Prof S P Mukherjee - Academia.edu (original) (raw)

Papers by Prof S P Mukherjee

Series on Quality, Reliability and Engineering Statistics, 1998

ABSTRACT Inference on R=P(X<Y), when X and Y are independent Weibull variables with unknow... more ABSTRACT Inference on R=P(X<Y), when X and Y are independent Weibull variables with unknown shape parameters, is of special interest. Assuming a common shape parameter for X and Y, approximate lower bounds for R are obtained from complete as well as censored (type-II) samples. The delta method as well as jackknife and bootstrap procedures for complete samples and the delta method and jackknife procedure for censored samples have been used here to derive estimates of the scale parameters and the common shape parameter. Findings of a simulation study have also been reported.

Calcutta Statistical Association Bulletin, 1997

Here we consider a two-component system where the components are identical but do not work indepe... more Here we consider a two-component system where the components are identical but do not work independently within the system. Assuming the joint distribution of component lives to be Bivariate Exponential (BVED), system (series, parallel or stand-by) life distribution comes out to be a proper mixture of x2-distributions. We approximate the system life distribution as a chi-square with a multiplier that depends on system configuration. Prediction intervals for a single future observation (on component life) are constructed on the basis of system life observations. Further, we have taken Gamma and Rectangular priors for the parameters of the BVED and have approximated the unconditional distribution of system life as Beta with suitable parameters. Taking logarithmic transformation, we get Bayesian prediction intervals.

Calcutta Statistical Association Bulletin, 1992

In this paper, we propose a new solution to a point demand inventory problem that minimises the m... more In this paper, we propose a new solution to a point demand inventory problem that minimises the mode of the distribution of total cost, Some analytic results are given for the case of gamma and beta distributed demand.

Calcutta Statistical Association Bulletin, 1979

Calcutta Statistical Association Bulletin, 1990

: Lehmann (1955, 1986), Bessler and Veinott (1966), Keilson and Sumita (1982), Ross (1983), Stoya... more : Lehmann (1955, 1986), Bessler and Veinott (1966), Keilson and Sumita (1982), Ross (1983), Stoyan (1983), Alzaid (1988), Mukherjee and Chatterjee (1991) considered several dominance relations between life distributions through reliability measures—indicating their interrelationships and consequences. In the present paper some closure or preservation properties of the said dominance relations have been studied under various reliability operations e.g. convolution, mixture, formation of coherent structure, monotone transformation of the random variables and limits in distribution.

Calcutta Statistical Association Bulletin, 1977

In analysing reliability characteristics of multicomponent systems it is rational to assume in ma... more In analysing reliability characteristics of multicomponent systems it is rational to assume in many cases that component life lengths are positively or negatively interdependent. This positive interdependence may be due to common environmental and incidental stresses, functional dependence on common sources of energy, 'mechanical sticking of assemblies' etc. Multivariate parametric families of distributions which have been proposed and studied (incompletely) to describe joint random variations of component failure times are multivariate generalisations of exponential, weibull, gamma and normal distributions. Although several useful results characterising life distributions of coherent systems of independent components have already been obtained (Barlow and Proschan, 1975), very little is yet known about dependent systems even of two components. Downton (1970) has worked out probability distributions, means and variances of the life of a series and a parallel system for the bivariate exponential (BVE) distribution arising out of the 'successive damage model' proposed by him as well for the one arising out of the 'shock model' due to Marshall and Olkin (1967) . An easily tractable form of the BVE distribution, proposed by Morgenstern (1956) and studied by Gumbel (1960) has the p.d.f.

Journal of Multivariate Analysis, 1989

Bivariate exponential distribution of Marshall-Olkin form, bivariate Rayleigh distribution, and b... more Bivariate exponential distribution of Marshall-Olkin form, bivariate Rayleigh distribution, and bivariate Weibull distribution have been characterized through some functional equations to be satisfied by the survival function and hazard function.

The Journal of the Operational Research Society, 1990

A queueing model with server vacations is studied in which it is assumed that the interarrival ti... more A queueing model with server vacations is studied in which it is assumed that the interarrival time has a general distribution, the service-time distribution is exponential and vacations are independently and indentically distributed with a general distribution. Using the embedded Markov chain technique, the equilibrium probability distributions of system size have been obtained at pre-arrival and at random epochs separately. Finally, the distribution of waiting time of a customer in the queue (excluding service) has been derived.

European Journal of Operational Research, 1989

Aima'act." An infinite-server queueing system is studied in which units arrive in batches of vari... more Aima'act." An infinite-server queueing system is studied in which units arrive in batches of variable size following a non-homogeneous compound Poisson process and each unit arriving at time t has its own arbitrary service time distribution. Using the standard properties of the Poisson process and elementary probability arguments, we derive the probability generating functions (PGF) of N(t), the number of units in the system at time t and D(t), the number of service completions up to time t or in the interval (0, t] in the transient state. Covariance functions between N(t), D(t); N(t), R(t) and R(t), D(t) are obtained separately where R(t) represents the number of arrivals in the time interval (0, t]. Expressions are obtained for the mean and variance of N(t) and D(t). Finally, some steady state results are obtained under certain conditions.

