Thesis (MComm)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Statistical process control (SPC) plays a very important role in monitoring and improving
industrial processes to ensure that products produced or shipped to the customer meet the
required specifications. The main tool that is used in SPC is the statistical control chart. The
traditional way of statistical control chart design assumed that a process is described by a
single quality characteristic. However, according to Montgomery and Klatt (1972) industrial
processes and products can have more than one quality characteristic and their joint effect
describes product quality. Process monitoring in which several related variables are of
interest is referred to as multivariate statistical process control (MSPC). The most vital and
commonly used tool in MSPC is the statistical control chart as in the case of the SPC. The
design of a control chart requires the user to select three parameters which are: sample size,
n , sampling interval, h and control limits, k.Several authors have developed control charts
based on more than one quality characteristic, among them was Hotelling (1947) who
pioneered the use of the multivariate process control techniques through the development of a
2 T -control chart which is well known as Hotelling 2 T -control chart.
Since the introduction of the control chart technique, the most common and widely used
method of control chart design was the statistical design. However, according to Montgomery
(2005), the design of control has economic implications. There are costs that are incurred
during the design of a control chart and these are: costs of sampling and testing, costs
associated with investigating an out-of-control signal and possible correction of any
assignable cause found, costs associated with the production of nonconforming products, etc.
The paper is about giving an overview of the different methods or techniques that have been
employed to develop the different economic statistical models for MSPC.
The first multivariate economic model presented in this paper is the economic design of the
Hotelling‟s 2 T -control chart to maintain current control of a process developed by
Montgomery and Klatt (1972). This is followed by the work done by Kapur and Chao (1996)
in which the concept of creating a specification region for the multiple quality characteristics
together with the use of a multivariate quality loss function is implemented to minimize total
loss to both the producer and the customer. Another approach by Chou et al (2002) is also
presented in which a procedure is developed that simultaneously monitor the process mean
and covariance matrix through the use of a quality loss function. The procedure is based on the test statistic 2ln L and the cost model is based on Montgomery and Klatt (1972) as well
as Kapur and Chao‟s (1996) ideas. One example of the use of the variable sample size
technique on the economic and economic statistical design of the control chart will also be
presented. Specifically, an economic and economic statistical design of the 2 T -control chart
with two adaptive sample sizes (Farazet al, 2010) will be presented. Farazet al (2010)
developed a cost model of a variable sampling size 2 T -control chart for the economic and
economic statistical design using Lorenzen and Vance‟s (1986) model.
There are several other approaches to the multivariate economic statistical process control
(MESPC) problem, but in this project the focus is on the cases based on the phase II stadium
of the process where the mean vector, and the covariance matrix, have been fairly well
established and can be taken as known, but both are subject to assignable causes. This latter
aspect is often ignored by researchers. Nevertheless, the article by Farazet al (2010) is
included to give more insight into how more sophisticated approaches may fit in with
MESPC, even if the mean vector, only may be subject to assignable cause.
Keywords: control chart; statistical process control; multivariate statistical process control;
multivariate economic statistical process control; multivariate control chart; loss function. / AFRIKAANSE OPSOMMING: Statistiese proses kontrole (SPK) speel 'n baie belangrike rol in die monitering en
verbetering van industriële prosesse om te verseker dat produkte wat vervaardig word, of na
kliënte versend word wel aan die vereiste voorwaardes voldoen. Die vernaamste tegniek wat
in SPK gebruik word, is die statistiese kontrolekaart. Die tradisionele wyse waarop statistiese
kontrolekaarte ontwerp is, aanvaar dat ‟n proses deur slegs 'n enkele kwaliteitsveranderlike
beskryf word. Montgomery and Klatt (1972) beweer egter dat industriële prosesse en
produkte meer as een kwaliteitseienskap kan hê en dat hulle gesamentlik die kwaliteit van 'n
produk kan beskryf. Proses monitering waarin verskeie verwante veranderlikes van belang
mag wees, staan as meerveranderlike statistiese proses kontrole (MSPK) bekend. Die mees
belangrike en algemene tegniek wat in MSPK gebruik word, is ewe eens die statistiese
kontrolekaart soos dit die geval is by SPK. Die ontwerp van 'n kontrolekaart vereis van die
gebruiker om drie parameters te kies wat soos volg is: steekproefgrootte, n , tussensteekproefinterval,
h en kontrolegrense, k . Verskeie skrywers het kontrolekaarte ontwikkel
wat op meer as een kwaliteitseienskap gebaseer is, waaronder Hotelling wat die gebruik van
meerveranderlike proses kontrole tegnieke ingelei het met die ontwikkeling van die
T2 -kontrolekaart wat algemeen bekend is as Hotelling se 2 T -kontrolekaart (Hotelling,
1947).
Sedert die ingebruikneming van die kontrolekaart tegniek is die statistiese ontwerp daarvan
die mees algemene benadering en is dit ook in daardie formaat gebruik. Nietemin, volgens
Montgomery and Klatt (1972) en Montgomery (2005), het die ontwerp van die kontrolekaart
ook ekonomiese implikasies. Daar is kostes betrokke by die ontwerp van die kontrolekaart
en daar is ook die kostes t.o.v. steekproefneming en toetsing, kostes geassosieer met die
ondersoek van 'n buite-kontrole-sein, en moontlike herstel indien enige moontlike korreksie
van so 'n buite-kontrole-sein gevind word, kostes geassosieer met die produksie van niekonforme
produkte, ens. In die eenveranderlike geval is die hantering van die ekonomiese
eienskappe al in diepte ondersoek. Hierdie werkstuk gee 'n oorsig oor sommige van die
verskillende metodes of tegnieke wat al daargestel is t.o.v. verskillende ekonomiese
statistiese modelle vir MSPK. In die besonder word aandag gegee aan die gevalle waar die
vektor van gemiddeldes sowel as die kovariansiematriks onderhewig is aan potensiële
verskuiwings, in teenstelling met 'n neiging om slegs na die vektor van gemiddeldes in
isolasie te kyk synde onderhewig aan moontlike verskuiwings te wees.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/71679 |
| Date | 12 1900 |
| Creators | Mudavanhu, Precious |
| Contributors | Van Deventer, P. J. U., Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 76 p. |
| Rights | Stellenbosch University |
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