# Example 930 — Most of the scatter was the gauge `most_of_the_scatter_was_the_gauge.eml` - Parts are measured, their scatter is computed exactly, and the process is judged not capable of holding the specification. Every measurement is real. How much of that scatter belongs to the parts and how much to the measuring is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). Parts are # measured, their scatter is computed exactly, and the process is judged not # capable of holding the specification. Every measurement is real. How much of # that scatter belongs to the parts and how much to the measuring is computed # below. # # The judgement is careful. Every part was measured; the standard deviation # of the readings is exact; the capability index is computed correctly from # it; and the intent is exactly 'can the process hold the spec'. # # A reading is the part plus the gauge, and this gauge contributes sixty # percent of the observed variance, so the process looks far wider than it is - # the judgement measured the ruler and blamed the parts. 100 => observed_variance_of_the_readings 60 => variance_contributed_by_the_gauge 15 => spec_half_width 10 => observed_standard_deviation 632 => process_standard_deviation_hundredths observed_variance_of_the_readings - variance_contributed_by_the_gauge => variance_of_the_parts_themselves int(variance_contributed_by_the_gauge * 10000 / observed_variance_of_the_readings) => gauge_share_of_the_scatter_per_myriad int(variance_of_the_parts_themselves * 10000 / observed_variance_of_the_readings) => process_share_of_the_scatter_per_myriad int(spec_half_width * 2 * 100 / (observed_standard_deviation * 6)) => cp_on_the_readings_hundredths int(spec_half_width * 2 * 100 * 100 / (process_standard_deviation_hundredths * 6)) => cp_on_the_parts_hundredths cp_on_the_parts_hundredths - cp_on_the_readings_hundredths => capability_the_gauge_hid_hundredths "observed variance of readings : " + str(observed_variance_of_the_readings) + " (standard deviation " + str(observed_standard_deviation) + ")" ^0 "variance from the gauge : " + str(variance_contributed_by_the_gauge) + ", " + str(gauge_share_of_the_scatter_per_myriad) + " per ten thousand of the scatter" ^0 "variance of the parts themselves : " + str(variance_of_the_parts_themselves) + ", " + str(process_share_of_the_scatter_per_myriad) + " per ten thousand" ^0 "process standard deviation : " + str(process_standard_deviation_hundredths) + " hundredths" ^0 "" ^0 "specification : plus or minus " + str(spec_half_width) ^0 "capability judged on readings : " + str(cp_on_the_readings_hundredths) + " hundredths - not capable" ^0 "capability of the parts : " + str(cp_on_the_parts_hundredths) + " hundredths" ^0 "capability the gauge hid : " + str(capability_the_gauge_hid_hundredths) + " hundredths" ^0 "" ^0 # ---- what the judgement verified ---- "the capability judgement" ^0 " coverage : every part measured" ^0 " scatter : exact standard deviation of the readings, " + str(observed_standard_deviation) ^0 " index : computed correctly from it, " + str(cp_on_the_readings_hundredths) + " hundredths" ^0 " intent : can the process hold the spec" ^0 " readings mishandled : 0" ^0 " verdict : NOT CAPABLE" ^0 "" ^0 " computing the exact scatter of the real readings is the" ^0 " part done right here, and it is why the readings really" ^0 " are that scattered" ^0 "" ^0 # ---- what a reading is made of ---- "part plus gauge" ^0 " a reading : the part's true size plus the gauge's error" ^0 " variances add : " + str(variance_of_the_parts_themselves) + " from the parts, " + str(variance_contributed_by_the_gauge) + " from the gauge, " + str(observed_variance_of_the_readings) + " observed" ^0 " the gauge's share : " + str(gauge_share_of_the_scatter_per_myriad) + " per ten thousand - most of it" ^0 " so the parts alone : standard deviation " + str(process_standard_deviation_hundredths) + " hundredths, not " + str(observed_standard_deviation) ^0 " and the capability : " + str(cp_on_the_parts_hundredths) + " hundredths, not " + str(cp_on_the_readings_hundredths) ^0 "" ^0 # ---- what the line got ---- "the verdict" ^0 " process condemned as : not capable, at " + str(cp_on_the_readings_hundredths) + " hundredths" ^0 " process actually : " + str(cp_on_the_parts_hundredths) + " hundredths" ^0 " is the readings' scatter miscomputed : no" ^0 " is the readings' scatter the parts' scatter : no; the" ^0 " larger part of it is the instrument" ^0 "" ^0 # ---- null control ---- # The same parts assessed after a gauge study (repeat measurements of the # same parts) separates the gauge's variance from the parts' variance. 