Question

1. Volatile compounds in human blood serum were measured by purge and trap gas chromatography/mass spectrometry. For quality control, serum was periodically spiked with a constant amount of 1,2-dichlorobenzene and the concentration (ng/g=ppb) was measured. Find the mean and standard deviation for the following spike data and prepare a control chart. State whether or not the observations meet each of the control criterion for stability in a control chart.

Day	Obs (ppb)	Day	Obs (ppb)	Day	Obs (ppb)	Day	Obs (ppb)	Day	Obs (ppb)
0	1.05	91	1.13	147	0.83	212	1.03	290	1.04
1	0.70	101	1.64	149	0.88	218	0.90	294	0.85
3	0.42	104	0.79	154	0.89	220	0.86	296	0.59
6	0.95	106	0.66	156	0.72	237	1.05	300	0.83
7	0.55	112	0.88	161	1.18	251	0.79	302	0.67
30	0.68	113	0.79	167	0.75	259	0.94	304	0.66
70	0.83	115	1.07	175	0.76	262	0.77	308	1.04
72	0.97	119	0.60	182	0.93	277	0.85	311	0.86
76	0.60	125	0.80	185	0.72	282	0.72	317	0.88
80	0.87	128	0.81	189	0.87	286	0.68	321	0.67
84	1.03	134	0.84	199	0.85	288	0.86	323	0.68

Answer 1

Here sum of all the observations = 9835.21

Number of observations= 110

Therefore, mean = sum of the observations / Number of observations

= 9835.21/110

=89.41

Variance = where X= observation, n= number of observations

Therefore, Sample Variance = = 12563.25

Standard Deviation (SD) = =112.09

Lower Control Limit (LCL)=mean -( 3 *SD) = 89.41 - (3*112.09) = - 246.86

Upper Control Limit (UCL) =mean + (3*SD) = 89.41 + (3*112.09) = 425.68

Control Chart is given below

Here we see that all the observations are within the control limit.

[ To find

= (0-89.41)^2 +(1-89.41)^2 +.......+(0.68-89.41)^2

=1369393.77 ]