Acceptance sampling plans for percentiles based on the inverse Rayleigh distribution

In this article, acceptance sampling plans are developed for the inverse Rayleigh distribution percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer’s risk. The operating characteristic values (and curves) of the sampling plans as well as the producer’s risk are presented. Two examples with real data sets are also given as illustration

Double-Acceptance Sampling Plan for Exponentiated Fréchet Distribution with Known Shape Parameters

We suppose that a product’s lifetime follow the exponentiated Fréchet distribution of defined shape parameters. Based on this assumption, a double-acceptance sampling plan is constructed. The zero and one failure framework is essentially thought of: if no errors are found from the first sample, then the lot is approved; also, if at least two failures occur, it is rejected. In the first sample, if one failure is observed, then the second sample is taken and decided for the same length as the first one. The cumulative sample sizes of the first and second samples are determined on the basis of the stated confidence level of the consumer to ensure that the actual median is longer than the given life. As indicated by the various ratios of the actual median life to specified median lifetime, the operating characteristics are calculated and placed in presented tables. To decrease the risk of the producer at the predefined level, the minimum ratios of this sort are additionally obtained. Lastly, examples are provided for representation reasons for the proposed model

Acceptance sampling based on life tests: Log-logistic model

The problem of acceptance sampling when the life test is truncated at a preassigned time is considered. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified average life, the minimum sample size necessary to ensure the specified average life, are obtained under the assumption that the lifetime variate of the test items follows a distribution belonging to Burr's family XII of distributions - called the log-logistic model. The operating characteristic values of the sampling plans and producer's risk are presented. The results are illustrated by an example.

Estimation of Reliability in Multicomponent Stress-Strength based On Inverse Rayleigh Distribution

A multicomponent system of k components having strengths following k– independently and identically distributed random variables and each component experiencing a random stress Y is considered. The systemis regarded as alive only if at least s out of k (s\u3c k) strengths exceed the stress. The reliability of such a system is obtained when strength, stress variates are given by inverse Rayleigh distribution with different scale parameters. The reliability is estimated using the Moment method and ML method of estimation when samples drawn from strength and stress distributions. The reliability estimators are compared asymptotically. The small sample comparison of the reliability estimates is made through Monte Carlo simulation