A Class of Distribution-Free Control Charts

Abstract

Summary. A class of Shewhart‐type distribution‐free control charts is considered. A key advantage of these charts is that the in‐control run length distribution is the same for all continuous process distributions. Exact expressions for the run length distribution and the average run length (ARL) are derived and properties of the charts are studied via evaluations of the run length distribution probabilities and the ARL. Tables are provided for implementation for some typical ARL values and false alarm rates. The charts proposed are preferable from a robustness point of view, have attractive ARL properties and would be particularly useful in situations where one uses a classical Shewhart X‐chart. A numerical illustration is given.

Nonparametric Predictive Inference in Statistical Process Control

“…For both approaches, of course, this probability is only correct under the assumption that the process is in-control. As the actual results of these two approaches are identical, our approach can be used for similar inferences using such precedence probabilities as discussed in more detail by Chakraborti and van del' Laan [2,3,5].…”

“…A different way of predictively comparing two independent samples might also be of interest, Another concept that can be used for statistical process control [5] makes use of so-called pr-ecedence probabilities. Let X(n+k)' for k = 1, ... , m, denote the k-th ordered value of the future observations X n + 1 ,··.…”

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

“…The idea of assuming a training sample was first used by Park and Reynolds [6] to develop distribution-free charts based on the Orban and Wolfe [7] placement statistic. Later, Hackl and Ledolter [8], Willemain and Runger [9], and Chakraborti et al [10] proposed nonparametric charts assuming the availability of a reference sample. Our proposed chart works by taking a random sample (test sample) from the process output at each monitoring stage.…”

A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules

“…In this context, one key problem is the lack of IC robustness of some of the well-known parametric charts (see, e.g. Chakraborti et al (2001Chakraborti et al ( , 2004). This, for example, means that there could be too many false alarms than what is nominally expected and obviously, this could mean considerable loss of time and resources.…”

“…In addition, nonparametric control charts are likely to share the well-known robustness properties of nonparametric tests and confidence intervals and are therefore are expected to be less impacted by outliers. Chakraborti et al (2004) considered a class of Phase II Shewhart-type nonparametric charts based on two order statistics from the reference sample. This is called the (basic) 1-of -1 precedence chart or simply the precedence chart.…”