1 Comparisons of capabilities of CAS and spreadsheets via the statistical quality control Mihály Klincsik Csaba Sárvári Department of Mathematics Pollack Mihály Faculty of Engineering University of Pécs Hungary

Content2 Content of the lecture  About the Statistical Quality Control course at PMMK  Teaching experiences with Excel through 2 examples  Capability of Maple 10 CAS enhanced by „ProcessControl” package through 2 examples  Special features of the statistical quality control  Comparisons the capabilities of using Excel and/or Maple  Our philosophy

Our philosophy/13 Each mathematical entities can be described by a certain approximation with our tools. The tools are now the Maple, the Excel programs and the brain, the subject is the statistical quality control. If we emphasize or focus to one feature of an entity than we push the others into the background. We can grasp only one particular segment of the mathematical things with our sense at the same time.

Our philosophy/24 When we recognize so many elements of this puzzle after than we have to put this pieces together into a whole unity. This concept is valid not only for learning situation but in research environment, too. We can grasp with the Excel’s tool effectively some elements of this subject, however the other elements can be supported actively with the Maple’s tools. We suggest that these tools are worthy to use together.

About the Statistical Quality Control course at PMMK/1 5 Statistical Methods for Quality Control Acceptance Sampling Total Quality Management studies for Engineering students at PMMK Statistical Process Control by charts course Topic 1 Topic 2 undergraduate students (cca 50 ) graduate students (cca 40 )

About the Statistical Quality Control course at PMMK/2 6 Control charts for groups of data Variable control charts If we can measure Attributes control charts Aim : monitoring the process characteristics over time X- control charts for average R- control charts for range S- control charts for deviation c- charts for counts of defectives p- charts for percent defectives Types of control charts If we can’t measure Control charts are statistical tools that monitor a process and alert us when the process has been disturbed so that it is now out of control. This is a signal to find and correct the cause of the disturbance.

About the Statistical Quality Control course at PMMK/3 7 Acceptance sampling Single sampling plan Aim : monitoring the quality of manufactured items supplied by the manufacturer to consumers in batches by procedures Double sampling plan Sequential Sampling Plan Types of sampling plan We want to decide whether the lot of products should be accepted or rejected on the basis of a sample randomly drawn from the batch.

Special features of the statistical quality control/1 8 All of the concepts are in close connections with the practical life and the processes Mathematical representations Thinking in formulas, symbols and theorems Fixing the concepts and schemes in mind throughout visual effects and experiences ELEMENTS OF THE ABSTARCT AND CONCEPTUAL THINKING Special features of the statistical quality control TRADITONAL ELEMENTS SPECIAL ELEMENTS Belief in the power of the numerical calculations Our decisions have immediate effects on the estimated parameters of the real process Practical representations

Special features of the statistical quality control/2 9 Mathematical representations of the operating characteristic (OC) -curve NumericalGraphicSymbolic Descriptive The OC curve is the primary tool for displaying and investigating the properties of an acceptance sampling plan. This curve plots the probability of accepting the lot (Y-axis) versus the lot fraction or percent defectives (X-axis). Binomial distribution

Special features of the statistical quality control/3 10 Practical representations of the operating characteristic (OC) -curve Practical interpretations When p = 0 there are no defective items in the batch and so the batch is certain to be accepted, thus OC(0) = 1. When p = 1 then all items are defective and so the batch is certain to be rejected, thus OC(1) = 0. When the quality of the batch becomes worse and worse - i.e. p is increasing - then the probability of the acceptance of this batch is decreasing. So OC(p) curve is a monotone decreasing function on p  [0,1].

Special features of the statistical quality control/4 11 Using flow charts to visualize the schemes Single sampling plan with rectifying scheme Accept the batch producer Consumer Select n items = sample d=Defectives ≤ c Inspection of sample Reject the batch Replace any defective items with good ones 100% inspection and rectification Yes No

Teaching experiences using Excel through 2 examples 12 Teaching experiences using Excel through 2 examples Control Charts using Excel spreadsheet Single Sampling Plan using Excel spreadsheet

Capability of Maple 10 CAS enhanced by "Process Control" package through 2 examples 13 Capability of Maple 10 CAS enhanced by „ProcessControl” package through 2 examples Control Charts using Maple Computer Algebra System Single Sampling Plan using Maple Computer Algebra System

Comparison of teaching and learning attitudes using Excel and/or Maple CAS/1 14 EXCEL MAPLE 10 License Well-known? Comparisons the capabilities of using Excel and/or Maple Unlimited Programmable Manageability Limited ASPECTS Can’t Generally the students don’t know the Maple CAS Easily Slightly difficult Own language The students know from the ICT lessons.

Comparison of teaching and learning attitudes using Excel and/or Maple CAS 15 Comparisons the capabilities of using Excel and/or Maple Numerical calculations wide range of functions Some extra features over the Excel facilities Help supports Symbolic capabilities Graphics capabilities Immediate and in Hungarian Easily handle with many auxiliary settings nothing Well equipped Black-box, white-box Not so comfortable as the E Excel Context sensitive and in English Mainly black-box Functions sometimes differ from the traditional EXCEL MAPLE 10 ASPECTS

16 Thank you for your attention!