Question

Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma)

LOADING...

for this problem.

Sampling

44

pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results:

  

Hour	Bold x overbarx	R	Hour	Bold x overbarx	R	Hour	Bold x overbarx	R	Hour	Bold x overbarx	R
1	3.153.15 "	0.650.65 "	7	3.053.05 "	0.580.58 "	13	3.113.11 "	0.800.80 "	19	4.514.51 "	1.611.61 "
2	3.103.10	1.181.18	8	2.552.55	1.081.08	14	2.732.73	1.311.31	20	2.792.79	1.141.14
3	3.223.22	1.481.48	9	3.023.02	0.660.66	15	3.023.02	1.011.01	21	2.552.55	1.081.08
4	3.493.49	1.211.21	10	2.952.95	1.281.28	16	2.742.74	0.500.50	22	3.283.28	0.510.51
5	3.073.07	1.121.12	11	2.832.83	1.171.17	17	2.762.76	1.431.43	23	2.942.94	1.581.58
6	2.762.76	0.420.42	12	3.073.07	0.350.35	18	2.642.64	1.291.29	24	2.742.74	0.920.92

Based on the sampling done,

the

control limits for 3-sigma

x overbarx

chart are (round all intermediate calculations to three decimal places before proceeding with further

calculations) :

Upper Control Limit

(UCL Subscript x overbarUCLx )

=

nothing

inches (round your response to three decimal places).

Lower Control Limit

(LCL Subscript x overbarLCLx )

=

nothing

inches (round your response to three decimal places).

Based on the

x overbarx -chart,

the wire cutting process has been

▼

OUT OF CONTROL

IN CONTROL

.

The control limits for the

3-sigma

R-chart are (round all intermediate calculations to three decimal places before proceeding with further

calculations) :

Upper Control Limit

(UCL Subscript Upper RUCLR )

=

nothing

inches (round your response to three decimal places).

Lower Control Limit

(LCL Subscript Upper RLCLR )

=

nothing

inches (round your response to three decimal places).

Based on the R-chart, the wire cutting process has been

▼

IN CONTROL

OUT OF CONTROL

.

Answer 1

Solution:

Based on the sampling done,the control limits for 3-sigma X bar chart are (round all intermediate calculations to three decimal places before proceeding with further calculations) :

Answer:

Where:

is the mean of sample means

is the mean of range

is the constant value for sub group size 4

Lower Control Limit

Where:

is the mean of sample means

is the mean of range

is the constant value for sub group size 4

Bases on the X bar chart, the wire cutting process has been out of control. Because sample mean for 19th sample is beyond the upper control limit

The control limits for the 3-sigma R-chart are (round all intermediate calculations to three decimal places before proceeding with further calculations) :

Upper Control Limit

Where:

is constant for subgroup size 4

is the mean of the range

Lower Control Limit

Where:

is constant for subgroup size 4

is the mean of the range

Based on the R-chart, the wire cutting process has been in control because all the ranges are within the control limits