Abstract
This paper analyzes the effect of subgroup size on the x-bar chart characteristics using sample influx (SIF) into forensic science laboratory (FSL). The characteristics studied include changes in out-or-control points (OCP), upper control limit UCLx, and zonal demarcations. Multi-rules were used to identify the number of out-of-control-points, Nocp as violations using five control chart rules applied separately. A sensitivity analysis on the Nocp was applied for subgroup size, k, and number of sigma above the mean value to determine the upper control limit, UCLx. A computer code was implemented using a FORTRAN code to create x-bar control-charts and capture OCP and other control-chart characteristics with increasing k from 2 to 25. For each value of k, a complete series of average values, Q(p), of specific length, Nsg, was created from which statistical analysis was conducted and compared to the original SIF data, S(t). The variation of number of out-of-control points or violations, Nocp, for different control-charts rules with increasing k was determined to follow a decaying exponential function, Nocp = Ae–α, for which, the goodness of fit was established, and the R2 value approached unity for Rule #4 and #5 only. The goodness of fit was established to be the new criteria for rational subgroup-size range, for Rules #5 and #4 only, which involve a count of 6 consecutive points decreasing and 8 consecutive points above the selected control limit (σ/3 above the grand mean), respectively. Using this criterion, the rational subgroup range was established to be 4 ≤ k ≤ 20 for the two x-bar control chart rules.
Highlights
The forensic science laboratory (FSL) studied comprises of three disciplines, which receive, examine, analyze and reports on evidence submitted in criminal cases from all over Tanzania
The method employed in this study, i.e., the x-bar control charts, has proved to be effective in identifying uncommon changes in the sample reception process
The rational subgroup size was established to range from 4 ≤ k ≤ 20, during which the exponential functions between Nocp and k exhibited high goodness of fit, R2, compared to other regions of k from 2 to 25
Summary
The forensic science laboratory (FSL) studied comprises of three disciplines (forensic biology and DNA, forensic chemistry and forensic toxicology), which receive, examine, analyze and reports on evidence submitted in criminal cases from all over Tanzania. The FSL is the sole legally authorized laboratory to examine evidence submitted by any Governmental agency investigating a criminal offense. Crime scenes are the primary point of detection, collection, and preservation of evidence, before submission to the FSL. The evidence received is viewed in the context of the crime, the persons involved, and the environment (both physical and temporal). Science applied at the scene can generate data for later analysis, provide quicker answers, and facilitate better analysis in the laboratory. The sample influx is overwhelming, which require statistical analysis and decision making
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