In this book, we study the different methods of statistical quality control based on a life distribution, namely as an exponentiated distribution of Fréchet (EFD). The maximum likelihood estimator and its asymptotic distribution are mainly concerned with estimating the reliability of R=P(Y< X) in the exponentiated Fréchet distribution proposed by Nadarajah and Kotz (2006) to construct an asymptotic confidence interval of R. It also studies the reliability estimate of the multi-component stress-strength model using the ML method together with asymptotic confidence intervals. The new acceptance sampling plan and economic reliability test plan were proposed by us. In order to ensure a percentile life when the life test is terminated at a pre-assigned time and when the observed number of failures does not exceed a given acceptance number, we developed sampling plans for finding the minimum sample size necessary.
An economic reliability test plan is taken into account and this plan yields
the minimum ratio of termination time required to test the items to decide
whether or not a lot submitted is good. For EFD, group acceptance sampling
plans are constructed when the lifetime of the product is truncated by known
percentile shape parameters. Parametric quantities of the plan, such as the
number of groups g and acceptance number c, are determined by simultaneously
considering the risk of the consumer and the risk of the producer. For EFD, a
two-stage group acceptance sampling plan with known shape parameters has been
developed. In order to ensure the quality of product life, we also developed a
group acceptance sampling plan (GASP) for lot resubmission. We built the
Process Capability Index attribute control chart and bootstrap confidence
intervals.
We determined the
control chart coefficient and discussed the average run length (ARL) behaviour
of the proposed control chart. We also built capacity index confidence
intervals using bootstrap methods through simulation. The standard bootstrap
confidence interval (SB), the percentile bootstrap confidence interval (PB) and
the bias-corrected percentile bootstrap confidence interval (BCPB) are considered
three types of bootstrap confidence intervals and the performance of these
bootstrap confidence intervals are compared using Monte Carlo simulation by
considering their coverage probabilities and average widths.
Author (s) Details
Sridhar
Babu Mothukuri
Department of Sciences, St. Mary’s College, 8-3-229,
Near Yousufguda Check Post, Yousufguda, Hyderabad, Telangana – 500045, India. D.
M. Dewaikar
Kanaparthi Rosaiah
Department of Statistics, Acharya Nagarjuna University, Nagarjuna Nagar,
Guntur District, Andhra Pradesh, India.
Gadde Srinivasa Rao
Department of Mathematics and Statistics, The University of Dodoma,
Tanzania.
View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/328
Keywords - Exponentiated Fréchet distribution, stress-strength model,
multi-component stressstrength,
acceptance sampling, producer’s risk, consumer’s risk, group acceptance
sampling, resubmitted lot, attribute control chart, process capability index, bootstrap
confidence interval.
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