Robust quality controlling: SPC with box plots and runs test

Abstract

PurposeThe purpose of this paper is to propose a methodology that may assist quality professionals in assessing process variation with a combination of tools based on simple robust statistics. The technique targets alternative way of screening and detection of common and special causes in individuals' control charts (ICC).Design/methodology/approachThe technique is using the classical box plot to detect and filter out outliers attributed to special causes. Then, the runs test is used to partition the data streak at points where the p‐value exceeds an assigned critical value. The transition between partitions is where the onset of a common cause is suspected.FindingsThe approach presented is supplemented with a case study from foundry operations in large‐scale can‐making operations. It is demonstrated how the magnesium content of an aluminium alloy is trimmed against special causes and then the location of the common causes is identified in a step‐by‐step fashion.Research limitations/implicationsThe proposed method is useful when the collected data do not seem to comply with a known reference distribution. Since it is rare that an initial monitoring of a process will abide to normality, this technique saves time in recycling control charting which point often to misleading assignable causes. This is because the outliers are identified through the box plot one and out.Practical implicationsThe technique identifies and eliminates quickly the off‐shoot values that tend to cause major instability in a process. Moreover, the onset for non‐assignable data points is detected in an expedient fashion without the need to remodel each time the inspected data series or to test against a score of multifarious test rules. The ingredients of the method have been well researched in the past, therefore, they may be implemented immediately without a further need to prove their worth.Originality/valueThe method mixes up two distinctive robust tools in a unique manner to aid quality monitoring to become fortified against data model inconsistencies. The technique is suitable for controlling processes that generate numerical readings. As such, the approach is projected to be useful for industrial as well as service operations.

Robust process capability performance

“…Cp, Cpk, Cpm and Cpmk for individual observations which are collected in the form of a continuous data streak. For the proper estimation of each of the four process capability indicators, it is instrumental to have initially the examined time series pretreated with box plots and runs test for individuals SPC as prescribed in Besseris (2013). Therefore, special causes (extremes) are robustly identified and judiciously eliminated from any further consideration in the investigated data sequence.…”

“…In Equations (5-8), USL and LSL are the upper and lower specification limits of the measured characteristic. Additionally, M i and IQR i are the median and interquartile range estimations (Besseris, 2013). M i and IQR i are evaluated in turn within a given, ith,…”

“…Interpreting a chemical content time series with the new PCIs We will examine the example published in Besseris (2013) which regards the probing of a time series of the magnesium content in a trendy aluminum can-making componentthe body structure of a beverage can. Chemical content stability is a very crucial issue because it affects the subsequent forming abilities of the alloyed product, thus influencing concurrently several terminal quality characteristics.…”

“…The technique should be functional even before observing any explicit evidence for normal control in an investigated time series. Our recommendation hinges upon the recent non-parametric SPC analysis for individuals in partitioned groups as it was described in Besseris (2013).…”

A regression spline control chart for monitoring characteristics exhibiting nonlinear profile over time

“…Control charts are traditionally used to ensure the stability of the processes (Singh and Prajapati, 2013;Besseris, 2013). The core logic of control chart is that if the characteristic under study is normally distributed with a mean µ and standard deviation σ, then the values of the characteristic will most certainly lie between µ − 3σ to µ + 3σ.…”