CLASS PROJECT
THE ENCLOSED PROJECT INCLUDES TWO CASE STUDIES. BOTH CASES
MUST BE COMPLETED FOR FULL CREDIT ON THIS PROJECT. FOR EACH
CASE, YOUR WRITEUP SHOULD INCLUDE A BRIEF SUMMARY OF THE CASE,
A DISCUSSION OF THE TECHNIQUES USED TO SOLVE THE CASE, ANY
COMPUTATIONS AS APPROPRIATE, AND A BRIEF SUMMARY OF RESULTS.
REMEMBER THAT BOTH CASES MUST BE COMPLETED FOR FULL CREDIT!!!!
10 PTS. CASE I – THE BURBANK POTATO COMPANY
THE QUALITY CONTROL MANAGER OF THE BURBANK POTATO COMPANY,
WILLY ARBUCKLE, IS CONCERNED ABOUT ADHERENCE TO WEIGHT REQUIRE-
MENTS OF BAGS OF POTATOES THAT THE COMPANY IS PRODUCING
AND DISTRIBUTING TO SUPERMARKETS. ACCORDING TO COMPANY REGULA-
TIONS, THE WEIGHT OF EACH BAG OF POTATOES SHOULD BE BETWEEN
12.00 AND 19.00 LBS. OF WEIGHT. THE Q.C. MANAGER HAS TAKEN 30
SAMPLES OF 6 BAGS EACH WITH WEIGHTS AS SHOWN AND RECORDED IN THE
TABLE BELOW. THE QUALITY CONTROL MANAGER HAS DECIDED TO DEVELOP
AN X-BAR CHART AND AN R CHART IN ORDER TO DETERMINE IF THE WEIGHT
OF THE BAGS OF POTATOES IS IN CONTROL.
THE Q.C. MANAGER WISHES TO DETERMINE THE FOLLOWING:
_
A) DEVELOP AN X QUALITY CONTROL CHART. PERFORM WHATEVER CALC-
ULATIONS ARE NECESSARY TO DETERMINE THE VALUES PLOTTED IN THE
CHART. FROM YOUR PLOT, DOES THE PROCESS APPEAR TO BE IN
CONTROL? MAKE SURE TO PLOT UCL AND LCL LINES AND PLOT THE
POINTS ON YOUR CHART!!!!!
B) DEVELOP AN R QUALITY CONTROL CHART. FROM YOUR CHART, DOES
THE PROCESS APPEAR TO BE IN CONTROL? MAKE SURE TO PLOT YOUR
UCL AND LCL LINES AND PLOT YOUR POINTS ON YOUR CHART!!!!!!
IN PARTS (A) AND (B) ABOVE, MAKE SURE TO SHOW YOUR CALCLULAT-
IONS FOR UPPER AND LOWER CONTROL LIMITS. USE THE APPROPRIATE
TABLES FROM THE CLASS HANDOUTS IN ORDER TO OBTAIN YOUR LIMITS.
C) USE THE “RUNS ABOVE AND BELOW THE MEDIAN” AND THE “RUNS UP
AND DOWN” TESTS TO DETERMINE WHETHER THERE IS ANY UNDERLYING
PATTERN IN YOUR DATA. SHOW YOUR CALCULATIONS FOR THIS. USE
A TEST WITHIN 3 STANDARD DEVIATIONS.
D) BASED ON YOUR RESULTS IN PART (C) ABOVE, DO YOU BELIEVE
THERE IS THE LIKELIHOOD OF THE PROCESS BEING OUT OF CONTROL
IN THE FUTURE? EXPLAIN YOUR REASONING. (HINT: IF YOU DO
NOT PASS BOTH OF THE RUNS TEST, THERE IS A HIGH LIKELIHOOD
OF THE PROCESS GOING OUT OF CONTROL IN THE NEAR FUTURE!!!!)
OBSERVATION (WT., LB.)
