In this paper, we develop two acceptance sampling plans where the lifetimes of the product follow Weibull Exponential and Weibull Lomax distributions both belonging to the new truncated Weibull–X family of distributions based on run lengths of the conforming items. The model parameters are estimated by using the maximum likelihood method contrary to the existing plans where authors have been selecting arbitrary values of the parameters. The efficiency of the proposed plan is established by comparing it with the existing plans based on the average number of inspected items. A real example of failure rates of a piece of electronic equipment operating in a specific mode is presented to illustrate the proposed plans for industrial use.