Statistical Quality Control Methods for Exponentiated Fréchet Distribution

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.

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