A Sales office vs Plant problem
I was through almost 3 days in the five day Green belt programme and I noticed in the evening a lady participant feverishly working on a xl sheet. Since it was time to close down and it is customary that I expect every one to leave before I leave, I asked her about the work she was doing. She said that this is the kind of problem she faces every month. I asked her to explain to me if it is OK. She was the planner for the manufacture of small motors working in the factory. She received the internal work orders from about ten sales offices all over the country. She had difficulties with the completeness of orders received. While some errors were trivial some really held up the shipments. There were instances where the orders did not mention the inspection by client or did not mention the paint colour. These triggered a lot of customer dissatisfaction. Every month, she calculated the average defective orders and mailed the data to management. She sometimes also wrote a strong letter that the sales offices were not acting in a responsible manner. Apparently, nothing happened except a few sales offices turned against her quoting the statistics that they were not the ones to blame.
I suggested to her to use Chi Square test instead of the usual average calculation and the comments on that.
The average defective orders could be the expected proportion. we could apply the chi square test to find out whether all sales offices were more or less equal in producing those defectives or whether a particular sales office was generating more defectives.
She tried and found that one sales office was generating defectives orders at level significantly higher than the rest of the offices. She then had to work on that office only for improvement. The improvement came very fast with the training of the concerned person. An example of the situation is given below.
Chennai Mumbai Delhi Kokata
OK 80 90 65 50
Not OK 20 10 35 50
Table analyzed
Statistic
Degrees of freedom 3
Contingency coefficient 0.3
Corrected contingency coefficient 0.4
Chi square 44.9
Chi2, critical 7.8
p value < 0.0001
Significantly different (p<0.05)? Yes
Significance level: 95%
Table with expected values
Chennai Mumbai Delhi Kokata
OK 71.2 71.2 71.2 71.2
Not OK 28.8 28.8 28.8 28.8
One branch is significantly different and it could be Kolkata office. *calculations done through Maxlite software