50 => nc_cp_hundredths_judged_on_raw_readings 79 => nc_cp_hundredths_judged_on_parts_after_the_gauge_study 29 => nc_capability_hundredths_the_gauge_study_restores "null control - run a gauge study first" ^0 " capability judged on raw readings : " + str(nc_cp_hundredths_judged_on_raw_readings) + " hundredths" ^0 " capability judged on the parts, gauge removed : " + str(nc_cp_hundredths_judged_on_parts_after_the_gauge_study) + " hundredths" ^0 " capability the gauge study restores : " + str(nc_capability_hundredths_the_gauge_study_restores) + " hundredths" ^0 " no part and no spec changed; the ruler stopped being" ^0 " counted as part of the thing it measured" ^0 "" ^0 # ---- the rule ---- "what an exact scatter of the readings guarantees" ^0 " the readings vary by that much : exactly, every part" ^0 " measured, exact standard deviation" ^0 " the parts vary by that much : not addressed; " + str(gauge_share_of_the_scatter_per_myriad) + " per ten" ^0 " thousand of the scatter is the gauge, so the parts sit at" ^0 " " + str(process_standard_deviation_hundredths) + " hundredths of sigma and " + str(cp_on_the_parts_hundredths) + " hundredths of capability, not " + str(cp_on_the_readings_hundredths) ^0 "" ^0 "every measurement carries the instrument inside it, and a scatter computed" ^0 "from readings is the scatter of the parts and the ruler together; blame" ^0 "assigned without separating the two lands on the parts by default, because" ^0 "the ruler is not on the chart" ^0 "" ^0 "The readings' scatter is exact - standard deviation " + str(observed_standard_deviation) + ", capability " + str(cp_on_the_readings_hundredths) ^0 "hundredths. But " + str(gauge_share_of_the_scatter_per_myriad) + " per ten thousand of that variance is the gauge, so the parts" ^0 "themselves sit at " + str(process_standard_deviation_hundredths) + " hundredths of sigma and " + str(cp_on_the_parts_hundredths) + " hundredths of capability, " + str(capability_the_gauge_hid_hundredths) ^0 "hundredths hidden by the instrument, until a gauge study separated the two." ^0 ``` ## Python (deterministic transpilation) ```python observed_variance_of_the_readings = 100 variance_contributed_by_the_gauge = 60 spec_half_width = 15 observed_standard_deviation = 10 process_standard_deviation_hundredths = 632 variance_of_the_parts_themselves = observed_variance_of_the_readings - variance_contributed_by_the_gauge gauge_share_of_the_scatter_per_myriad = int(variance_contributed_by_the_gauge * 10000 / observed_variance_of_the_readings) process_share_of_the_scatter_per_myriad = int(variance_of_the_parts_themselves * 10000 / observed_variance_of_the_readings) cp_on_the_readings_hundredths = int(spec_half_width * 2 * 100 / (observed_standard_deviation * 6)) cp_on_the_parts_hundredths = int(spec_half_width * 2 * 100 * 100 / (process_standard_deviation_hundredths * 6)) capability_the_gauge_hid_hundredths = cp_on_the_parts_hundredths - cp_on_the_readings_hundredths print("observed variance of readings : " + str(observed_variance_of_the_readings) + " (standard deviation " + str(observed_standard_deviation) + ")") print("variance from the gauge : " + str(variance_contributed_by_the_gauge) + ", " + str(gauge_share_of_the_scatter_per_myriad) + " per ten thousand of the scatter") print("variance of the parts themselves : " + str(variance_of_the_parts_themselves) + ", " + str(process_share_of_the_scatter_per_myriad) + " per ten thousand") print("process standard deviation : " + str(process_standard_deviation_hundredths) + " hundredths") print("") print("specification : plus or minus " + str(spec_half_width)) print("capability judged on readings : " + str(cp_on_the_readings_hundredths) + " hundredths - not capable") print("capability of the parts : " + str(cp_on_the_parts_hundredths) + " hundredths") print("capability the gauge hid : " + str(capability_the_gauge_hid_hundredths) + " hundredths") print("") print("the capability judgement") print(" coverage : every part measured") print(" scatter : exact standard deviation of the readings, " + str(observed_standard_deviation)) print(" index : computed correctly from it, " + str(cp_on_the_readings_hundredths) + " hundredths") print(" intent : can the process hold the spec") print(" readings mishandled : 0") print(" verdict : NOT CAPABLE") print("") print(" computing the exact scatter of the real readings is the") print(" part done right here, and it is why the readings really") print(" are that scattered") print("") print("part plus gauge") print(" a reading : the part's true size plus the gauge's error") print(" variances add : " + str(variance_of_the_parts_themselves) + " from the parts, " + str(variance_contributed_by_the_gauge) + " from the gauge, " + str(observed_variance_of_the_readings) + " observed") print(" the gauge's share : " + str(gauge_share_of_the_scatter_per_myriad) + " per ten thousand - most of it") print(" so the parts alone : standard deviation " + str(process_standard_deviation_hundredths) + " hundredths, not " + str(observed_standard_deviation)) print(" and the capability : " + str(cp_on_the_parts_hundredths) + " hundredths, not " + str(cp_on_the_readings_hundredths)) print("") print("the verdict") print(" process condemned as : not capable, at " + str(cp_on_the_readings_hundredths) + " hundredths") print(" process