Question

The following data (read the data down first and then over to the right) represent the weekly accounts receivable balance (in $1000) of a hardware distributor over a 30-week period.

128.703 120.649 126.215 129.426 135.816 125.131 131.122 121.774 125.367 121.076

119.848 127.251 153.923 125.658 122.172 129.268 122.912 125.351 130.572 116.875

122.587 127.677 132.364 130.950 118.662 131.902 132.220 128.522 132.270 122.671

1. Set up a (individuals) control chart on the accounts balance and a moving range chart (i.e. calculate the appropriate centerline and control limits). Plot the charts and supplement the individuals control chart with supplementary runs rules (i.e. apply the Western Electric runs rules for detecting non-random patterns on control charts). Note: Use the X-Y chart in Excel to plot the control charts.
2. Were there any out-of-control points identified in part (a)? If so, assume a special-cause explanation can be given to the associated point(s).
3. From the result of part (b), what are the appropriate prospective/trial limits for the charts?

Answer 1

a. Using Excel find Mean and Standard Deviation of the range.

Mean: =AVERAGE(Starting Cell:Ending Cell)

Standard Deviation: =STDEV.S(Starting Cell:Ending Cell)

In this problem:

Mean = 127.30(Centerline); Standard Deviation = 6.91

Hence,

Upper Control Limit = Mean + (3 X Std Deviation) = 127.30 + (3 X 6.91) = 148.03

Lower Control Limit = Mean - (3 X Std Deviation) = 127.30 - (3 X 6.91) = 106.56

The excel table and the graph looks like below:

Week	Account Balance (in $1000)	Mean	LCL	UCL
1	128.703	127.30	106.56	148.03
2	120.649	127.30	106.56	148.03
3	126.215	127.30	106.56	148.03
4	129.426	127.30	106.56	148.03
5	135.816	127.30	106.56	148.03
6	125.131	127.30	106.56	148.03
7	131.122	127.30	106.56	148.03
8	121.774	127.30	106.56	148.03
9	125.367	127.30	106.56	148.03
10	121.076	127.30	106.56	148.03
11	119.848	127.30	106.56	148.03
12	127.251	127.30	106.56	148.03
13	153.923	127.30	106.56	148.03
14	125.658	127.30	106.56	148.03
15	122.172	127.30	106.56	148.03
16	129.268	127.30	106.56	148.03
17	122.912	127.30	106.56	148.03
18	125.351	127.30	106.56	148.03
19	130.572	127.30	106.56	148.03
20	116.875	127.30	106.56	148.03
21	122.587	127.30	106.56	148.03
22	127.677	127.30	106.56	148.03
23	132.364	127.30	106.56	148.03
24	130.95	127.30	106.56	148.03
25	118.662	127.30	106.56	148.03
26	131.902	127.30	106.56	148.03
27	132.22	127.30	106.56	148.03
28	128.522	127.30	106.56	148.03
29	132.27	127.30	106.56	148.03
30	122.671	127.30	106.56	148.03

b. As is evident from the excel table and the associated graph above, during Week 13 the account balance was out of control. The possible reasoning could be a surge in demand due to a festival or an unpredictable event.