Time truncated attribute control chart for the generalized Rayleigh distributed quality characteristics and beyond

Abstract

Purpose First is to develop the time truncated median control chart for the Rayleigh distribution (RD) and generalized RD (GRD), respectively. Second is to evaluate the performance of the proposed attribute control chart which depends on the average run length (ARL) and third is to include real life examples for application purpose of the proposed attribute control chart.Design/methodology/approach (1) Select a random sample of size n from each subgroup from the production process and put them on a test for specified time t, where t = ? × µe. Then, count the numbers of failed items in each subgroup up to time t. (2) Step 2: Using np chart, define D = np, the number of failures, which also a random variable follows the Binomial distribution. It is better to use D = np chart rather than p chart because the authors are using number of failure rather than proportion of failure p. When the process is in control, then the parameters of the binomial distribution are n and p0, respectively. (3) Step 3: The process is said to be in control if LCL = D = UCL; otherwise, the process is said to be out of control. Hence, LCL and UCL for the proposed control chart.Findings From the findings, it is concluded that the GRD has smaller ARL values than the RD for specified values of parameters, which indicate that GRD performing well for out of control signal as compared to the RD.Research limitations/implications This developed control chart is applicable when real life situation coincide with RD and GRD.Social implications Researcher can directly use presented study and save consumers from accepting bad lot and also encourage producers to make good quality products so that society can take benefit from their products.Originality/value This article dealt with time truncated attribute median control chart for non-normal distributions, namely, the RD and GRD, respectively. The structure of the proposed control chart is developed based on median lifetime of the RD and GRD, respectively.