Question

A random sample of surgical procedures was selected each month for 30 consecutive months, and the number of procedures with post-operative complications was recorded. The data are listed in the accompanying table.

1. What type of control chart is the most appropriate to analyze the process?
2. Compute the critical boundaries for the control chart.
3. Interpret the chart. Does the process appear to be in control? Explain.

Months	Complications	Procedure Sampled
1	8	107
2	7	90
3	12	70
4	7	103
5	8	70
6	50	100
7	7	65
8	5	80
9	7	97

Answer 1

Answer:-

Given That:-

A random sample of surgical procedures was selected each month for 30 consecutive months, and the number of procedures with post-operative complications was recorded. The data are listed in the accompanying table.

What type of control chart is the most appropriate to analyze the process?

Data is of Yes/No Type is i.e,

# of defectives/cpmplications in a sample. attribute chart is suitable.

Since sample size varies

Therefore p chart is most appropriate.

Compute the critical boundaries for the control chart.

For p-chart (proportion complication)

(for constant sample size)

Since sample sizes are variables.

Therefore Control limits will also be varrying.

is proportion complication for each month

= 111/782

= 0.141944

Therefore For variable Sample size

So From p-chart.

sample # 6 fail & is out of control.

Interpret the chart. Does the process appear to be in control? Explain.

Therefore Process is out of control because sample # 6 has to highest # of complication.

Therefore one need to inspect for the pressure of special cause going to failure of process to remain in control.

	Sample sie	Complications
	107	8
	90	7
	70	12
	103	7
	70	8
	100	50
	65	7
	80	5
	97	7
Sum	782	111

Below is the minitab output.

Above is the test conducted for special cause. sample # 6 has failed in 1st test so process is out of control.

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