Abstract In this paper, a generalization of the Harris family of distributions, namely, the Harris generalized linear exponential distribution is discussed. The use of the model is established by fitting it to a real data set. Also, we derive a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes following this distribution.
{"title":"Reliability Test Plans for Percentiles Based on the Harris Generalized Linear Exponential Distribution","authors":"K. K. Jose, Albin Paul","doi":"10.1515/eqc-2017-0025","DOIUrl":"https://doi.org/10.1515/eqc-2017-0025","url":null,"abstract":"Abstract In this paper, a generalization of the Harris family of distributions, namely, the Harris generalized linear exponential distribution is discussed. The use of the model is established by fitting it to a real data set. Also, we derive a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes following this distribution.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"124 1","pages":"61 - 70"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74286787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.
{"title":"Topp–Leone Linear Exponential Distribution","authors":"Bol A. M. Atem, Suleman Nasiru, K. Nantomah","doi":"10.1515/eqc-2017-0022","DOIUrl":"https://doi.org/10.1515/eqc-2017-0022","url":null,"abstract":"Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"18 1","pages":"31 - 43"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89401680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper describes the application of simple quality control charts to monitor the traffic intensity of single server queues, a still uncommon use of what is arguably the most successful statistical process control tool. These charts play a vital role in the detection of increases in the traffic intensity of single server queueing systems such as the M / G / 1 {M/G/1} , G I / M / 1 {GI/M/1} and G I / G / 1 {GI/G/1} queues. The corresponding control statistics refer solely to a customer-arrival/departure epoch as opposed to several such epochs, thus they are termed short-memory charts. We compare the RL performance of those charts under three out-of-control scenarios referring to increases in the traffic intensity due to: a decrease in the service rate while the arrival rate remains unchanged; an increase in the arrival rate while the service rate is constant; an increase in the arrival rate accompanied by a proportional decrease in the service rate. These comparisons refer to a broad set of interarrival and service time distributions, namely exponential, Erlang, hyper-exponential, and hypo-exponential. Extensive results and striking illustrations are provided to give the quality control practitioner an idea of how these charts perform in practice.
{"title":"Comparing Short-Memory Charts to Monitor the Traffic Intensity of Single Server Queues","authors":"Marta Santos, M. Morais, A. Pacheco","doi":"10.1515/eqc-2017-0030","DOIUrl":"https://doi.org/10.1515/eqc-2017-0030","url":null,"abstract":"Abstract This paper describes the application of simple quality control charts to monitor the traffic intensity of single server queues, a still uncommon use of what is arguably the most successful statistical process control tool. These charts play a vital role in the detection of increases in the traffic intensity of single server queueing systems such as the M / G / 1 {M/G/1} , G I / M / 1 {GI/M/1} and G I / G / 1 {GI/G/1} queues. The corresponding control statistics refer solely to a customer-arrival/departure epoch as opposed to several such epochs, thus they are termed short-memory charts. We compare the RL performance of those charts under three out-of-control scenarios referring to increases in the traffic intensity due to: a decrease in the service rate while the arrival rate remains unchanged; an increase in the arrival rate while the service rate is constant; an increase in the arrival rate accompanied by a proportional decrease in the service rate. These comparisons refer to a broad set of interarrival and service time distributions, namely exponential, Erlang, hyper-exponential, and hypo-exponential. Extensive results and striking illustrations are provided to give the quality control practitioner an idea of how these charts perform in practice.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"67 1","pages":"1 - 21"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84057355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In industry when a lot of items is sent for inspection, double acceptance sampling plans (DASP) are considered as a way to decide on acceptance or rejection of the lot. If the lot contains items with high sensitivity, then the measuring of quality characteristics is destructive or costly. So we are looking for a method to decide that it has high performance. Using the ranked set sampling (RSS) method will make it stricter and more accurate whether or not to accept a lot. Moreover, it is affordable and will not burden extra costs on the buyer or the producer. In this paper, by using a special type of RSS, with the name of maxima nomination sampling (MNS), we design a DASP with regards to the total loss function. The results indicate that the total loss function, which is acquired by the MNS method, has lower values than the one using the simple random sampling (SRS) method.
{"title":"An Economic Design of Rectifying Double Acceptance Sampling Plans via Maxima Nomination Sampling","authors":"M. Razmkhah, B. Sadeghpour Gildeh, J. Ahmadi","doi":"10.1515/eqc-2017-0018","DOIUrl":"https://doi.org/10.1515/eqc-2017-0018","url":null,"abstract":"Abstract In industry when a lot of items is sent for inspection, double acceptance sampling plans (DASP) are considered as a way to decide on acceptance or rejection of the lot. If the lot contains items with high sensitivity, then the measuring of quality characteristics is destructive or costly. So we are looking for a method to decide that it has high performance. Using the ranked set sampling (RSS) method will make it stricter and more accurate whether or not to accept a lot. Moreover, it is affordable and will not burden extra costs on the buyer or the producer. In this paper, by using a special type of RSS, with the name of maxima nomination sampling (MNS), we design a DASP with regards to the total loss function. The results indicate that the total loss function, which is acquired by the MNS method, has lower values than the one using the simple random sampling (SRS) method.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"78 1","pages":"104 - 99"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77512664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We consider the Dagum distribution for estimating the reliability of a k-component stress-strength system with different shape values of the shape parameter. We assume that the system has strength modelled by k independent and identically distributed random variables, and each system’s component experiences random stress. We construct maximum likelihood estimators for the system’s reliability and study their asymptotic properties. We evaluate the small sample performance of the estimators through Monte Carlo simulation. Finally, we illustrate the procedure using real data.
