Optimal design of multiple dependent state repetitive group sampling plan for Inverse Power Lomax distribution

Abstract

A sampling plan named as Multiple Dependent State Repetitive Group Sampling (MDSRGS) plan is introduced for a time-truncated life test given that the underlying distribution of the product's lifetime is Inverse Power Lomax distribution (IPLD). The proposed sampling plan is developed with the help of two already developed sampling plans (MDS and RGS). The two-point approach OC function known as the producer's risk and customer's risk is used to determine the parameters of the proposed plan. An optimization method is used for different values of customer's risk and producer's risk, for static values of experiment termination ratio and mean ratio, to find out plan parameters (minimum size of the sample, the number of acceptance and rejection, and the number of successive lots). Tables are created for different known values of shape parameters of Inverse Power Lomax distribution. The efficiency of the proposed MDSRGS plan is examined by conducting a comparative study. To accompany the results, graphs are also used for visualizing the average sample and acceptance probabilities with the specific mean ratio. Two real-life applications are also incorporated to demonstrate the operating procedure of the proposed plan.