p-Charts: Control Charts for Attributes
Ref: Monty 7e, Section 7.2
defective or non-conforming
effective or conforming
Such binary or Bernoulli sequence data are also called attribute data.
Xij B (1, p) Bernoulli.
Recall E (Xij )
= p, V ar(Xij ) = p(1 p)
Control (p) chart. Plot pi versus i, i = 1,2, . . .
Control lines at p 3 p(1 p)/n (if LCL negative, replace by zero.)
Value of p comes from (a) historical (b
c-Charts: Control Charts for Defects
Ref: Monty 7e Section 7.3
c = Number of defects (or non-conformities) in an item or sample of items.
In control: Model c
Poisson (). Recall E (X ) =
V ar(X ) = .
Control (c-chart). Let ci denote the total number
Ref: Monty 7e, pages 208210, 321.
Serves as an adjunct to c-chart, when defects can be of differing types.
A Pareto chart is simply a bar chart (or frequency histogram) with categories of
defect put in decreasing order of frequency from
Ref: Monty 7e, 210212, 321323
This diagram, along with the Pareto chart, is useful for trouble-shooting. It aids
discovering what defects are most important and nding the causes of these
Because of its appearance, th
PROBABILITY PLOTS: BASIC IDEA
Reference: Monty 7e, Section 3.4 and 8.2.2
a continuous random variable
Proposed cdf F ()
X(1) X(2) . . . X(n) The order statistics
Question: Are the sample data consistent with the proposed
Question : Consider X(i) . Not supposing anything, what is your best guess at
the proportion of future sample observations should have values less than X(i) ?
(i 1 + 1 )/n = (i 1 )/n.
Why: We have observed (i 1) values less than X(i) ; and