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Homework answers / question archive / The manager of a retail sales branch of a brokerage office is concerned with the number of undesirable trades made by the sales staff

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

Accounting

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.

  1. Construct an appropriate control chart for these data.
  2. 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 77
26 12 88
27 4 66
28 11 72
29 13 118
30 15 138

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(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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