Lecture #13. Prof. John W. Sutherland. Sept. 26, 2005
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1 Lecture #13 Prof. John W. Sutherland Sept. 26, 2005
2 Example Blood & Gore, a Halloween gift store, claims that the store revenue averages a $100k/mo. with a std. dev. of $20k. Monthly revenue is normally distributed. The IRS (Internal Revenue Service) wants to check the claim. Part 1: The IRS randomly selects four months of data -- sample mean revenue calculated to be $120k. Assuming a risk level of α = 0.05, evaluate the claim. Part 2: Want to find upper and lower rejection limits to automate the hypothesis testing for a single X. Use α=0.05. Find the values for X L and X U.
3 Example #3 Part 3: Draw the graph for β risk.
4 Chapter #4 The origins and nature of variability Process evolution over time Shewhart s concept of statistical control Managing variability using control charts The process of statistical process control
5 Origin and Nature of Variability We focus on variation in product function Outer Noise - external sources or environmental effects Inner Noise - internal changes (wear, aging, etc.) Variational Noise: uncertainties due to manufacturing Consider a football... Consider a baseball bat...
6 Nominal Value Mfg Process Prod. Use Prod. use over time
7 Manufacturing/Process Variation Faults Local faults System faults Special causes Common causes Sporadic problems Chronic problems Assignable causes Chance causes Examples Action Correctable locally Requires a system change
8 Summary - Variation Understanding origin of variation is key to knowing what action to take and determining who is responsible Quality - loss due to functional variation. Functional variation: manufacturing variation + inner noise + outer noise SPC can address manufacturing variation Robust design can address all sources of functional variation
9 Process as a Statistical Distn. Process 11 AM AM AM Statistical Model ??
10 Process Behavior over Time time The behavior of the process as a function of time - this is a big piece of the puzzle
11 Changes in Process Behavior 8am 9am 10am 11am 12n 1pm 2pm 8am 9am 10am 11am 12n 1pm 2pm 8am 9am 10am 11am 12n 1pm 2pm
12 Changes in Mean & Variability
13 Summary - Evolution of Process Behavior Data collected over time may be used to develop a statistical model for the process -- assumes process is subject to only common causes Process mean and variability may change over time -- indicates a lack of process stability, inconsistency, "out of control", not predictable Track process behavior (periodic sampling) -- detect changes in mean / variability
14 Shewhart s View of SPC Shewhart s book - Economic Control of Quality of Manufactured Product (1931) - preface establishes the principles of SPC 1. Fundamental focus is on the process: "ways and means of satisfying human wants." 2. Overarching objective - economic process operation: "Reduce everything possible to routines requiring a minimum amount of effort."
15 3. Normal process operation - behavior w/in predictable limits: "It has been found possible to set up limits within which the results of routine efforts must lie if they are to be economical." 4. Deviations outside the limits signal presence of problems that are jeopardizing economic success: "Deviations in the results of a routine process outside such limits indicate that the routine has broken down and will no longer be economical." 5. Deviations outside the limits - find root cause of the trouble in the process and remove it: "The routine has broken down and will no longer be economical until the cause of trouble is removed."
16 Comments No mention of the product or conformance of the product to specifications. A controlled process is one where, based on experience, we can predict (within limits) future behavior. Special causes are sources of waste/inefficiency When a process is not in control (i.e., special causes present), it is no longer operating routinely/ predictably, economic success is jeopardized.
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