Mathematical Sciences

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Browsing Mathematical Sciences by Author "Aslam, Muhammad"

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    Control charts for monitoring process capability index using median absolute deviation for some popular distributions
    (Multidisciplinary Digital Publishing Institute, 2019) Aslam, Muhammad; Rao, G. Srinivasa; AL-Marshadi, Ali Hussein; Ahmad, Liaquat; Jun, Chi-Hyuck
    A control chart monitoring the process capability index (PCI) using median absolute deviation (MAD) is proposed to analyze the industrial process performance. Extensive simulation studies were carried out to evaluate the performance of MAD-based PCI control charts under the low, moderate, and high asymmetric conditions when the process characteristic follows Weibull, log-normal, and gamma distributions. The performance of the proposed control charts was evaluated based on the average run lengths. The practical implementation of the proposed charts was also illustrated with industrial data.
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    Estimation of reliability in a multicomponent stress–strength system for the exponentiated moment-based exponential distribution
    (Multidisciplinary Digital Publishing Institute, 2019) Rao, Srinivasa G.; Bhatti, Fiaz Ahmad; Aslam, Muhammad; Albassam, Mohammed
    A multicomponent system of k components with independent and identically distributed random strengths X 1, X 2 , … X k , with each component undergoing random stress, is in working condition if and only if at least s out of k strengths exceed the subjected stress. Reliability is measured while strength and stress are obtained through a process following an exponentiated moment-based exponential distribution with different shape parameters. Reliability is gauged from the samples using maximum likelihood (ML) on the computed distributions of strength and stress. Asymptotic estimates of reliability are compared using Monte Carlo simulation. Application to forest data and to breaking strengths of jute fiber shows the usefulness of the model.
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    Evaluation of bootstrap confidence intervals using a new non-normal process capability index
    (Multidisciplinary Digital Publishing Institute, 2019) Rao, Gadde Srinivasa; Albassam, Mohammed; Aslam, Muhammad
    This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) forWeibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index Cpkw over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.
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    Mixed EWMA–CUSUM chart for COM-Poisson distribution
    (Taylor & Francis, 2020) Rao, Gadde Srinivasa; Aslam, Muhammad; Rasheed, Umer; Jun, Chi-Hyuck
    In this article, we develop a mixed (SPC) control chart for monitoring moderate and/or small shift in the process following the Conway Maxwell Poisson (COM-Poisson) distribution. To determine the ability and performance of the proposed mixed EWMA-CUSUM control chart, we evaluate the average run lengths and compare with different control charts. We will compare the efficiency of the proposed control chart over the existing control charts in terms of average run length. The results show an improvement in ARL when compared with the existing charts. A real example and a simulation study is also added to use the chart in the industry.
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    Two-stage sampling plan using process loss index under neutrosophic statistics
    (Taylor & Francis, 2019) Rao, Srinivasa G.; Aslam, Muhammad; Khan, Nasrullah; Ahmad, Liaquat
    This article develops the designing of two-stage process loss using neutrosophic statistics (NS). The neutrosophic operating characteristic for the two-stage sampling is developed under NS. Neutrosophic plan parameters are obtained using non-linear optimization using the neutrosophic statistical interval method for the constraints. A comparative study is carried out with the existing scheme. Some tables are provided and explained with an example under uncertainty.
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    A variable control chart based on process capability index under generalized multiple dependent state sampling
    (Institute of Electrical and Electronics Engineers, 2019) Rao, G. Srinivasa; Raza, Muhammad Ali; Aslam, Muhammad; AL-Marshadi, Ali Hussein; Jun, Chi-Hyuck
    This paper proposed a process capability index-based control chart under the new extended form of multiple-dependent state sampling (MDS) named generalized MDS (GMDS). The scheme is based on inner and outer control limits and utilizes the previous state of the samples. The performance comparisons of the proposed chart with the existing charts are made by using out-of-control ARL. The simulation study showed the superiority of the proposed chart over the existing PCI-based control charts under Shewhart and MDS schemes. An empirical illustration is also given to demonstrate the application of the proposed chart.
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    A variable sampling plan using generalized multiple dependent state based on a one-sided process capability index
    (2019) Rao, Srinivasa G.; Aslam, Muhammad; Jun, Chi-Hyuck
    In this manuscript, a sampling plan based on one-sided process capability index is designed using the generalized multiple dependent state (GMDS) sampling. The operating characteristic function is developed using the exact distribution of the estimated PCI. The plan parameters of the proposed sampling plans are determined through the non-linear optimization problem at specified producer’s risk and consumer’s risk. An example is reported with the help of real data from the industry. The efficiency of the proposed sampling plan is compared with the existing multiple dependent state (MDS) sampling in terms of sample size.