{"title":"Estimation of Reliability in Multicomponent Stress-Strength Based on Dagum Distribution","authors":"A. Fulment, P. Josephat, G. Srinivasa Rao","doi":"10.1515/eqc-2017-0009","DOIUrl":"https://doi.org/10.1515/eqc-2017-0009","url":null,"abstract":"Abstract We consider the Dagum distribution for estimating the reliability of a k-component stress-strength system with different shape values of the shape parameter. We assume that the system has strength modelled by k independent and identically distributed random variables, and each system’s component experiences random stress. We construct maximum likelihood estimators for the system’s reliability and study their asymptotic properties. We evaluate the small sample performance of the estimators through Monte Carlo simulation. Finally, we illustrate the procedure using real data.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"37 1","pages":"77 - 85"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79185229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Nosocomial epidemics are infectious diseases which spread among different types of susceptible individuals in a health-care facility. To model this type of epidemics, we use a multi-type branching process with a multivariate negative binomial offspring distribution. In particular, we estimate the basic reproduction number R 0 {R_{0}} and study its relationship with the parameters of the offspring distribution. in case of a single-type epidemic, we investigate the effect of contact tracing on the estimates for R 0 {R_{0}} .
{"title":"Multi-Type Branching Processes Modeling of Nosocomial Epidemics","authors":"Zeinab Mohamed, T. Oraby","doi":"10.1515/eqc-2017-0026","DOIUrl":"https://doi.org/10.1515/eqc-2017-0026","url":null,"abstract":"Abstract Nosocomial epidemics are infectious diseases which spread among different types of susceptible individuals in a health-care facility. To model this type of epidemics, we use a multi-type branching process with a multivariate negative binomial offspring distribution. In particular, we estimate the basic reproduction number R 0 {R_{0}} and study its relationship with the parameters of the offspring distribution. in case of a single-type epidemic, we investigate the effect of contact tracing on the estimates for R 0 {R_{0}} .","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"60 1","pages":"63 - 75"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78868079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Al-Omari, Amjad D. Al-Nasser, Fatima S. Gogah, M. A. Haq
Abstract A double acceptance sampling plan (DASP) based on truncated life tests is suggested in this paper when the lifetime of a product follows the exponentiated generalized inverse Rayleigh distribution (EGIR). For a fixed value of the consumer’s confidence level, the minimum sample sizes of the first and second samples needed to ensure the specified mean life are obtained. The operating characteristic values according to the different quality levels are obtained and the minimum ratios of the mean life to the specified life are calculated. The important tables based on the suggested DASP are calculated and illustrated.
{"title":"On the Exponentiated Generalized Inverse Rayleigh Distribution Based on Truncated Life Tests in a Double Acceptance Sampling Plan","authors":"A. Al-Omari, Amjad D. Al-Nasser, Fatima S. Gogah, M. A. Haq","doi":"10.1515/eqc-2017-0007","DOIUrl":"https://doi.org/10.1515/eqc-2017-0007","url":null,"abstract":"Abstract A double acceptance sampling plan (DASP) based on truncated life tests is suggested in this paper when the lifetime of a product follows the exponentiated generalized inverse Rayleigh distribution (EGIR). For a fixed value of the consumer’s confidence level, the minimum sample sizes of the first and second samples needed to ensure the specified mean life are obtained. The operating characteristic values according to the different quality levels are obtained and the minimum ratios of the mean life to the specified life are calculated. The important tables based on the suggested DASP are calculated and illustrated.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"17 1","pages":"37 - 47"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84182230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, an exponential model with only one shape parameter, which can be used in modeling survival data, reliability problems and fatigue life studies, is studied. We derive explicit expressions for some of its statistical and mathematical quantities including the ordinary moments, generating function, incomplete moments, order statistics, moment of residual life and reversed residual life. The model parameter is estimated by using the maximum likelihood method. A real data application is given to illustrate the flexibility of the model. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study.
{"title":"The One-Parameter Odd Lindley Exponential Model: Mathematical Properties and Applications","authors":"M. C. Korkmaz, H. Yousof","doi":"10.1515/eqc-2017-0008","DOIUrl":"https://doi.org/10.1515/eqc-2017-0008","url":null,"abstract":"Abstract In this article, an exponential model with only one shape parameter, which can be used in modeling survival data, reliability problems and fatigue life studies, is studied. We derive explicit expressions for some of its statistical and mathematical quantities including the ordinary moments, generating function, incomplete moments, order statistics, moment of residual life and reversed residual life. The model parameter is estimated by using the maximum likelihood method. A real data application is given to illustrate the flexibility of the model. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"84 1","pages":"25 - 35"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88291750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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