The manager of a retail sales branch of a brokerage office is concerned with the number of undesirable trades made by

Question

The manager of a retail sales branch of a brokerage office is concerned with the number of undesirable trades made by the sales staff. A trade is considered undesirable if there is an error on the trade ticket. Trades that are in error must to be cancelled and resubmitted. The cost of correcting errors is billed to the brokerage. In studying the problem, the manager wants to know whether the proportion of undesirable trades is in a state of statistical control so he can plan the next step in a quality improvement process. Data are collected for a 30-day period and present in the excel sheet. Construct an appropriate control chart for these data. Is the process in a state of statistical control? If not, on which days is it out of control? Day Undesirable Trades Total Trades 1 2 74 2 12 85 3 13 114 4 33 136 5 5 97 6 20 115 7 17 108 8 10 76 9 8 69 10 18 98 11 3 104 12 12 98 13 15 105 14 6 98 15 21 204 16 3 54 17 12 74 18 11 103 19 11 100 20 14 88 21 4 58 22 10 69 23 19 135 24 1 67 25 11

Help In Homework · Accepted Answer

(a) Day Undesirable Trades Total Trades proportion of Undesirable trade(p) 1 2 74 0.027 2 12 85 0.141 3 13 114 0.114 4 33 136 0.243 5 5 97 0.052 6 20 115 0.174 7 17 108 0.157 8 10 76 0.132 9 8 69 0.116 10 18 98 0.184 11 3 104 0.029 12 12 98 0.122 13 15 105 0.143 14 6 98 0.061 15 21 204 0.103 16 3 54 0.056 17 12 74 0.162 18 11 103 0.107 19 11 100 0.110 20 14 88 0.159 21 4 58 0.069 22 10 69 0.145 23 19 135 0.141 24 1 67 0.015 25 11 77 0.143 26 12 88 0.136 27 4 66 0.061 28 11 72 0.153 29 13 118 0.110 30 15 138 0.109 346 2888 pbar = Total undiserable trade/ Total no of trade = 346/2888 =0.119 3 sigma Control chart UCL = pbar + 3 Sqroot {pbar (1-pbar)/n} (n=30) UCL =0.119 + 3 Sqroot {0.119(1-0.119)/30}=0.119 + 3 Sqroot{0.119*0.881/30}=0.119+3Sqroot(0.0035} UCL=0.119+3*0.059=0.119+0.177=0.296 LCL = pbar - 3 Sqroot {pbar (1-pbar)/n} (n=30) LCL =0.119 - 3 Sqroot {0.119(1-0.119)/30}=0.119 - 3 Sqroot{0.119*0.881/30}=0.119-3Sqroot(0.0035} LCL=0.119-3*0.059=0.119-0.177= -0.058 If LCL is negative , it should be considered as 0 . LCL =0 please see the attached file for the complete solution.

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The manager of a retail sales branch of a brokerage office is concerned with the number of undesirable trades made by the sales staff

Expert Solution

Archived Solution

Day	Undesirable Trades	Total Trades
1	2	74
2	12	85
3	13	114
4	33	136
5	5	97
6	20	115
7	17	108
8	10	76
9	8	69
10	18	98
11	3	104
12	12	98
13	15	105
14	6	98
15	21	204
16	3	54
17	12	74
18	11	103
19	11	100
20	14	88
21	4	58
22	10	69
23	19	135
24	1	67
25	11	77
26	12	88
27	4	66
28	11	72
29	13	118
30	15	138

Day	Undesirable Trades	Total Trades	proportion of Undesirable trade(p)
1	2	74	0.027
2	12	85	0.141
3	13	114	0.114
4	33	136	0.243
5	5	97	0.052
6	20	115	0.174
7	17	108	0.157
8	10	76	0.132
9	8	69	0.116
10	18	98	0.184
11	3	104	0.029
12	12	98	0.122
13	15	105	0.143
14	6	98	0.061
15	21	204	0.103
16	3	54	0.056
17	12	74	0.162
18	11	103	0.107
19	11	100	0.110
20	14	88	0.159
21	4	58	0.069
22	10	69	0.145
23	19	135	0.141
24	1	67	0.015
25	11	77	0.143
26	12	88	0.136
27	4	66	0.061
28	11	72	0.153
29	13	118	0.110
30	15	138	0.109
	346	2888