#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
        global side1 side2 side3 side4 side5
        global side6 side7 side8 spares_95
        global side9 side10 side11 side12 side13
        global testcase_number iteration_number
        foreach item { 1 2 3 4 5 6 7 8 9 10 11 12} {
            set side$item 0 }
        proc fuzzy_round_up {args } {
            set lister {}
            foreach item $args {
                if { $item > [int $item ] &&  $item > 0. } { lappend lister [+ [int $item ] 1.]}
                if { $item == [int $item ] } { lappend lister [* $item 1.] }
                if { $item < [int $item ] &&  $item < 0. } { lappend lister [+ [int $item ] -1.]}
            }
            return $lister }
        proc MTTF_exponential_model {warranty_hours } {
            set MTTF [* $warranty_hours [- [exp .5 ] 1. ] 1. ]
            return $MTTF }
        proc AFR_exponential_model {warranty_hours } {
            set AFR [/ 1. [* $warranty_hours [- [exp .5 ] 1. ] 1. ] ]
            return $AFR }
        proc extra_credit  {  } {
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global side9 side10 side11 side12 side13
            global side14 
            global warranty_hours failure_rate_hours percentile
            global testcase_number
            set side4 [/ 1. $side2]
            set side5 [ fuzzy_round_up [ MTTF_exponential_model $side1 ] ]
            set side7 [ AFR_exponential_model $side1 ]
            set side8 [/ $side1 [/ 1. $side2] ]
            set side9 [ fuzzy_round_up [/ $side1 [/ 1. $side2] ] ]
            set side11 [- $side1 $side4 ]
            set side12 [/ $side4 $side1  ]
            set side13 [* 2. $side4 ]
            return 1 }
        proc poissonx {warranty_hours failure_rate_hours percentile} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global side9 side10 side11 side12
            global side13 side14
            global testcase_number iteration_number
            incr testcase_number
            set side1 $warranty_hours
            set side2 $failure_rate_hours
            set side3 $percentile
            extra_credit
            set parts_prob 0
            set percentile_factor [* $percentile 1.E-2 ]
            foreach item { 1 2 3 4 5 6 7 8 9 10 } {
                incr iteration_number
                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 \n "
                set side10 $parts_prob 
                if { $iteration_number > 9 } { puts "testcase $testcase_number, $iteration_number iterations exceeded & short of solution"; return $item}
                if { $parts_prob > 1. } { puts "testcase $testcase_number, $iteration_number iterations exceed prob. unity & short of solution"; return $item}
                if { $parts_prob > $percentile_factor } {reportx ; set iteration_number 0 ; return $item  } }
                return  0 }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global side9 side10 side11 side12 side13
            global side14 
            global testcase_number iteration_number
            set spares95 $iteration_number
            set availability_with_spares_experimental [* [- [* $side10 1.E2 1. ] 1. ] 1.E-2 ]
            puts "%|table $testcase_number, Spare Parts for one operating device from iterative poisson solution|printed in| tcl wiki format|% "
            puts "%| quantity| value| comment, if any|% "
            puts "&| testcase number:|$testcase_number | iterative solution from poisson|&"
            puts "&| $side1 :|warranty hours or expected lifetime, MTBF hours | mean time between failures   |&"
            puts "&| $side2 :|failure rate per hours | usually given in specs |& "
            puts "&| $side3 :|percentile for iterative solution | usually 95 |& "
            puts "&| $side4 :|answers: MTTF hours from givens  | mean time to failure |&"
            puts "&| $side11 :|MTTR hours from givens, mean time to repair | MTTR=MTBF-MTTF  |&"
            puts "&| $side12 :|availability without spares  | A0=MTTF/MTBF  |&"
            puts "&| $side13 :|MTTFD without spares, mean time to dangerous failure  | MTTFD=2*MTTF  |&"
            puts "&| $availability_with_spares_experimental :|experimental availability from probability with spares  | A0=experimental formula  |&"
            puts "&| $side5 :|experimental MTTF from exponential model |  |&"
            puts "&| $side7 :|experimental failure_rate_per_hours from exponential model |  |&"
            puts "&| $side8 :|average failures across warranty period |  |&"
            puts "&| $side8 :|simple replacement of average failures with spares, approx. 50%C |  |& "
            puts "&| $side9 :|rounded up simple replacement of average failures  |   |&"
            puts "&| $side10 :|probability on last iteration |& "
            puts "&| $spares95 :|iterations for solution from poisson distribution|  |& "
            puts "&| $spares95 :|poisson spare parts from iterative solution  |  |& "
        }
        puts " poisson spare parts from home_brew [ poissonx 400. 0.003534 95  ]  "
        puts " 4 spares are required for above 95 percent confidence level "
        puts " poisson spare parts from home_brew [ poissonx 400. 0.003534 90  ]  "
        puts " poisson spare parts from home_brew [ poissonx 400. 0.003534 60  ]  "
        

        # 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
        # Initial 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 poissonx {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 " poisson spare parts from home_brew [ poissonx 400. 0.003534 95  ]  "
        puts " 4 spares are required for above 95 percent confidence level "