Question

Given the sample results (100 units in each sample):

Sample Number	Number of Errors	Fraction Defective
1	0	0.00
2	9	0.09
3	6	0.06
4	7	0.07
5	2	0.02
6	7	0.07
7	7	0.07
8	5	0.05
9	4	0.04
10	5	0.05

Compute:

a. p-bar

b. the 95.5% (z=2) upper and lower control limits

c. just by observation, does the process appear to be in control? Why?

Answer 1

The following answers can be computed using simple calculations in Excel.

The number of units in each sample (N) = 100

The value of Z = 2

The first step is the formulation of the table.

Formulas used

p-bar is the average value of the fraction defective of the samples.

Ans a)

The value of P-bar as seen by the calculation in the above spreadsheets is 0.052

Ans b)

The 2 sigma control limits are as follows.

Upper control limit (UCL) is-

UCL = 0.096

Lower control limit (LCL) is-

LCL = 0.008

Ans c)

Although sample 1 lies outside the control limits, still the process appears to be in control as Sample 1 had 0 defects. All the other samples lie within the control limits.