Acceptance Sampling Plans based on Percentiles of Exponentiated Inverse Kumaraswamy Distribution

Abstract

Objectives: To prepare the percentile-based acceptance sampling plans for the Exponentiated Inverse Kumaraswamy Distribution (EIKD) at a specific truncation time to inspect the defective lots corresponding to the desired acceptance level. Methods: The failure probability value is estimated using the cumulative probability function F(.) at time ‘t’ which is converted in terms of the scale parameter σ as 100th percentile using quantile function. The minimum size of the sample, Operating Characteristic (OC) and the minimum ratios are calculated for a required levels of consumer’s as well as producer’s risk. Findings: The percentile-based sampling plans are obtained through the minimal size of the sample ‘n’ under a truncated life test with a target acceptance number c in a manner that the proportion of accepting a lot which is not good (consumer’s risk) would not be more than . These values are calculated at The function of probability of acceptance for variations in the quality of a lot (OC function) L(p) of the sample plan are evaluated for the acceptance values of c=1 and c=5. The minimum ratio values are calculated for the acceptability of the lot with producers’ risk of using the sampling plan. Novelty: The modernity of this study is the designing of the acceptance sampling plans to a non-normal data using an asymmetrical distribution that has all three shape parameters. Also, the monitor of the implementation and suitability of statistical quality control and process control aspects using Exponentiated Inverse Kumaraswamy Distribution when compared to other asymmetrical distributions which has at least one scale parameter. Keywords: Sampling plans, Consumer's risk, Operating characteristics function, Truncated life tests, Producer's risk