MA30118: Management Statistics


Timetable:

lectures are Monday 14:15 (5W2.4) and Tuesday 10:15 (5W2.4).

problem classes are Monday 15:15

Lecturer:

Simon Shaw; s.c.shaw at maths.bath.ac.uk

Credits:

6

Level:

Honours

Semester:

2

Assessment:

EX60CW40

Requisites:

Before taking this unit you must take MA20097 or take MA20035 or take EC20019

Aims & Learning Objectives:
This unit is designed primarily for DBA Final Year students who have taken the First and Second Year management statistics units but is also available for Final Year Statistics students from the Department of Mathematical Sciences. Well qualified students from the IMML course would also be considered. It introduces three statistical topics which are particularly relevant to Management Science, namely quality control, forecasting and decision theory.
Aims: To introduce some statistical topics which are particularly relevant to Management Science.
Objectives: On completing the unit, students should be able to implement some quality control procedures, and some univariate forecasting procedures. They should also understand the ideas of decision theory.
Content:
Introduction to decision analysis for discrete events: Revision of Bayes' Theorem, admissibility, Bayes' decisions, minimax. Decision trees, expected value of perfect information.Utility, subjective probability and its measurement.
Quality Control: Acceptance sampling, single and double schemes, SPRT applied to sequential scheme. Process control, Shewhart charts for mean and range, operating characteristics, ideas of cusum charts.
Practical
forecasting: Time plot. Trend-and-seasonalmodels. Exponential smoothing. Holt's linear trend model and Holt-Winters seasonal forecasting. Autoregressive models. Box-Jenkins ARIMA forecasting.


Introduction to decision analysis for discrete events

We won't follow a book as such but useful references include:

  1. D.R. Anderson, Sweeney, D.J. and Williams, T.A., An Introduction to Management Science Quantitative Approaches to Decision Making, Seventh Edition, 1994. See Chapter 14 pp.593-645 512.747.9 AND
  2. D.A. Lind, Marchal, W.G. and Mason, R.D., Statistical techniques in Business and Economics, Twelfth Edition, 2004. See Chapter 20 pp.726-744 512.760.33 LIN
  3. R.I. Levin and Rubin, D.S., Statistics for Management, Seventh Edition, 1998. See Chapter 17 pp.969-1026 512.760.33 LEV

The interested student may find more mathematical treatments (and more breadth than this course) at the shelfmark 512.794. Two such are:


  1. D.V. Lindley, Making Decisions, Second Edition, 1985. 512.794 LIN
  2. S. French, Decision theory: an introduction to the mathematics of rationality, 1986. 512.794 FRE


2005/06 schedule:

Lecture 1 (6 Feb 06): 1 Introduction: 1.1 Actions, 1.2 States of nature, 1.3 Worked example: Duff beer, 1.4 Payoff.
Lecture 2 (7 Feb 06): 1.5 Admissibility, 1.6 Minimax regret, 2 Decision making with probabilities: 2.1 Maximising expected monetary value.
Lecture 3 (13 Feb 06): 2.2 Decision trees, 2.3 Value of perfect information.
Lecture 4 (14 Feb 06): 2.4 A brief review of some probability theory. 2.5 An example with sequential decisions.

Lecture 5 (20 Feb 06): 3 Decision analysis with sample information: 3.1 Calculating the expected payoff with sample information.
Lecture 6 (21 Feb 06): 3.2 The value of sample information, 3.3 Efficiency of sample information. 4 Utility: 4.1 The St. Petersburg paradox.
Lecture 7 (27 Feb 06): 4.2 Preferences, 4.3 Gambles, 4.4 Utility.
Lecture 8 (28 Feb 06): 4.5 General method for constructing utility function, 4.6 Worked example using utilities, 4.7 Uniqueness of utility.
Lecture notes: pdf or postscript (up to, and including, Lecture 8)

Homework -

Question Sheet One: pdf or postscript

Solution Sheet One: pdf or postscript

Question Sheet Two: pdf or postscript

Solution Sheet Two:pdf or postscript


Quality Control (Acceptance Sampling and Process Control)

We won't follow a book as such but the library shelfmark 512.766 contains plenty of examples. Books I consulted include:

  1. G.B. Wetherill, Sampling Inspection and Quality Control, Second Edition, 1977. Acceptance Sampling is covered in Chapter 2 and Chapter 3 discusses Control Charts. 512.766 WET
  2. D.C. Montgomery, Introduction to Statistical Quality Control, Fourth Edition, 2001. 512.766 MON
  3. R.I. Levin and Rubin, D.S., Statistics for Management, Seventh Edition, 1998. See Chapter 10 pp.511-565 512.760.33 LEV


2005/06 schedule:

Lecture 9 (6 Mar 06): Introduction to Acceptance Sampling.

Lecture 10 (7 Mar 06): Single sampling schemes, operating characteristic (OC) curve, AQL and producer's risk.

Lecture 11 (13 Mar 06): LTPD and consumer's risk, worked example of calculating single sampling scheme.

Lecture 12 (14 Mar 06): Rectifying schemes, average outgoing quality (AOQ), average outgoing quality limit (AOQL), double sampling schemes, construction of the OC-curve for double sampling.

Lecture 13 (20 Mar 06): Worked example of construction of the OC-curve for double sampling, average sample number (ASN), sequential probability ratio test (SPRT).

Lecture 14 (21 Mar 06): Continuation rule in the SPRT, worked example of construction of the continuation rule. Introduction to Process Control and its objectives.

Lecture 15 (27 Mar 06): Introduction to Process Control and its objectives. Description of control chart and general model, mean and range charts.

Lecture 16 (28 Mar 06): mean and range charts when and σ are unknown, worked example of construction of mean and range chart in this case, interpretation of control charts.

Lecture notes: pdf or postscript (Lectures 9-16)
Homework -

Question Sheet Three: pdf or postscript

Solution Sheet Three: pdf or postscript

Question Sheet Four: pdf or postscript Solution Sheet Four: pdf or postscript


Forecasting

2005/06 schedule:

Lecture 17 (24 Apr 06): Introduction, time series models. Components of a time series: trend, seasonality, cyclical variation, irregular variation

Lecture 18 (25 Apr 06): Exponential smoothing, worked example of forecasting using exponential smoothing (Handout: pdf or postscript).

Lecture 19 (2 May 06): Criterion for determining the smoothing constant α, mean square deviation (MSD)

Lecture 20 (8 May 06): Holt's linear trend method, Holt-Winter's multiplicative model.

Lecture 21 (8 May 06): Introduction to Box-Jenkins methodology, autoregressive models of order p, AR(p), moving average models of order q, MA(q), mixture of autoregressive and moving average models, ARMA(p, q).

Lecture 22 (9 May 06): Achieving stationarity through differencing, autoregressive integrated moving average models, ARIMA(p, d, q), forecasting with ARIMA(p, d, q) models with worked example.

Lecture notes: pdf or postscript (Lectures 17-22). These notes include a brief mention of Box-Jenkins model identification via the autocorrelation function (ACF) and partial autocorrelation function (PACF). This is for interest only and will not be examined.
Homework -

Question Sheet Five: pdf or postscript

Solution Sheet Five: pdf or postscript


Coursework:
        2003/04 assignment: pdf or postscript
        2004/05 assignment: pdf or postscript
        2005/06 assignment: pdf or postscript The journal article is available here and the data set here (text file) or here (excel file).
        2005/06 answers: pdf or postscript

Last revision:
09/05/06

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