Question

Operator takes a sample of 3 tablets once per hour and measures their weights. Data for the first 10 hours is shown below.

Time (hr)	Weight-1	Weight-2	Weight-3
0	253.31	246.03	253.57
1	247.97	248.31	251.57
2	249.47	250.04	250.15
3	248.38	247.74	254.81
4	250.55	241.08	251.35
5	242.40	248.07	250.43
6	254.59	247.63	252.42
7	248.38	252.33	252.61
8	256.07	248.46	254.95
9	245.84	250.97	247.68

• Construct an X-bar and range charts for tablet weight based on this data (manually – it’s okay if your plot is not perfect).
• Comment on the observations.
• Explain what these control charts may be used for.

Answer 1

Answer :- Operator takes a sample of 3 tablets, once per hour and measures their weight.

=> To construct X̄ and R chart for tablet weight for the given data :-

Given data :-

• m = 10

• n = 3

=> X̄ = ∑X̄i /m

= 2499.0533 /10

[ X̄ = 249.9053 ]

=> R bar = ∑Ri /m

= 61.12/10

[ 6.112 ]

• The control Limits for X̄ chart is :-

Hear we take : [ A2 = 1.023 for n = 3 ]

=> Upper Control Limit = X̄ + (A2) (R bar)

=> UCL = 249.9053 + (1.023) (6.112)

= 249.9053 + 6.2525

= 256.1578

[ UCL = 256.16 ]

[ CL = 249.90 ]

=> Lower Control Limit = X̄ - (A2)(R bar)

=> LCL = 249.9053 - (1.023) (6.112)

= 249.9053 - 6.2525

= 243.6528

[ LCL = 243.65 ]

• The control Limits for R chart is :-

Here we take ( D4 = 2.575 for n = 3 )

=> Upper Control Limit = D4 (R bar)

=> UCL = 2.575 × 6.112

= 15.7384

[ UCL = 15.74 ]

CL = 6.112 ~ [ CL = 6.11 ]

=> Lower Control Limit = D3 (R bar)

Here (D3 = 0 for n =3)

=> LCL = (0) (6.112)

= 0

[ LCL = 0 ]

Conclusion :-

• X̄ chart :- The process is in control because all the points in X̄ chart is above Lower Control Limit and below Upper Control Limit.

• R-chart :- The process is in control because all the points in R-chart is above Lower Control Limit and below Upper Control Limit.