Question

Calculate the control limits for the X-bar chart with 0.005 probability limits (instead of 3-sigma limits). That is, here the type I error rate (false alarm rate) is now set to α = 0.005. Use Excel for any calculations, not Minitab.

Day	x1	x2	x3	x4	x5
1	839	585	583	613	768
2	706	527	956	644	612
3	322	614	807	282	170
4	1001	904	419	522	430
5	259	811	847	603	572
6	681	523	665	397	873
7	799	874	553	173	296
8	263	585	546	445	455
9	591	637	739	927	825
10	372	997	496	283	641
11	633	371	425	625	752
12	294	522	599	740	468
13	714	600	738	694	610
14	311	829	216	447	506
15	720	446	393	431	707
16	306	550	633	845	394
17	561	574	370	495	580
18	431	500	580	349	626
19	404	791	773	576	1073
20	640	687	754	627	482

Answer 1

Formulas:

Methodology:

Step 1: Find the average of all sample (X-bar)

Step 2: Find the standard deviation of the operation using STDDEVA() formula and select all data.

Step 3: Std. Dev of Sample Mean

n = Sample Size = 5

Step 4: Find the average of sample mean (X -double bar)

Control Limits

Central Limit (CL) = X- double bar = 584.24

We need to find the Z -value for p = 1- 0.005 = 0.995

Z = 2.575