normal operating conditions. The lifetime data of a product at a constant stress level are assumed to have an exponentiated power Lindley distribution, and the model's shape...

Inference for Matusita measure between independent generalized inverted exponential distributions (GIEDs) is investigated under progressive first-failure censoring. When both GIEDs have common scale but different shape parameters, maximum likelihood estimator of the Matusita measure along with the existence and uniqueness of model estimators are es...

Lan and Leemis (2008) introduced logistic-exponential (LE) distribution which has varied applications in lifetime modellings. In this article, we consider para-metric bootstrap control charts (BCCs) for detecting a shift in the percentile of LE distribution in a process monitoring situation. Four parametric BCCs based on maximum likelihood method,...

Using progressive Type-II censoring data, this study deals with the estimation of parameters of the Unit-Weibull distribution using two classical methods and the Bayesian method. In the classical methods, maximum likelihood and the maximum product of spacing (MPS) methods are used to obtain the parameters of the model by utilizing the Newton-Raphso...

The mathematical modeling of the coronavirus disease-19 (COVID-19) pandemic has been attempted by a large number of researchers from the very beginning of cases worldwide. The purpose of this research work is to find and classify the modelling of COVID-19 data by determining the optimal statistical modelling to evaluate the regular count of new COV...

A new re-parameterize form of the Wilson-Hilferty distribution for data modelling with increasing, decreasing and bathtub shape hazard rates has been considered. This paper takes into account the estimation for the unknown model parameters, reliability function and hazard function based on two frequentist methods and Bayesian method of estimation u...

Based on record values and inter-record times, this paper develops inference procedures for the estimation of the parameters of generalized inverted exponential distribution (GIED). First, based on inverse and random sampling schemes, we derive the maximum likelihood estimators (MLEs) and associated asymptotic confidence intervals of the unknown pa...

This paper explore statistical inferences when the lifetime of product follows the inverse Nakagami distribution using progressive Type-II censored data. First, likelihood based estimation method and maximum product of spacing (MPS) method are considered for estimating parameters of the model. In addition, approximate confidence intervals are const...

The aim of this study is to describe the both frequentist and Bayesian parametric estimation methods for the gamma distribution using progressive Type II censoring data. We first take into account, maximum likelihood method and its competitive method, known as the maximum product of spacing method for estimation of parameters of the model. In addit...

In this article, we are interested to estimate a new capability index C0 pm which is based on asymmetric loss function (linear-exponential) when the underlying process follows normal distribution. We estimate the parameters of the model using maxi- mum likelihood method, bias-corrected maximum likelihood method and bootstrap bias corrected maximum...

Right-skewed heavy-tailed survival data commonly arise in health-related studies, and the probability distributions proposed to model such survival data are not adequately described in the literature. Although a wide selection of survival distributions is available, applied researchers often face the challenge of choosing a right model for analyzin...

This paper has investigated the estimation problem for the competing risks model where the data are adaptive progressively type-II censored and follow the Rayleigh distribution. Maximum likelihood and Bayesian methods are used to estimate the unknown parameters. To generate the interval estimates of the model parameters, approximate confidence inte...

In this paper, statistical inference is discussed for left-truncated and right- censored (LTRC) competing risks data. For modeling the latent dependent competing risks variables, a flexible bivariate lifetime model is constructed with a general class of inverse exponentiated marginal distribution, and asso- ciated distribution properties are provid...

Data analysis in real life often relies mainly on statistical probability distributions. However, data arising from different fields such as environmental, financial, biomedical sciences and other areas may not fit the classical distributions. Therefore, the need arises for developing new distributions that would capture high degree of skewness and...

This paper develops a modified chain group acceptance sampling inspection plan (MChGSIP) for inverse log-logistic distribution with known shape parameter when the life test is truncated at a pre-assumed time. The proposed modified sampling plan requires a smaller sample size than the commonly used sampling inspection plan, such as group acceptance...

In this article, we explore a new model with three parameters called Gamma-Gompertz (GGo) distribution which is generated by the gamma-X family. The GGo distribution provides better fits than some competing distributions such as three-parameter Gompertz, Gompertz-Lindley, Gompertz-geometric, Gompertz-poisson, and inverse Gompertz distributions. Som...

In this article, we explore a new probability density function, called the power modified Lindley distribution. Its main feature is to operate a simple trade-off among the generalized exponential, Weibull and gamma distributions, offering an alternative to these three well-established distributions. The proposed model turns out to be quite flexible...

This paper addresses the different methods of estimation of the unknown parameter of one parameter $A{\alpha}$ distribution from the frequentist point of view. We briefly describe different approaches, namely, maximum likelihood estimator, least squares estimator, weighted least squares estimator, Cram\'{e}r-von Mises estimator and maximum product...

