A sampling plan named as Multiple Dependent State Repetitive Group Sampling (MD-SRGS) 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.

A new scheme ‘Rhombus Ranked Set Sampling’ (RRSS) is developed in this research together with its properties for estimating the population means. Mathematical validation along with the simulation evaluation is presented. The proposed method is an addition to the family of different sampling methods and generalization of ‘Folded Ranked Set Sampling’ (FRSS). For the simulation process, nine probability distributions are considered for the efficiency comparison of proposed scheme from which four are symmetric and rest are asymmetric among which Weibull and beta distributions which are used twice, unlike parametric values. (Al-Naseer, 2007 and Bani-Mustafa, 2011). Through simulation processes, it is observed that RRSS is competent and more reliable relative to simple random sampling (SRS), ranked set sampling (RSS) and folded ranked set sampling (FRSS). It is noted that for all the underlying distributions, an increase in the efficiency of Rhombus Ranked Set Sampling (RRSS) is achieved via increasing the size of the sample ‘p’. Besides the efficiency comparison, consistency of the proposed method is also valued by using Co-efficient of Variation (CV).  Secondary data on zinc (Zn) concentration and lead (Pb) contamination in different parts and tissues of freshwater fish was collected to illustrate the evaluation of RRSS against SRS, RSS, FRSS and ERSS (extreme ranked set sampling). The results obtained through real life illustration defend the simulation study and hence indicates that the RRSS estimator is efficient substitute for existing methods (Al-Omari, 2011).

The present study proposes a new modified group chain sampling plan for truncated life test when the lifetime of products follow a Kumaraswamy Generalized Power Weibull (KGPW) distribution. The results of optimal group size, mean ratio of true mean to the specified mean, operating characteristic values, minimum angles, acceptance quality level, lower quality level are obtained against the specified producer's, consumer's risk, test termination time and mean ratios. The performance of the proposed chart is also monitored through a real life dataset of 63 single carbon fibers' measurements with specified gauge length. Control limits are constructed to check the quality of strength of a single carbon fibers at gauge length of 20-mm. From the results, it is observed that when the test termination time increases the operating characteristic and mean ratio of proposed plan also increase disproportionately.