# COMPARATIVE STATISTICAL ANALYSIS OF SELECTED CONTROL CHARTS FOR HIGHLY CAPABLE PROCESSES

## Ekonomika a management

### COMPARATIVE STATISTICAL ANALYSIS OF SELECTED CONTROL CHARTS FOR HIGHLY CAPABLE PROCESSES

The statistical process control (SPC) is widely used in industry. Its aim is to achieve proces stability and improve capability through the reduction of variability and it is included for example in the Six Sigma or Lean Six Sigma methodologies. The control of attribute data represents a considerable part of it. Until recently, the same approach was used to monitor variables or attributes data. In this approach, subgroups of items are taken from a process and sample characteristics are plotted in a control chart to see whether their variation is only random or whether it is affected by an assignable cause. The presence of such cause is indicated by exceeding the control limits that are based on the sample characteristic distribution.
Jméno a příjmení autora:

#### Eva Jarošová, Darja Noskievičová

Rok:
2019
Ročník:
22
Číslo:
2
Klíčová slova:
CCC chart, CCC-r chart, CCC-CUSUM chart, ANOS, zero-state scenario, fixed shift steady-state scenario, random shift steady-state scenario, simulation
JEL klasifikace:
DOI (& full text):
Odkazy:
Anotace:
When a high-quality process is to be controlled by 100% inspection and yes-no decision is employed, several types of charts come into account, e.g. CCC, CCC-r or geometric CUSUM (CCC-CUSUM). The aim…více
When a high-quality process is to be controlled by 100% inspection and yes-no decision is employed, several types of charts come into account, e.g. CCC, CCC-r or geometric CUSUM (CCC-CUSUM). The aim of the paper is to examine performance of these charts so that a suitable one can be chosen for a given process. The charts are compared according to the quickness with which the upward shift in the fraction of nonconforming items is detected. The average number of observations to signal (ANOS) instead of the usual average run length (ARL) is determined. While ANOS for CCC or CCC-r charts can be easily calculated based on a geometric or a negative binomial distribution, its computation is quite difficult in the case of CCC-CUSUM chart. The corrected diffusion (CD) approximation was used to determine ANOS and the results were verified by Monte Carlo simulation. Zero-state and steady-state (both fixed-shift and random-shift model) analyses were performed to take different scenarios of the process shift occurrence into account. CCC-3 or CCC-2 and CCC-CUSUM charts were compared. The order r for CCC-r chart was chosen as an optimal value for the given process based on the semi-economic model suggested in Brodecká (2013). Our study revealed that for in-control p0 equal to 0.0002 the CCC-CUSUM chart performs best especially for shifts around the pre-specified out-of-control fraction nonconforming. The CCC-r chart may be comparable or even better in detecting larger shifts. The results of the comparative study were utilized for the choice of the most suitable and best performing control chart to control the high-yield process producing ERG (Exhaust Gas Recirculation) sensors. Comparisons of CCC-r and CCC-CUSUM charts can be found elsewhere in literature, but conclusions seem to be rather inconsistent. To our best knowledge no study dealing with such small in-control fraction nonconforming together with the low risk of false alarm has been published yet. The choice of CUSUM’s parameters and consequent values of ANOS can help practitioners who need to control high-quality processes.
Sekce:
Ekonomika a management

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