Question

Units Produced Defects Observed Opportunities Operation per Unit Build Rotating Group & Inspect 851 10 75 Install Rotating Group in Housing and Install Fittings 1202 72 Perform Functional Test 943 Clean and Paint and 894 70 Perform Final Inspection Install Pulley and Labels 4 1200 What is the Short-Term Z-Score for the first process step?

Answer 1

This is a simple problem related to calculation of the Z score (short term ) for the first process which is "build rotating groups and Inspect" .

For this process which is the first process of the procedure, the total number of oportunities/unit is 10 , total units produced is 851 and total defects is 75 .

To start with we shall calculate the DPMO (defects per million opportunities)

In our case there are 75 defects and 851 units are produced from 10 opportunities per nuit.

In other words , there are 75 defects and 8510 units are produced overall.

Thus total defect ratio/defects in 1 unit=defects /total units

=75/8510

Thus total defects in a million units

=75/8510*10⁶

=8813

Now to the Z (short term )

It is given mathematically as

$Z_{ST}= \Theta ^{-1} (1-DPMO/10^6)+1.5$ , Here 1.5 is the Z shift which is added to cater to the short term window.

Where $\Theta ^{-1}$ is the inverse normal distribution function)

keeping values,

ZST = Θ-1 (1-88 13/10°) + 1.50

or,

ZsT-Θ-1 (0.991187) 1.50

From the excel sheet and by online resources we can find the value of inverse normal distribution probability value of 0.991187

(when we take excel help ,we can use the function NORMSINV(calculated probability)

Thus

Θ-1 (0.991 187)-2.373383

thus

ZsT-Θ-1 (0.991187) 1.50

2.3733 + 1.50

- 3,8733

Thus the z(short term ) for first process is 3.8733 .