Question 3:

Case study: Excel Logistics Services

Use the workbook ExcelLogistics.xlsx to answer this question.

Supporting material for the case:

p-Charts in Statistical Process Control (SPC)

Used when an item (or service) is either good or bad (a yes-no decision).

p=number defectivenumber of observations (sample size, n)

UCL=p+zsp LCL=p-zsp where sp is the sample standard deviation of fraction defective, p, and z=3 for 3-sigma control limits. Note that if the formula for LCL gives a negative result, LCL is set to 0, since can never have less than 0 fraction defective.

Number defective follows the binomial distribution, however for large number of observations, one can assume it to follow the normal distribution (normal approximation to binomial). Thus, one can assume p~N(p, (sp)2), where

sp=p(1-p)n

Rather than the questions at the end of the case study, answer the following questions:

1. Calculate the fraction of total errors in each sample of transactions, i.e. p. Using these fractions, calculate p and sp (as defined above) and the control chart limits for a p-chart. Assume only points outside the control limits indicate an out-of-control situation.
2. Customer service requirements determine that receiving process errors should never exceed 2 percent on any given day. What percentage of days is likely to exceed 2 percent error, given the current performance at receiving? Assume a total of 8,000 transactions per day. Briefly comment on the results of parts a and b; is the process in statistical control, is the quality level acceptable?

c) The data in part a reveal that the majority of the errors occur at the slotter function. You decided to use SPC (p-chart) for the slotter errors to identify opportunities to improve the slotter operations. Establish a p-chart to be used to monitor the slotter function.

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