Accelerated Life Test has been introduced as a tool to aid in obtaining sufficient failure time data of test units quickly and extrapolating lifetime information under use conditions. When the lifetime of units is distributed by the Lindley model, the estimations for the unknown parameters and the reliability function are established based on two f...

In this paper, the interest is in estimating the Weibull products when the available data is obtained via generalized progressive hybrid censoring. The testing scheme conducts products of interest under a more flexible way and allows collecting failure data in efficient and adaptable experimental scenarios than traditional lifetime testing. When th...

Please cite this article as: L. Wang, Y.M. Tripathi, S. Dey et al., Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes, Mathematics and Computers in Simulation (2021), doi: https://doi. Abstract In this paper, studies of left-truncated and right-censored data with dependent competing...

Estimation of stress-strength reliability is considered based on frequentist and Bayesian methods of estimation when both stress and strength variables follow unit generalized exponential distributions. In frequentist method we consider maximum likelihood , least squares, weighted least squares and maximum product spacing methods to estimate system...

In this paper, we introduce a new process capability index, C pmk based on an asymmetric loss function (linear exponential) for normal process. To estimate C pmk , we first obtain eight different classical methods of estimation and then consider objective Bayesian methods of estimation under the squared error loss function and the linear exponentia...

In practice, the data related to rates and proportion may have excess of ones wherein the beta distribution does not fit well. To deal with the inflation of ones, this article introduces unit Nadarajah and Haghighi distribution. Besides deriving statistical properties of the proposed distribution, several estimation methods are discussed. In partic...

In this paper, inference of multicomponent system is presented under constant-stress accelerated life test. When the lifetime of the components of the mul-ticomponent system follows a generalized inverted exponential distribution (GIED), different from standard extrapolation approach where only the scale parameter depends on the stress conditions,...

This paper addresses the different methods of estimation of the unknown parameter of one parameter A(α) α)) distribution from the frequentist point of view. We briefly describe different approaches, namely, maximum likelihood estimator, least square and weighted least square estimators, maximum product spacing estimators, Cram´er-von Mises estimato...

In this paper, a new three-parameter lifetime model called the Topp-Leone odd log-logistic exponential distribution is proposed. Its density function can be expressed as a linear mixture of exponentiated exponential densities and can be reversed-J shaped, skewed to the left and to the right. Further, the hazard rate function of the new model can be...

In this paper, we introduce a new flexible distribution called the Weibull Marshall-Olkin power-Lindley (WMOPL) distribution to extend and increase the flexibility of the power-Lindley distribution to model engineering related data. The WMOPL has the ability to model lifetime data with decreasing, increasing, J-shaped, reversed-J shaped, unimodal,...

In this article, an acceptance sampling inspection plan is proposed when the quality characteristic follows the Lindley distribution. In this sampling plan, an exact approach has been introduced using the Lindley distributed quality characteristic while an approximate approach of acceptance sampling inspection has also been provided using the power...

Estimation of parameters of Poisson Nadarajah-Haghighi (PNH) distribution from the frequentist and Bayesian point of view is discussed in this article. To this end, we briefly described ten different frequentist approaches, namely, the maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estim...

Process capability indices (PCIs) are most effective devices/techniques used in industries for determining the quality of products and performance of manufacturing processes. In this article, we consider the PCI Cpc which is based on the proportion of conformance and is applicable to normally as well as non-normally and continuous as well as discre...

In this article, seven classical estimation methods are employed to estimate the parameters of unit Burr III distribution proposed by Modi and Gill (2019). Further, the associated second-order bias corrections of the MLEs of its parameters are obtained by using Cordeiro and Klein (1994) modified version of the Cox and Snell (1968) approach. Besides...

In manufacturing industries and several other fields, accelerated life testing is used widely for obtaining sufficient failure time data of test units quickly as compared to normal use conditions. It is assumed that the lifetime of a product at constant stress level follows generalized inverse Lindley distribution. It is common observation that whi...

Accelerated Life Testing (ALT) is an effective technique which has been used in different fields to obtain more failures in a shorter period of time. It is more economical than traditional reliability testing. In this article, we propose Bayesian inference approach for planning optimal constant stress ALT with Type I censoring. The lifetime of a te...

The objective of this article is to compare highest posterior density (HPD) credible interval with three bootstrap confidence intervals (BCIs) as well as with asymptotic confidence interval (ACI) using maximum likelihood and Bayesian approaches of a new process capability index, S pmk suggested by Chen and Ding (2001) when the underlying distributi...

This paper introduces a new class of distributions by compounding the inverse Lindley distribution and power series distributions which is called compound inverse Lindley power series (CILPS) distributions. An important feature of this distribution is that the lifetime of the component associated with a particular risk is not observable, rather onl...

