In this paper, a hybrid group acceptance sampling plan is introduced for a truncated life test if life times of the items follow size biased Lomax model. The minimum number of testers and acceptance number are obtained when the consumer's risk and the test termination time and group size are pre-specified. The operating characteristic values, minimum ratios of the true mean life to the specified mean life for the given producer's risk are also derived. The results are discussed through an example, a comparative study of proposed sampling plan with existing sampling plan are elaborated.
A combination of Pareto and Rayleigh distributions considered for a new T-X probability model named as Pareto-Rayleigh distribution (PR distribution). We have chosen a life time random variable X from PR distribution whose lots are to be decided for acceptance or otherwise based on sample lifetimes drawn from the lot. A sampling scheme is developed in such way that the sample is divided into different groups and experiment is terminated whenever the first failure noticed in each group. The theory of ordered statistics is applied for the criterion of acceptance and is compared with the similar works proposed by other authors.
A new probability model size biased Lomax is considered for a life time random variable. The problem of acceptance sampling when the life test is truncated at a pre-assigned time is discussed with a known shape parameter. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure the specified mean life time is evaluated. The operating characteristic functions of the sampling plans are derived. Producer's risk is also discussed. A table for the ratio of true mean life to a specified mean life that ensure acceptance with a pre-assigned probability is provided. The results are given by an example.
Control charts are one of the powerful techniques of Statistical Process Control. Control charts are widely accepted and applied in industry which can be used to improve productivity, prevent defects and unnecessary process adjustment. Moreover, they also provide information in diagnosis and process capability. Life time data generally contain the failure times of sample products or inter failure times or number of failures experienced in a given time. The time to failure of a product is to be considered as a quality characteristic to assess the quality of the product. Control limits are evaluated for the time to failure. In this paper the time to failure of a product is considered to follow Inverse Rayleigh and Inverse Half Logistic distributions. Life time data are compared with the control limits to judge the quality performance of the product.
Lomax Distribution (Pareto Type IV) is fitted for a life time random variable which can be studied for the data belongs to Actuarialscience, medical diagnosis and Queuing theory etc. In the time of day events observed in cycles like hourly, daily, weekly, monthlyor yearly are in circular distribution. By adopting the technique of wrapping an attempt is made to identify a new circular probabilitymodel originate as Wrapped Lomax Distribution. The concept of circular model is introduced and strategy of wrapping is given forLomaxDistribution. Wrapped Lomax Distribution PDF and CDF are derived, their graphs are also studied. The trigonometric momentsand characteristic function of Wrapped Lomax Distribution are obtained and their graphs are also depicted. The characteristics likemean, variance, skewness, kurtosis and circular standard deviation for various values of location and scale parameters are derived in this paper.
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