Calcutta Statistical Association Bulletin, 1994

Here was a man who could accept and discharge many responsibilities with his broad shoulders, who... more Here was a man who could accept and discharge many responsibilities with his broad shoulders, who could win over a myriad of men and women with his broad heart and who could ignore personal discomfitures with a broad smile. Professor Bose remained totally identified with the Department of Statistics and Calcutta Statistical Association throughout his career and was their spokesman to the outside world. It will not be fair to characterise Professor Bose as merely a distinguished teacher or research worker in statistics. He was much more. He was an eminent scientist with a deep concern for the welfare of the country and its people.

Indian journal of psychiatry, 1986

A field survey of psychiatric morbidity was conducted in a village by a door to door survey. The ... more A field survey of psychiatric morbidity was conducted in a village by a door to door survey. The survey was repeated after 10 years by the same team and by the same method. The aim was to compare the rates of mental morbidity of the community at the interval of a decade and to trace out during the second survey all the persons - both ill and well - found in the first survey and to assess their mental health status.Though the total morbidity did not change from 1972 to 1982 there was a definite rise in the rates of morbidity of Hysteria and Anxiety showed a slight fall in 1982. The health population of 1972 traced and assessed in 1982 showed a lower rate of morbidity than the total population of 1982. The rate of recovery of the morbid stock assessed after ten years was about 29 % and as many as 14.8% of the morbid people died during this period. This death rate is much higher than that of healthy population assessed after ten years (h.9%). 47.8% of the cases detected in the first su...

Indian journal of psychiatry, 1997

A door to door field-survey was conducted in two villages by a team of psychiatrists with the aim... more A door to door field-survey was conducted in two villages by a team of psychiatrists with the aim of assessing the mental morbidity of the population. The present communication is restricted to the mental morbidity of the elderly population aged 60 years and above. The total sample comprised 183 persons (male 85, female 98). Majority of the families (44.2%) belonged to class IV according to Pareek and Trivedi's scale. Sixty one percent of the elderly population was mentally ill. Women had a higher rate of morbidity than men (77.6% and 42.4% repetitively). The overwhelming majority of the affected persons were depressives. Rate of dementia was low.

Journal of Multivariate Analysis, 1998

A general approach for the development of multivariate survival models, based on a set of given m... more A general approach for the development of multivariate survival models, based on a set of given marginal survivals, is presented. Preservation of IFR and IFRA properties and the nature of dependence among the variables are examined, and a recursive relation is suggested to obtain the resultant density function. In particular, an absolutely continuous Weibull distribution is derived and a few of its properties are studied.

Indian Statistical Institute Series, 2021

Calcutta Statistical Association Bulletin, 1985

Stochastic Models describing occupational mobility have been suggested, among others, by Bartholo... more Stochastic Models describing occupational mobility have been suggested, among others, by Bartholomew (1967) and Ginsberg (1971, 1972a). But none of the measures of mobility based on such models can be treated as a rate of occupational mobility. The present paper offers a crude rate of occupational mobility based on renewal theory and counting process. Expressions for the mean and variance of the suggested rate have been obtained.

Calcutta Statistical Association Bulletin, 2017

Various reliability properties, including some characterization results, have been investigated f... more Various reliability properties, including some characterization results, have been investigated for two finite range life distributions. One of these, namely, the exponentiated rectangular distribution, exhibits a bath-tub failure rate when the shape parameter has a value less than unity and, as expected, does not conform to certain results relating to ageing properties, which hold in the case of distributions with monotone failure rates. Moments as well as best percentile estimates of the shape parameter for this distribution have been worked out. Stress–strength reliability when stress and strength follow the same distribution of this type over the same range, but with different shape parameter values, has been derived and shown to be related to the Bhattacharyya distance between the two probability distributions. Distributions of parallel and standby system lives for two independent components, with this distribution having varying shape parameters, have been derived.

Calcutta Statistical Association Bulletin, 1983

A static inventory model where lots received (against orders) are accepted through a curtailed si... more A static inventory model where lots received (against orders) are accepted through a curtailed single sampling inspection plan has been considered. Since the proportion of non-defective units in a lot is not likely to be known in advance, a probability Jaw has been assumed for the same. The optimal order quantity has been obtained by maximizing the expected net profit, taking into account selling price, purchase cost, carrying cost, shortage cost, salvage cost and inspcctioo cost.

Calcutta Statistical Association Bulletin, 1967

Indian journal of psychiatry, 1983

Relationship of different symptoms, personal history, some measures of Rorschach, neuroticism, eg... more Relationship of different symptoms, personal history, some measures of Rorschach, neuroticism, ego strength score with prognosis of depression was studied. Out of 60 items studied in 60 cases, eleven were found to have statistically significant association with improvement. Multiple regression of percentage of improvement on 23 items (12 from personal and family history and 13 measurable items of Rorschach) was determined. To check the ability of this multiple regression to expl. in differences in responsiveness, predicted values were obtained for 24- cases (not included in the previous regression analysis). In most cases considerable differences was found in observed and predicted values. Then a regression coefficient using only 12 items (other than 13 Rorschach items) was determined similarly. Using this regression equation, predicted Values for percentage of improvement was obtained for the same 24 cases. There was insignificant association between observed and predicted Values. ...

Total Quality Management, 1995

... such as liberal vs professional) at different levels (such as elementary, secondary and highe... more ... such as liberal vs professional) at different levels (such as elementary, secondary and higher ... is being gradually realized that, to arrest these disturbing trends in our education system, we ... and better advantage of the precept and practice of total quality management (TQM)Ðbut at ...