The performance of the Shewhart sign control chart for finite horizon processes

Abstract

In many manufacturing environments, the production horizon of the same part code between two consecutive set-ups should be limited to a few hours or shifts. When 100 % sampling is not possible, on-line quality control on a quality characteristic should be immediately started by means of a control chart. In this paper, we investigate the statistical performance of a nonparametric (distributionfree) Shewhart Sign (SN) control chart for monitoring the location of a quality characteristic in a production process with a finite horizon and a small number of scheduled inspections. The observations taken from the process are assumed to be continuous random variables. By implementing a SN control chart, any model assumption about the distribution of observations is needless to guarantee a nominal in-control (IC) performance: after each process set-up, this overcomes the important problem of lack of information about the distribution of the observations collected for the quality characteristic to be monitored. An extensive simulation study is conducted to compare the statistical performance of the distribution-free Shewhart SN control chart to the normal theory-based Shewhart Student's t control chart: several types of distributions of observations and different numbers of scheduled inspections are considered to show the advantages related to the implementation of the Shewhart SN control chart. An illustrative example presents the implementation of the Shewhart SN control chart on a real data set collected in a beverage company.

An EWMA sign control chart with varying control limits for finite horizon processes

“…Conversely, when the production horizon is finite, detecting the deviation from nominal ( on‐target ) location is the main goal of practitioners, who also want to compute the false alarm probability and the control chart's ability to detect the presence of an assignable cause by the end of the run. Hence, for the on‐target performance, similarly to Celano et al,() here we consider as a measure of performance the false alarm probability F A P ( I ) of having at least one false alarm signal during the production run. At the design stage of the control chart, a nominal false alarm probability F A P 0 is fixed.…”

“…The performance of these four control charts is also compared with the Shewhart S N control chart proposed by Celano et al Similarly to previous literature (see Graham et al and Celano et al()), the following distributions of observations have been taken into account: Symmetric . Normal N (0,1), Student's t (8); Asymmetric .…”

“…Examples of finite horizon processes include job shop and small lot production: for these processes, the demand‐driven planning forces to the presence of limited inventory and to fix very short due dates. High‐volume production with frequent changeovers occurring every few shifts should also be considered as an example of finite horizon process when the inspection rate is very slow or a few inspections can be scheduled during the production run (see Celano et al). Given the limited number of scheduled inspections, in these processes, the quality practitioner cannot plan the retrospective phase I implementation of the control chart to get reliable estimates of the control limits and then proceed with the phase II implementation of the control chart to monitor the process.…”

“…Control charts for normal observations have been investigated in Celano et al, Gao, and Gu et al to monitor the process location. Very recently, the nonparametric Shewhart sign S N control chart has been studied by Celano et al(): These two papers show the efficiency of the Shewhart S N control chart for the high‐volume and low‐volume production in an FPH process, respectively. This control chart monitors the process location by plotting a sample sign statistic related to the deviation from an in‐control quantile of the process parameter distribution.…”

On‐line monitoring of extreme values of geometric profiles in finite horizon processes

“…On the other hand, the aim of this paper is in investigating the challenges related to the implementation of SPM for the extreme values of geometrical features of the surfaces. We consider processes with finite production horizon; see Celano et a et al and Celano and Castagliola: An FPH process is such that the number of inspections scheduled before it ends should be restricted to a few tens. Job shop and small lot production of customized parts are examples of finite horizon processes.…”