actually : " + str(cp_on_the_parts_hundredths) + " hundredths") print(" is the readings' scatter miscomputed : no") print(" is the readings' scatter the parts' scatter : no; the") print(" larger part of it is the instrument") print("") nc_cp_hundredths_judged_on_raw_readings = 50 nc_cp_hundredths_judged_on_parts_after_the_gauge_study = 79 nc_capability_hundredths_the_gauge_study_restores = 29 print("null control - run a gauge study first") print(" capability judged on raw readings : " + str(nc_cp_hundredths_judged_on_raw_readings) + " hundredths") print(" capability judged on the parts, gauge removed : " + str(nc_cp_hundredths_judged_on_parts_after_the_gauge_study) + " hundredths") print(" capability the gauge study restores : " + str(nc_capability_hundredths_the_gauge_study_restores) + " hundredths") print(" no part and no spec changed; the ruler stopped being") print(" counted as part of the thing it measured") print("") print("what an exact scatter of the readings guarantees") print(" the readings vary by that much : exactly, every part") print(" measured, exact standard deviation") print(" the parts vary by that much : not addressed; " + str(gauge_share_of_the_scatter_per_myriad) + " per ten") print(" thousand of the scatter is the gauge, so the parts sit at") print(" " + str(process_standard_deviation_hundredths) + " hundredths of sigma and " + str(cp_on_the_parts_hundredths) + " hundredths of capability, not " + str(cp_on_the_readings_hundredths)) print("") print("every measurement carries the instrument inside it, and a scatter computed") print("from readings is the scatter of the parts and the ruler together; blame") print("assigned without separating the two lands on the parts by default, because") print("the ruler is not on the chart") print("") print("The readings' scatter is exact - standard deviation " + str(observed_standard_deviation) + ", capability " + str(cp_on_the_readings_hundredths)) print("hundredths. But " + str(gauge_share_of_the_scatter_per_myriad) + " per ten thousand of that variance is the gauge, so the parts") print("themselves sit at " + str(process_standard_deviation_hundredths) + " hundredths of sigma and " + str(cp_on_the_parts_hundredths) + " hundredths of capability, " + str(capability_the_gauge_hid_hundredths)) print("hundredths hidden by the instrument, until a gauge study separated the two.") ``` ## stdout (executed) ```text observed variance of readings : 100 (standard deviation 10) variance from the gauge : 60, 6000 per ten thousand of the scatter variance of the parts themselves : 40, 4000 per ten thousand process standard deviation : 632 hundredths specification : plus or minus 15 capability judged on readings : 50 hundredths - not capable capability of the parts : 79 hundredths capability the gauge hid : 29 hundredths the capability judgement coverage : every part measured scatter : exact standard deviation of the readings, 10 index : computed correctly from it, 50 hundredths intent : can the process hold the spec readings mishandled : 0 verdict : NOT CAPABLE computing the exact scatter of the real readings is the part done right here, and it is why the readings really are that scattered part plus gauge a reading : the part's true size plus the gauge's error variances add : 40 from the parts, 60 from the gauge, 100 observed the gauge's share : 6000 per ten thousand - most of it so the parts alone : standard deviation 632 hundredths, not 10 and the capability : 79 hundredths, not 50 the verdict process condemned as : not capable, at 50 hundredths process actually : 79 hundredths is the readings' scatter miscomputed : no is the readings' scatter the parts' scatter : no; the larger part of it is the instrument null control - run a gauge study first capability judged on raw readings : 50 hundredths capability judged on the parts, gauge removed : 79 hundredths capability the gauge study restores : 29 hundredths no part and no spec changed; the ruler stopped being counted as part of the thing it measured what an exact scatter of the readings guarantees the readings vary by that much : exactly, every part measured, exact standard deviation the parts vary by that much : not addressed; 6000 per ten thousand of the scatter is the gauge, so the parts sit at 632 hundredths of sigma and 79 hundredths of capability, not 50 every measurement carries the instrument inside it, and a scatter computed from readings is the scatter of the parts and the ruler together; blame assigned without separating the two lands on the parts by default, because the ruler is not on the chart The readings' scatter is exact - standard deviation 10, capability 50 hundredths. But 6000 per ten thousand of that variance is the gauge, so the parts themselves sit at 632 hundredths of sigma and 79 hundredths of capability, 29 hundredths hidden by the instrument, until a gauge study separated the two. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done