Statistical control of multiple-stream processes — a literature review

1. Statistical control ofmultiple-stream processes— a literature review Eugenio K. Epprecht PUC-Rio Rio de Janeiro, Brazil ISQC 2013 - Syney

2. multiple-stream processes • processes in which a same type of item is manufactured in several streams of output in parallel • continuous processes in which several measures are taken at a cross section of the product ISQC 2013 - Syney

3. examples Source: Lanning et al. (2002) ISQC 2013 - Syney

4. MSP • literature on this topic: scarce • first literature review on this topic (to my knowledge) • Focus: Industrial applications • Main points/works (stressing essential differences between approaches) • Opportunities for research, challenges and • Other fields for application ISQC 2013 - Syney

5. Classic SPC scheme for MSP: group-charts(Boyd, 1950) recommended in textbooks and guides: Burr (1976); Pyzdek (1992), Wise and Fair (1998), Montgomery (until 3rd edition, 1997) ISQC 2013 - Syney

6. Group-charts (Boyd, 1950) Source: Pyzdek (1992) ISQC 2013 - Syney

7. Boyd (1950) reported : “the group chart for X-bar and R was developed by the British during World War II and was described in ‘A First Guide to Quality Control for Engineers’, a British Ministry of Supply publication compiled by Dr. E. H. Sealy and issued in 1943.” ISQC 2013 - Syney

8. Between 1943 and 1995: • OttandSnee (JQT, 1973) • Nelson’s runs scheme (JQT, 1986) ISQC 2013 - Syney

9. Assumptions(validity conditions for application) • Streams with same distribution; Or it is possible to adjust them in the same mean value, and they have roughly the same variance • No serial correlation; • No cross correlation between streams. Nelson admits the possibility of the existence of cross-correlation, but does not tackle this case: he says that if the streams are 100% correlated, one chart will suffice; and considers then the case where the streams present no correlation (or negligible) Assumptions not realistic in many practical situations ISQC 2013 - Syney

10. Otherlimitations Overall false-alarm rate (multiplicityissue) • Scarcelyconsidered (ifever) in earlyworks Limitedsensitivity, dueto: • Necessarilywidelimits • Veryfewobservations (oftenonlyone) per stream ISQC 2013 - Syney

11. A reasonable model for typical MSPs:two components of variation value of the quality variable at stream i in time t: xi(t) = b(t) + ei(t) where b(“mean level”): common component - may be random or have some dynamics; e :individual component of stream i ei(t) ~ N(0, s2) i.i.d. over t and i,and independent from b ISQC 2013 - Syney

12. Limitations of the classic group chart Large variance requires large limits Reduced sensitivity to shifts in one stream if V(b) is relevant with respect to V(e) ISQC 2013 - Syney

13. Limitation of the classic group chart: example(Mortell & Runger, 1995) ISQC 2013 - Syney

14. Limitations of the classic group chart converse situation: when V(e) is large with respect to V(b): the GCCwill have little sensitivity to causes that affect all streams — at least less sensitivity than a chart on the average of the measurements across all streams (since this one will have tighter limits than the GCC) ISQC 2013 - Syney

15. Recent schemes - using the model xi(t) = b(t) + ei(t) • Mortell & Runger (1995) • Runger, Alt & Montgomery (1996) • Epprecht & Barbosa (2008) Monitoring statistics: For b(t): the average of all streams in time t Chart:according to the dynamics of b(t) ISQC 2013 - Syney

16. Schemes using the model xi(t) = b(t) + ei(t) Monitoring statistics for ei(t): • Mortell & Runger(1995): the range between streams(Rt-chart) • Runger, Alt & Montgomery (1996): the variance between streams(S2-chart) • Epprecht & Barbosa (2008): the differences between each stream and the average over streams(residuals GCC) ISQC 2013 - Syney

17. ISQC 2013 - Syney

18. Other approaches / particular problems: • Amin et al. (1999): MaxMinEWMAchart (largest and smallest observations in each sample) • WludykaandJacobs (2002): groupchart and runs scheme for MS binomial processes • Lanning et al. (2008): MSP“where it is possible to monitor only a fraction of the total streams at a given time”: VSSI chart for the average of all streams (shifts in a single stream or in a very few streams were rare and/or not relevant) ISQC 2013 - Syney

19. Other approaches / particular problems (cont.) • Bothe (2008): capability index (average Cpk) • Liu et al. (2008): multiplegauges in parallel • Xiang and Tsung (2008): multiple-stream model to monitor a multi-stageprocess • Mei (2010): sum (over all streams) of CUSUM statistics of the individual streams. (The individual CUSUM statistics are based on the logarithm of a likelihood ratio statistic). ISQC 2013 - Syney

20. Other approaches / particular problems (cont.) • Epprecht and Barros (2013): real filling process where the stream means differed, wandered, changed from day to day, were very difficult to adjust, and production runs were too short to enable good estimation of the parameters of the individual streams • Jirasettapong and Rojanarowan (2011):selection of the appropriatecontrolcharts for monitoring a MSP ISQC 2013 - Syney

21. Perspectives: other applications, open issues, challenges and opportunitiesfor research Other applications • Similarity between MSPs and the “large number of multiple streams of data” used in health-related surveillance, for example “data available over time on a number of different subregions, hospitals or physicians” (Woodall, 2000) • ... underlying assumptions of the models and methods for industrial MSPs “may be too restrictive for these methods to be applied directly to health-relatedmonitoring.” • “...it can be a challenge to control the rate of false alarms and yet retain power to detect meaningful outbreaks.” ISQC 2013 - Syney

22. Perspectives: other applications, open issues, challenges and opportunities for research (cont.) Open issues and challenges • Some processes may have hundreds of streams  how to control the false-alarm rate while keeping enough detection power?? • Real multiple-stream processes can be very ill-behaved. Example: I have seen a plant with six 20-stream filling processes in which the stream levels had different means and variances and could not be adjusted separately (one single pump and 20 hoses). For many real cases with particular twists like this one, it happens that no previous solution in the literature is applicable. Developing methods for such specific real cases is a need. ISQC 2013 - Syney

23. Perspectives: other applications, open issues, challenges and opportunities for research (cont.) Characterizing the process in order to select the appropriate monitoring scheme (or adapt one, or develop a new one), according to: dynamic behaviour of the process over time, degree of cross-correlation between streams, ratio between the variabilities of the individual streams and of the common component, type and size of shifts that are likely and/or relevant to detect, ease or difficulty to adjust all streams in the same target, process capability, on the number of streams, feasibility of taking samples of more than one observation per stream at each sampling time (or even the feasibility of taking one observation of every stream at each sampling time!), length oftheproductionruns, etc... This may not be trivial for the average practitioner in industry.  A methodological guide for such an analysis can be a very useful contribution. ISQC 2013 - Syney

24. Perspectives: other applications, open issues, challenges and opportunities for research (cont.) • Phase I analysis • etc., etc... ISQC 2013 - Syney