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12 34 56178901111213 ChE376K Process Evaluation and Quality Control
' Project
Due on 8th Dec 2007 Evening 5 PM Instruction: Work in groups of three. Please select your group before
29th Nov, and mail the list to me. I will assign a data number that you can
use to download the particular data you have to use. Please do not share your
data and Excel ﬁle with your friend. Please write or type your answer and
conclusion separately. Please upload the executable EXCEL ﬁles or JUMP
ﬁles in blackboard.  1. (60% Project) In class we talked in detail about EWMA control chart
to detect small shifts in process mean and when we have small rational
subgroup (usually when n = 1). Another method that can be used when n = 1 and to detect small shift in process mean is cumulative Sum Control Chart (CUSUM). (Read p681687 in your text book).
The data can be downloaded from blackboard. (a) Is there a serious problem with the autocorrelation in these data?
Plot both scattered plot and autocorrelation function plot. Is the
process stationary? (b) set up a control chart for individuals with a moving range used to
estimate process variability. what conclusion can you draw from
this chart? ‘ (c) Design a CUSUM control scheme for this process, assuming that
the observations are uncorrelated. How does the CUSUM per—
form? (d) Set up an EWMA control chart with A = 0.15 for this process.
How does this chart perform? (e) Set up a moving average control chart with w = 6 (6 day average).
How does this chart perform? (f) Set up a moving centerline EWMA control chart? How does this
perform? (g) Select an ARIMA model to represent the data. Find the param
eters of ARIMA model. Give reasons for your choice. (h) Repeat part .(b), (c), (d), (e), and (f) using the'uncorrelated
residues. . 2. (40 % Project) In this course we learned about Shewhart Control
Charts for process mean. Sometimes instead of process mean, we would
like to compare the process means of current batch with a standard ref
erence batch. The reference batch consists of the same product that are produced under controlled process conditions except possibly being
inﬂuenced by uncontrolled factors. ” Difference Control Charts” are de—
veloped to monitor the difference between the reference mean ,LLRef and the current production lot mean your (a) Assume that URef and do,“ are known. ii.
iii.
iv. v. 1. Calculate central line, UCL, and LCL for a Difference Control
Chart. ' How would you calculate typeI error.
How would you calculate type—II error.
Construct an OC—curve plot.
Construct an ARL curve plot. (b) Assume that variance is not known but (aﬁef = can). Repeat the
calculations as in the previous part. ChE37 6K Process Evaluation and Quality Control
. Homework9
Due on 27th Nov 2007 Evening 5 PM 1. Consider the EWMA statistic
2;» = A331 + (1 — A)zi_1 (a) What are the center line and control limits for the EWMA and
Moving Average control chart for rational subgroup of size n = 1? (b) How will you modify these limits when considering a rational sub—
group of size n > 1? (c) Show that if
2 (w+1) for the EWMA control chart, then this control chart is equivalent
to a wperiod moving average control chart in the sense that the
control limits are identical in the steady state. (d) The current data mi in EWMA statistic is weighted by a factor A.
Compute the weights used for sci1, $¢_2, and $i_3. /\= 2. A shewhart 50 chart has center line at 10 with U CL = 16 and LCL = 4.
Suppose you wish to supplement this chart with an EWMA control
chart using A = 0.1 and the same control limit width in a—units as
employed on the 53 chart. What are the values of the steady state
upper and lower control limits on the EWMA Chart? 3. An EWMA control chart uses A :04. How wide will the limits be on
the Shewhart control chart, expressed as a multiple of the width of the
steady—state EWMA limits? 4. Consider the AR(1) and AR(2) processes xt = + 0.6$t_1 + 6: 0'; = 4
mt = + V0.8:L't_1 — 0.25375—2 'l— 613 0'? = 1 (a) Are these processes stationary?
(b) Graph the theoretical autocorrelation function. (0) If $45 = 12, would you expect $46 to be greater than or less than
the mean of the series? ...
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 Spring '08
 Dunia
 Control Chart, average control chart, ewma control chart

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