Question

Top Billers processes invoices for business clients. Lately, Top Billers has been getting complaints about errors in the invoices they have processed. The quality manager for Top Billers decides to select one client at random each day and sample all of that client’s invoices to measure the extent of the problem.

a)   If the manager decides to construct a u-chart, what values will be used for the center line, lower control limit, and the minimum and maximum values of the upper control limit of the control chart?

b)   Create the control chart.

c)   Does the process appear to be in statistical control? Why or why not?

d)   What conclusion can be drawn about the overall quality of the service Top Billers offers?

	No. of Invoices	No. of Invoices
Sample	Reviewed	With Errors
1	171	2
2	194	1
3	121	3
4	200	0
5	159	1
6	162	3
7	186	4
8	182	1
9	155	2
10	185	2
11	179	4
12	160	3
13	159	1
14	154	1
15	151	2
16	169	0
17	189	3
18	178	4
19	161	2
20	198	1
21	174	1
22	120	2
23	152	3
24	166	4
25	182	3
26	185	2
27	161	5
28	129	1
29	170	4
30	143	1

Answer 1

a) u bar =	0.0132
Sample	Reviewed - n	With Errors - c	Defects/ Unit (u)	UCL	LCL
1	171	2	0.01	0.0396	-0.0132
2	194	1	0.01	0.0380	-0.0115
3	121	3	0.02	0.0446	-0.0181
4	200	0	0.00	0.0376	-0.0112
5	159	1	0.01	0.0406	-0.0141
6	162	3	0.02	0.0403	-0.0139
7	186	4	0.02	0.0385	-0.0121
8	182	1	0.01	0.0388	-0.0123
9	155	2	0.01	0.0409	-0.0145
10	185	2	0.01	0.0386	-0.0121
11	179	4	0.02	0.0390	-0.0126
12	160	3	0.02	0.0405	-0.0140
13	159	1	0.01	0.0406	-0.0141
14	154	1	0.01	0.0410	-0.0146
15	151	2	0.01	0.0413	-0.0148
16	169	0	0.00	0.0397	-0.0133
17	189	3	0.02	0.0383	-0.0119
18	178	4	0.02	0.0391	-0.0126
19	161	2	0.01	0.0404	-0.0140
20	198	1	0.01	0.0377	-0.0113
21	174	1	0.01	0.0394	-0.0129
22	120	2	0.02	0.0447	-0.0183
23	152	3	0.02	0.0412	-0.0148
24	166	4	0.02	0.0400	-0.0136
25	182	3	0.02	0.0388	-0.0123
26	185	2	0.01	0.0386	-0.0121
27	161	5	0.03	0.0404	-0.0140
28	129	1	0.01	0.0436	-0.0171
29	170	4	0.02	0.0397	-0.0132
30	143	1	0.01	0.0421	-0.0156
TOTAL	4995	66

The above values are calculated using the formula given below:

b)

c) Yes the process is under control since all the points lie in between the UCL and LCL.

d) The Top Billers offers a good quality service to its customers. The quality is GOOD.