Probability-type, Shewhart-type and EWMA control charts for individual observations from the two-parameter Lindley distribution

Lindley distribution is a continuous distribution with various applications some of which are in medicine, genetics, epidemiology, biology, finance and actuarial sciences, ecology, meteorology, sociology, demography, agriculture, hydrology, geosciences, reliability and engineering, life testing and survival analysis, airborne systems and communications, environmental studies and modeling and describing of human mistakes, strikes, accidents, behavioural and emotional or IQ test scores and waiting times of customers in queues until service, etc. Due to its variety of applications, it appears to be important that control charts for detected shifts in a process should be constructed under the assumption that the quality characteristic of interest follows a Lindley-related distribution. Here, we construct probability-type, Shewhart-type and EWMA control charts (and deal with the optimal choice of its parameters) for individual observations from the two-parameter Lindley distribution, investigate and compare their performance and illustrate them using examples with both simulated and real data. The whole analysis reveals the superiority of using skewness correction for the construction of the control charts against not using it.