Question

Each value represents the number of mistakes (defects) found on a student loan application. Values for 50 consecutive loan applications are given. Calculate the appropriate centerline and 3-sigma control limits for the c-chart, and then plot the data and create a control chart. Does the process appear to be in a state of statistical control? Why or why not?

Upper control limit (UCL) =

Centerline (CL) =

Lower control limit (LCL) =

Process in statistical control?

Acme Company - Daily Output
Day	June	July	August
1	7940	7809	7401
2	7952	7747	7344
3	7870	7869	7490
4	7985	7784	7488
5	8015	7822	7685
6	8038	7839	7466
7	8027	7839	7511
8	7990	7845	7491
9	7928	7872	7353
10	7972	7725	7521
11	7981	7819	7376
12	7909	7852	7633
13	8038	7805	9542
14	7972	7820	7562
15	8041	7773	7455
16	7984	7837	7686
17	7978	7747	7477
18	7833	7776	7482
19	8043	7749	7603
20	7972	7823	7671
21	7901	7806	7535
22	7993	7747	7360
23	8014	7785	7519
24	7929	7778	7507
25	7922	7802	7597
26	8025	7732	7487
27	7983	7849	7452
28	7932	7909	7407
29	8069	7875	7407
30	7923	7734	7434
31		7563	7684

Answer 1

solution:

Upper control limit (UCL) = mean of means of sample - (3* standard deviation)

Centerline (CL) = mean

Lower control limit (LCL) = mean of means of sample - (3* standard deviation)

Where Each value represents the number of mistakes (defects) found on a student loan application.

std dev

132.8711

between the 11 to 13 given process is out of control because some values are larger than the upper limit .

Thank you..!!

Day	Jun	July	Aug	xbar	xbar bar	LCL	UCL
1	7940	7809	7401	7716.667	7778.978	7380.365	8177.592
2	7952	7747	7344	7681	7781.056	7382.442	8179.669
3	7870	7869	7490	7743	7784.506	7385.892	8183.119
4	7985	7784	7488	7752.333	7785.988	7387.375	8184.601
5	8015	7822	7685	7840.667	7787.235	7388.621	8185.848
6	8038	7839	7466	7781	7785.179	7386.566	8183.793
7	8027	7839	7511	7792.333	7785.347	7386.733	8183.96
8	7990	7845	7491	7775.333	7785.056	7386.442	8183.669
9	7928	7872	7353	7717.667	7785.478	7386.865	8184.092
10	7972	7725	7521	7739.333	7788.561	7389.947	8187.174
11	7981	7819	7376	7725.333	7790.905	7392.292	8189.518
12	7909	7852	7633	7798	7794.183	7395.57	8192.797
13	8038	7805	9542	8461.667	7793.982	7395.369	8192.596
14	7972	7820	7562	7784.667	7756.889	7358.276	8155.502
15	8041	7773	7455	7756.333	7755.255	7356.642	8153.868
16	7984	7837	7686	7835.667	7755.188	7356.574	8153.801
17	7978	7747	7477	7734	7749.822	7351.209	8148.435
18	7833	7776	7482	7697	7750.952	7352.339	8149.566
19	8043	7749	7603	7798.333	7755.103	7356.489	8153.716
20	7972	7823	7671	7822	7751.5	7352.887	8150.113
21	7901	7806	7535	7747.333	7745.091	7346.478	8143.704
22	7993	7747	7360	7700	7744.867	7346.253	8143.48
23	8014	7785	7519	7772.667	7749.852	7351.239	8148.465
24	7929	7778	7507	7738	7747	7348.387	8145.613
25	7922	7802	7597	7773.667	7748.286	7349.672	8146.899
26	8025	7732	7487	7748	7744.056	7345.442	8142.669
27	7983	7849	7452	7761.333	7743.267	7344.653	8141.88
28	7932	7909	7407	7749.333	7738.75	7340.137	8137.363
29	8069	7875	7407	7783.667	7735.222	7336.609	8133.835
30	7923	7734	7434	7697	7711	7312.387	8109.613
31	7928	7563	7684	7725	7725	7326.387	8123.613