In this article, to estimate the generalized process capability index (GPCI) C pyk when the process follows the power Lindley distribution, we have used five methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares method of estimation, the maximum product of spacings method of estimation, and Baye...

In this paper, inference upon stress-strength reliability is considered for unit-Weibull distributions with a common parameter under the assumption that data are observed using progressive type II censoring. We obtain different estimators of system reliability using classical and Bayesian procedures. Asymptotic interval is constructed based on Fish...

In health related studies, we sometimes come across left-skewed heavy-tailed survival data and vary often the probability distributions proposed in the literature to fit the model of such survival data is not adequate. In this article, we explore a new probability density function with bounded domain. The new distribution arises from the Lomax dist...

In this paper, we consider Dagum distribution which is capable of modeling various shapes of failure rates and aging criteria. Based on progressively type-I interval censoring data, we first obtain the maximum likelihood estimators and the approximate confidence intervals of the unknown parameters of the Dagum distribution. Next, we obtain the Baye...

Based on progressive Type-II censored samples, we first derive the recurrence relations for the single and product moments of progressively Type-II censored order statistics from two parameter Rayleigh distribution. These recurrence relations enable us to compute the mean and variances of all progressively Type-II censored order statistics for all...

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers a mixture of the Marshall–Olkin extended Weibull distribution for efficient modeling of failure, survival, and...

This paper presents methods of estimation of the parameters and acceleration factor for Nadarajah-Haghighi distribution based on constant-stress partially accelerated life tests. Based on progressive Type-II censoring, Maximum likelihood and Bayes estimates of the model parameters and acceleration factor are established, respectively. In addition,...

Accelerated Life Testing is an efficient tool frequently adopted for obtaining failure time data of test units in a lesser time period as compared to normal use conditions. We assume that the lifetime data of a product at constant level of stress follows an exponentiated Poisson-exponential distribution and the shape parameter of the model has a lo...

A new continuous four-parameter lifetime distribution is introduced by compounding the distribution of the maximum of a sequence of an independently identically exponentiated Lomax distributed random variables and zero truncated Pois-son random variable, defined as the complementary exponentiated Lomax Poisson (CELP) distribution. The new distribut...

In this paper, the maximum likelihood and Bayesian estimation of the parameters of location-scale Rayleigh distribution with partly interval censored data is considered. For computing the maximum likelihood estimators with partly interval censored data, three methods are used, namely, Newton-Raphson, Expectation-Maximization and Monte-Carlo Expecta...

In this paper, reliability estimation of multicomponent system under a multilevel accelerated life testing. When the lifetime of components follows Weibull distribution, the problem of point and interval estimates are discussed from different perspectives. Under a general life-stress assumption that there are multiple nonconstant and stress depend...

A comprehensive review of transmuted distributions is provided. Nearly thirty such distributions are reviewed. Real data applications are provided comparing the reviewed distributions to other classes of distributions. This review could serve as an important reference and encourage developments of further transmuted distributions that could model c...

Design/methodology/approach { We derive inference for the unknown parametric function using classical and Bayesian approaches. In sequel, (weighted) least square and maximum product of spacing methods are used to estimate the reliability. Bootstrapping is also considered for this purpose. Bayesian inference is derived under gamma prior distribution...

This paper deals with single and double acceptance sampling plan (SASP and DASP) for the transmuted Rayleigh distribution when the lifetime experiment is truncated at a prefixed time. For the proposed sampling plans, we consider zero failure scheme for SASP and zero and one failure schemes for DASP, respectively. The minimum sample sizes of first a...

The process capability index (PCI) C pmk is a well-known loss-based index. This loss based index is not only sensitive, but it can also provide more information about the location of the process mean as compared to other classical PCIs. Most of the traditional PCIs perform well when process follows a normal distribution. In this article, we conside...

An extension of the exponential distribution due toNadarajah and Haghighi referred to as Nadarajah and Haghighi (NH) distribution is an alternative that always provides better fits than the gamma, Weibull, and the generalized exponential distributions whenever the data contains zero values. However, in practice, discrete data is easy to collect as...

An indicator to evaluate the process performance and capability is the process capability index (PCI). It is of great significance to quality control engineers as it quantifies the relation between the actual performance of the process and the pre-set specifications of the product. Most of the traditional PCIs performed well when process follows th...

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes , a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers mixture of Topp-Leone distributions under classical and Bayesian perspective based on complete sample. The ne...

This article accentuates the estimation of a two-parameter generalized Topp-Leone distribution using dual generalized order statistics (dgos). In the part of estimation, we obtain maximum likelihood (ML) estimates and approximate confidence intervals of the model parameters using dgos, in particular, based on order statistics and lower record value...