Generalized Control Charts for Non-Normal Data Usingg-and-kDistributions

BayesianX̄control limits for exponentially distributed measurements

“…The credible interval found by using this algorithm satisfies the statement given in Equation (3). It is very similar to the HPD estimation algorithm given by Chen et al [24] (see [24, p. 213] for further details).…”

“…In this manner, we obtain more accurate estimates for the control limits for each sample due to the accumulation of information gathered from the process of interest. The accumulation is the result of the sequential use of Bayes' theorem, which is not considered by Haynes et al [3]. The effect of non-normality and asymmetry in the distribution of control chart statistics is eliminated, all information gathered from the samples are progressively updated by our approach and hence small or large shifts are effectively captured.…”

“…Also, we analyse the performance of the mentioned control limits for exponentially distributed data under various scenarios. It is possible to evaluate and compare the performance of approaches given by Zhang et al [19] and Haynes et al [3] with the performance of the proposed approach. However, this is a huge undertaking.…”

“…The exponential distribution can be considered to be a special case of g-and-k distributions. Thus, the approach of Haynes et al [3] can be used for exponential charts.…”

Control Limits Based on the Narrowest Confidence Interval

“…Another alternative is to transform the non normal distribution to normal distribution and use the 3-sigma limits. For example, Xie et al (2000) and Liu et al (2007) used the double square root transformation for geometric distribution and exponential data, respectively; Chou et al (2005) and Lin and Chou (2005) used the Burr distribution to approximate various non normal distributions, Lin and Chou (2007) pointed out that the variable parameters X chart is more effective than the other adaptive control charts in detecting small process mean shifts under non-normality; Haynes et al (2008) used g-and-k distribution to better capture the true shape of the underlying distribution of the control statistic for non normal data. However, each of these normal approximation methods for non normal data is often influenced by the approximation precision of the adopted transformation, which may has large effect on the performance of the control chart.…”