Studies On X (bar)- Control Chart With Pareto In-Control Times for Non Normal Variates

In this paper we develop and analyse economic statistical design of X (bar) control chart with the assumption that the sample average of the quality characteristic (follows a Johnson distribution and the process in-control times follow Pareto distribution. The Johnson distribution is generally taken for all types of skewed and kurtic variables. Here, the Pareto distribution is chosen since in many production processes at places like Fertilisers, chemicals, etc., the in-control times are having long upper tail and suits to the Pareto distribution. The expected cost per a unit time is derived with the use of the cost model developed for the X (bar) control chart. Minimizing the expected cost per a unit time, the optimal design parameters like sample size and the time interval between two successive samples are derived for given Type I and Type II errors associated with the control chart. The sensitivity of the model with respect to the parameters and costs are also studied. This design is extended to the case when the time to search for an assignable cause and time to repair are also random and follow a Weibull distribution. The effect of randomness on these times is also investigated.