SUMMARYThis paper proposes a heuristic method of constructingX, cumulative sum and exponentially weighted moving average control charts for skewed populations with weighted standard deviations obtained by decomposing the standard deviation into upper and lower deviations adjusted in accordance with the direction and degree of skewness. These control charts, however, reduce to standard control charts when the underlying distribution is symmetric. Simple formulae are derived to estimate unknown process parameters from means and ranges of subgroups. The false alarm rates of these control charts are compared with those of existing control charts when the underlying distribution is Weibull, gamma, or lognormal. Simulation results show that considerable improvement over the existing methods can be achieved when the underlying distribution is skewed.

SUMMARYThis paper proposes a new method of constructing process capability indices (PCIs) for skewed populations. It is based on a weighted standard deviation method which decomposes the standard deviation of a quality characteristic into upper and lower deviations and adjusts the value of the PCI using decomposed deviations in accordance with the skewness estimated from sample data. For symmetric populations, the proposed PCIs reduce to standard PCIs. The performance of the proposed PCIs is compared with those of standard and other PCIs, and finite sample properties of the estimates are investigated using Monte Carlo simulation. Numerical studies indicate that considerable improvements over existing methods can be achieved by the use of the weighted standard deviation method when the underlying distribution is skewed.

This paper proposes a heuristic method of constructing multivariate T 2 control charts for skewed populations based on 'weighted standard deviations', obtained by decomposing the standard deviation into upper and lower deviations according to the direction and degree of skewness. The proposed method adjusts the variancecovariance matrix of quality characteristics and modifies the ellipsoidal probability density function contour of the multivariate normal distribution to a shape similar to that of the skewed distribution. False alarm rates and out-of-control average run lengths of the proposed control chart are compared with those of the standard control chart for multivariate lognormal, Weibull and gamma distributions, and the results show that considerable improvement over the standard method can be achieved when the distribution is skewed.

This article proposes a heuristic method of constructing multivariate cumulative sum and exponentially weighted moving average control charts for skewed populations based on the weighted standard deviation method which adjusts the variancecovariance matrix of quality characteristics and approximates the probability density function using several multivariate normal distributions. These control charts, however, reduce to the conventional control charts when the underlying distribution is symmetric. In-control and out-of-control average run lengths of the proposed control charts are compared with those of the conventional control charts for multivariate lognormal and Weibull distributions. Simulation results show that considerable improvements over the standard method can be achieved when the underlying distribution is skewed.

Conventional process capability indices (PCIs) are usually determined under the assumption that quality characteristics follow a normal distribution. If a process does not follow a normal distribution, however, conventional PCIs do not provide valid measures of process capability, especially in terms of the number of nonconforming parts. Methods to remedy the shortcoming of the conventional PCIs when the population is skewed can be divided into five categories; to use normalizing transformations like Box–Cox power transformation or Johnson transformation, to fit an empirical distribution or a known three‐ or four‐parameter distribution such as Burr or Pearson distribution to the original data and use the quantiles of the fitted distribution, to modify the standard definition of PCIs in order to increase their robustness to skewness, to construct PCIs with estimate of the process yield, and to develop heuristic methods adequate for skewed distributions. This article provides a compact survey and brief comments on the skewed PCIs.