SAMPLE 1 2 3 4 5 6
1 12.43 12.45 12.41 12.44 12.45 12.46
2 12.56 12.56 12.58 12.55 12.58 12.57
3 12.60 12.62 12.63 12.63 12.65 12.67
4 12.35 12.38 12.38 12.39 12.35 12.37
5 12.48 12.48 12.50 12.49 12.46 12.47
6 12.32 12.34 12.35 12.31 12.35 12.36
7 12.51 12.51 12.53 12.56 12.57 12.55
8 12.66 12.64 12.64 12.65 12.65 12.66
9 12.45 12.47 12.47 12.49 12.50 12.46
10 12.46 12.48 12.51 12.51 12.49 12.47
11 12.58 12.58 12.58 12.60 12.57 12.59
12 12.44 12.44 12.46 12.45 12.48 12.44
13 12.56 12.58 12.59 12.56 12.55 12.55
14 12.54 12.53 12.52 12.54 12.54 12.55
15 12.60 12.62 12.61 12.63 12.62 12.61
16 12.63 12.63 12.65 12.65 12.64 12.63
17 13.21 13.44 13.25 13.21 13.12 13.33
18 13.11 13.35 13.52 13.27 13.53 13.41
19 13.64 13.27 13.48 13.66 13.34 13.22
20 13.01 13.44 13.29 13.28 13.26 13.46
21 13.23 13.32 13.20 13.25 13.31 13.23
22 13.11 13.26 13.51 13.27 13.31 13.44
23 14.33 14.01 14.89 14.67 14.55 14.62
24 14.78 14.88 14,38 14,99 14,98 14,90
25 15.01 15.32 15.77 15.26 15.81 15.75
26 15.98 16.00 16.11 16.23 16.21 16.07
27 16.01 15.88 16.34 16.78 16.54 16.38
28 16.66 16.82 16.99 17.04 17.33 17.49
29 17.21 17.25 17.44 17.58 17.18 17.68
30 17.62 17.96 17.82 18.04 18,20 18.32
10 PTS. CASE II – THE ALPHA-ONE CELL PHONE COMPANY RETURNS
THE OPERATIONS MANAGER OF THE ALPHA-ONE CELL PHONE COMPANY
WISHES TO DETERMINE IF THERE HAS BEEN ANY IMPACT OF RETURNS
OF CELL PHONES SINCE THEY HAVE ESTABLISHED A POLICY OF NOT
CHARGING CUSTOMERS A DISCONNECT FEE FOR TERMINATING SERVICE.
THE MANAGER HAS MAINTAINED DATA REGARDING THE NUMBER OF PHONES
RETURNED OVER THE LAST 48 WEEKS. THE MANAGER WISHES TO DETER-
MINE IF THE PROCESS OF PHONE RETURNS IS IN CONTROL. THE DATA
COLLECTED IS AS SHOWN BELOW:
WEEK 1 2 3 4 5 6 7 8
PHONES 12 14 14 16 16 15 11 12
RETURNED
WEEK 9 10 11 12 13 14 15 16
PHONES 13 15 17 17 19 20 17 15
RETURNED
WEEK 17 18 19 20 21 22 23 24
PHONES 14 14 16 19 20 22 18 16
RETURNED
WEEK 25 26 27 28 29 30 31 32
PHONES 22 25 24 27 29 29 33 35
RETURNED
WEEK 33 34 35 36 37 38 39 40
PHONES 29 33 34 34 36 38 37 39
RETURNED
WEEK 41 42 43 44 45 46 47 48
PHONES 38 40 40 42 46 45 49 50
RETURNED
THE QUALITY CONTROL MANAGER FOR OPERATIONS WISHES TO PERFORM
THE FOLLOWING ANALYSES:
A) CONSTRUCT A C-CHART USING THREE(3)-SIGMA LIMITS FOR THE
PROCESS. MAKE SURE TO PLOT YOUR POINTS AND TO INCLUDE THE
UCL AND LCL VALUES ON YOUR CHART. SHOW YOUR CALCULATIONS
FOR THESE VALUES.
B) DOES THE PROCESS APPEAR TO BE IN CONTROL? EXPLAIN.
C) THE Q.C. MANAGER ALSO WISHES TO EXAMINE WHETHER THERE IS
ANY PATTERN IN THE CHART BY DEVELOPING A “RUNS ABOVE AND
BELOW THE MEDIAN” TEST, AND A “RUNS UP-AND-DOWN” TEST.
COMMENT ON YOUR RESULTS FOR THESE!!!!!!!!
D) FROM THE RUNS TESTS, DO YOU BELIEVE THERE IS ANY SIGNIF-
ICANT CHANGE IN PHONES RETURNED OVER TIME? EXPLAIN BRIEFLY.
(HINT: REMEMBER THAT YOU HAVE TO PASS BOTH RUNS TESTS IN
ORDER TO CONCLUDE THAT THERE IS NO SIGNIFICANT PATTERN IN
THE RETURNS DATA!!!!)
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