#pseudocode can be developed from rules of thumb.
     #pseudocode: some problems can be solved by proportions (rule of three), to some order of magnitude
     #pseudocode: enter quantity1,  quantity2, quantity3 and expected output (quantity4) for testcases.
     #pseudocode: enter time in years, number of remaining items
     #pseudocode: output fraction of (remaining items) over (items at time zero)
     #pseudocode: ouput remaining items as fraction or percent
     #pseudocode: output fraction of (quantity4 ) over ( quantity1 at time zero)
     #pseudocode: output fraction of (quantity2) * (quantity3 ) over (quantity1 at time zero)
     #pseudocode: outputs should be in compatible units.
     #pseudocode: rules of thumb can be 3 to 15 percent off, partly since g..in g..out.
     #pseudocode: need test cases > small,medium, giant
     #pseudocode: need testcases within range of expected operation.
     #pseudocode: are there any cases too small or large to be solved?

        # pretty print from autoindent and ased editor
        # written on Windows XP on eTCL
        # working under TCL version 8.6.2 and_or eTCL 1.0.1
        # gold on TCL WIKI, 5nov2014
        # Console program for spare parts in warranty period
        # based on poisson distribution, lamda=1
        # calculate spare parts for 95% confidence level (eg. > 95%C).  
        package require Tk
        namespace path {::tcl::mathop ::tcl::mathfunc}
        console show
        proc poissionx {warranty_hours failure_rate_hours percentile} {
        set parts_prob 0
        set percentile_factor [* $percentile 1.E-2 ]          
        foreach item { 1 2 3 4 5 6 7 8 9 10 } {
         set exponent [* $warranty_hours $failure_rate_hours -1. ]
            set parts_prob [+ $parts_prob [exp $exponent ] ]
            puts "spares $item prob.  $parts_prob   /n
            product warranty_hours  $warranty_hours /n
            failure_rate_per_hours $failure_rate_hours MTTF=1/L=283 hours /n
            average failures across warranty period is 400/283 or 1.4 /n
            simple replacement would rounded 1.4 or 2 spares at approx. 50%C /n
            additional spares needed for 95%C "
            if { $parts_prob > $percentile_factor } { return $item } }               
            return  0 }
        puts " poission spare parts from home_brew [ poissionx 400. 0.003534 95  ]  "
        puts " 4 spares are required for above 95 percent confidence level "