A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

Abstract

This paper develops a distribution-free (or nonparametric) Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process. The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training) sample of observations taken when the process was operating in-control. The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution. Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar), the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric) continuous probability distributions. The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution. Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output. Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution.

Empirical distribution function as a tool in quality control

“…"Quality control is a procedure or set of procedures intended to ensure that a manufactured product or performed service adheres to a defined set of quality criteria or meets the re-Manuscript received January 25, 2020. ; accepted April 11,2020. Vesna Jevremović, Atif Avdović are with the State University of Novi Pazar, Department of Mathematical Sciences, Novi Pazar, Serbia quirements of the client or customer" [5].…”

An Attribute np Control Chart for Monitoring Mean Life Using Multiple Deferred State Sampling Based on Truncated Life Tests

“…Bakir 31 pointed out that "Realistically, however, when a special cause influences a process, it may cause a shift in more than one parameter (location, scale, skewness, etc.) of the process distribution".…”

Efficiency and losses in mechanical harvesting of soybeans due to the plots format

“…A normal distribution of the data is a pre-requisite of statistical process control and the calculation of process capability indices to more accurately estimate process capability over time (Montgomery, 2004). Bakir (2012) reported that a normal distribution is desirable for performing process capability analysis and for such analysis to be representative. Further information on studies of normality associated with the use of statistical process control can be found in Chakraborti (2006) and Zhou and Tsung (2010).…”